Phase Models (thermo.phases)¶

Base Class
Ideal Gas Equation of State
Cubic Equations of State
- Gas Phases
- Liquid Phases
Virial Equations of State
- Gas Phase Object
- Corresponding States Virial Model
Activity Based Liquids
Fundamental Equations of State
CoolProp Wrapper

The phases subpackage exposes classes that represent the state of single phase mixture, including the composition, temperature, pressure, enthalpy, and entropy. Phase objects are immutable and know nothing about bulk properties or transport properties. The goal is for each phase to be able to compute all of its thermodynamic properties, including volume-based ones. Use settings to handle different assumptions.

Base Class ¶

class thermo.phases.Phase[source]¶

Bases: object

Phase is the base class for all phase objects in thermo. Each sub-class implements a number of core properties; many other properties can be calculated from them.

Among those properties are H, S, Cp, dP_dT, dP_dV, d2P_dT2, d2P_dV2, and d2P_dTdV.

An additional set of properties that can be implemented and that enable more functionality are dH_dP, dS_dT, dS_dP, d2H_dT2, d2H_dP2, d2S_dP2, dH_dT_V, dH_dP_V, dH_dV_T, dH_dV_P, dS_dT_V, dS_dP_V, d2H_dTdP, d2H_dT2_V, d2P_dTdP, d2P_dVdP, d2P_dVdT_TP, d2P_dT2_PV.

Some models may re-implement properties which would normally be calculated by this Phase base class because they have more explicit, faster ways of calculating the property.

When a phase object is the result of a Flash calculation, the resulting phase objects have a reference to a ChemicalConstantsPackage object and all of its properties can be accessed from from the resulting phase objects as well.

A ChemicalConstantsPackage object can also be manually set to the attribute constants to enable access to those properties. This includes mass-based properties, which are not accessible from Phase objects without a reference to the constants.

Attributes

CASs: CAS registration numbers for each component, [-].
Carcinogens: Status of each component in cancer causing registries, [-].
Ceilings: Ceiling exposure limits to chemicals (and their units; ppm or mg/m^3), [various].
GWPs: Global Warming Potentials for each component (impact/mass chemical)/(impact/mass CO2), [-].
Gfgs: Ideal gas standard molar Gibbs free energy of formation for each component, [J/mol].
Gfgs_mass: Ideal gas standard Gibbs free energy of formation for each component, [J/kg].
H_calc
Hcs: Higher standard molar heats of combustion for each component, [J/mol].
Hcs_lower: Lower standard molar heats of combustion for each component, [J/mol].
Hcs_lower_mass: Lower standard heats of combustion for each component, [J/kg].
Hcs_mass: Higher standard heats of combustion for each component, [J/kg].
Hf_STPs: Standard state molar enthalpies of formation for each component, [J/mol].
Hf_STPs_mass: Standard state mass enthalpies of formation for each component, [J/kg].
Hfgs: Ideal gas standard molar enthalpies of formation for each component, [J/mol].
Hfgs_mass: Ideal gas standard enthalpies of formation for each component, [J/kg].
Hfus_Tms: Molar heats of fusion for each component at their respective melting points, [J/mol].
Hfus_Tms_mass: Heats of fusion for each component at their respective melting points, [J/kg].
Hsub_Tts: Heats of sublimation for each component at their respective triple points, [J/mol].
Hsub_Tts_mass: Heats of sublimation for each component at their respective triple points, [J/kg].
Hvap_298s: Molar heats of vaporization for each component at 298.15 K, [J/mol].
Hvap_298s_mass: Heats of vaporization for each component at 298.15 K, [J/kg].
Hvap_Tbs: Molar heats of vaporization for each component at their respective normal boiling points, [J/mol].
Hvap_Tbs_mass: Heats of vaporization for each component at their respective normal boiling points, [J/kg].
InChI_Keys: InChI Keys for each component, [-].
InChIs: InChI strings for each component, [-].
LFLs: Lower flammability limits for each component, [-].
MWs: Molecular weights for each component, [g/mol].
ODPs: Ozone Depletion Potentials for each component (impact/mass chemical)/(impact/mass CFC-11), [-].
PSRK_groups: PSRK subgroup: count groups for each component, [-].
P_calc
Parachors: Parachors for each component, [N^0.25*m^2.75/mol].
Pcs: Critical pressures for each component, [Pa].
Psat_298s: Vapor pressures for each component at 298.15 K, [Pa].
Pts: Triple point pressures for each component, [Pa].
PubChems: Pubchem IDs for each component, [-].
Q: Method to return the actual volumetric flow rate of this phase.
Q_calc: Method to return the actual volumetric flow rate of this phase.
Qg: Method to return the volume flow rate of this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref.
Qg_calc: Method to return the volume flow rate of this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref.
Qgs: Method to return the volume flow rate of each component in this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref.
Qgs_calc: Method to return the volume flow rate of each component in this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref.
Ql: Method to return the volume flow rate of this phase as an ideal liquid, using the configured standard molar volumes Vml_STPs.
Ql_calc: Method to return the volume flow rate of this phase as an ideal liquid, using the configured standard molar volumes Vml_STPs.
Qls: Method to return the volume flow rate of each component in this phase as an ideal liquid, using the configured V_liquids_ref.
Qls_calc: Method to return the volume flow rate of each component in this phase as an ideal liquid, using the configured V_liquids_ref.
RI_Ts: Temperatures at which the refractive indexes were reported for each component, [K].
RIs: Refractive indexes for each component, [-].
S0gs: Ideal gas absolute molar entropies at 298.15 K at 1 atm for each component, [J/(mol*K)].
S0gs_mass: Ideal gas absolute entropies at 298.15 K at 1 atm for each component, [J/(kg*K)].
STELs: Short term exposure limits to chemicals (and their units; ppm or mg/m^3), [various].
Sfgs: Ideal gas standard molar entropies of formation for each component, [J/(mol*K)].
Sfgs_mass: Ideal gas standard entropies of formation for each component, [J/(kg*K)].
Skins: Whether each compound can be absorbed through the skin or not, [-].
StielPolars: Stiel polar factors for each component, [-].
Stockmayers: Lennard-Jones Stockmayer parameters (depth of potential-energy minimum over k) for each component, [K].
TWAs: Time-weighted average exposure limits to chemicals (and their units; ppm or mg/m^3), [various].
T_calc
Tautoignitions: Autoignition temperatures for each component, [K].
Tbs: Boiling temperatures for each component, [K].
Tcs: Critical temperatures for each component, [K].
Tflashs: Flash point temperatures for each component, [K].
Tms: Melting temperatures for each component, [K].
Tts: Triple point temperatures for each component, [K].
UFLs: Upper flammability limits for each component, [-].
UNIFAC_Dortmund_groups: UNIFAC_Dortmund_group: count groups for each component, [-].
UNIFAC_Qs: UNIFAC Q parameters for each component, [-].
UNIFAC_Rs: UNIFAC R parameters for each component, [-].
UNIFAC_groups: UNIFAC_group: count groups for each component, [-].
VF: Method to return the vapor fraction of the phase.
VF_calc
Van_der_Waals_areas: Unnormalized Van der Waals areas for each component, [m^2/mol].
Van_der_Waals_volumes: Unnormalized Van der Waals volumes for each component, [m^3/mol].
Vcs: Critical molar volumes for each component, [m^3/mol].
Vfgs_calc
Vfls_calc
Vmg_STPs: Gas molar volumes for each component at STP; metastable if normally another state, [m^3/mol].
Vml_60Fs: Liquid molar volumes for each component at 60 °F, [m^3/mol].
Vml_STPs: Liquid molar volumes for each component at STP, [m^3/mol].
Vml_Tms: Liquid molar volumes for each component at their respective melting points, [m^3/mol].
Vms_Tms: Solid molar volumes for each component at their respective melting points, [m^3/mol].
Zcs: Critical compressibilities for each component, [-].
aliases: Aliases for each component, [-].
atomss: Breakdown of each component into its elements and their counts, as a dict, [-].
beta: Method to return the phase fraction of this phase.
beta_mass: Method to return the mass phase fraction of this phase.
beta_volume: Method to return the volumetric phase fraction of this phase.
beta_volume_liquid_ref: Method to return the standard liquid volume fraction of this phase.
charges: Charge number (valence) for each component, [-].
conductivities: Electrical conductivities for each component, [S/m].
conductivity_Ts: Temperatures at which the electrical conductivities for each component were measured, [K].
constants
correlations
dipoles: Dipole moments for each component, [debye].
economic_statuses: Status of each component in in relation to import and export from various regions, [-].
energy: Method to return the energy (enthalpy times flow rate) of this phase.
energy_calc: Method to return the energy (enthalpy times flow rate) of this phase.
energy_reactive: Method to return the reactive energy (reactive enthalpy times flow rate) of this phase.
energy_reactive_calc: Method to return the reactive energy (reactive enthalpy times flow rate) of this phase.
force_phase
formulas: Formulas of each component, [-].
legal_statuses: Status of each component in in relation to import and export rules from various regions, [-].
logPs: Octanol-water partition coefficients for each component, [-].
m: Method to return the mass flow rate of this phase.
m_calc
molecular_diameters: Lennard-Jones molecular diameters for each component, [angstrom].
ms: Method to return the mass flow rates of each component in this phase.
ms_calc: Method to return the mass flow rates of each component in this phase.
n: Method to return the molar flow rate of this phase.
n_calc
names: Names for each component, [-].
ns: Method to return the molar flow rates of each component in this phase.
ns_calc: Method to return the molar flow rates of each component in this phase.
omegas: Acentric factors for each component, [-].
phase_STPs: Standard states (‘g’, ‘l’, or ‘s’) for each component, [-].
result
rhocs: Molar densities at the critical point for each component, [mol/m^3].
rhocs_mass: Densities at the critical point for each component, [kg/m^3].
rhog_STPs: Molar gas densities at STP for each component; metastable if normally another state, [mol/m^3].
rhog_STPs_mass: Gas densities at STP for each component; metastable if normally another state, [kg/m^3].
rhol_60Fs: Liquid molar densities for each component at 60 °F, [mol/m^3].
rhol_60Fs_mass: Liquid mass densities for each component at 60 °F, [kg/m^3].
rhol_STPs: Molar liquid densities at STP for each component, [mol/m^3].
rhol_STPs_mass: Liquid densities at STP for each component, [kg/m^3].
rhos_Tms: Solid molar densities for each component at their respective melting points, [mol/m^3].
rhos_Tms_mass: Solid mass densities for each component at their melting point, [kg/m^3].
sigma_STPs: Liquid-air surface tensions at 298.15 K and the higher of 101325 Pa or the saturation pressure, [N/m].
sigma_Tbs: Liquid-air surface tensions at the normal boiling point and 101325 Pa, [N/m].
sigma_Tms: Liquid-air surface tensions at the melting point and 101325 Pa, [N/m].
similarity_variables: Similarity variables for each component, [mol/g].
smiless: SMILES identifiers for each component, [-].
solubility_parameters: Solubility parameters for each component at 298.15 K, [Pa^0.5].
ws_calc
zs_calc

Methods

`A`()	Method to calculate and return the Helmholtz energy of the phase.
`API`()	Method to calculate and return the API of the phase.
`A_dep`()	Method to calculate and return the departure Helmholtz energy of the phase.
`A_dep_flow`()	Method to return the flow rate of the difference between the ideal-gas Helmholtz energy of this phase and the Helmholtz energy of the phase This method is only available when the phase is linked to an EquilibriumStream.
`A_dep_mass`()	Method to calculate and return the departure mass Helmholtz energy of the phase.
`A_flow`()	Method to return the flow rate of Helmholtz energy of this phase.
`A_formation_ideal_gas`()	Method to calculate and return the ideal-gas Helmholtz energy of formation of the phase (as if the phase was an ideal gas).
`A_formation_ideal_gas_mass`()	Method to calculate and return the ideal-gas formation mass Helmholtz energy of the phase.
`A_ideal_gas`()	Method to calculate and return the ideal-gas Helmholtz energy of the phase.
`A_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas Helmholtz energy of the phase.
`A_mass`()	Method to calculate and return mass Helmholtz energy of the phase.
`A_reactive`()	Method to calculate and return the Helmholtz free energy of the phase on a reactive basis.
`A_reactive_mass`()	Method to calculate and return mass Helmholtz energy on a reactive basis of the phase.
`Actinium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Actinium, [atoms/s]
`Actinium_atom_flow`()	Method to calculate and return the mole flow that is Actinium, [mol/s]
`Actinium_atom_fraction`()	Method to calculate and return the mole fraction that is Actinium element, [-]
`Actinium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Actinium element, [kg/s]
`Actinium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Actinium element, [-]
`Aluminium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Aluminium, [atoms/s]
`Aluminium_atom_flow`()	Method to calculate and return the mole flow that is Aluminium, [mol/s]
`Aluminium_atom_fraction`()	Method to calculate and return the mole fraction that is Aluminium element, [-]
`Aluminium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Aluminium element, [kg/s]
`Aluminium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Aluminium element, [-]
`Americium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Americium, [atoms/s]
`Americium_atom_flow`()	Method to calculate and return the mole flow that is Americium, [mol/s]
`Americium_atom_fraction`()	Method to calculate and return the mole fraction that is Americium element, [-]
`Americium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Americium element, [kg/s]
`Americium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Americium element, [-]
`Antimony_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Antimony, [atoms/s]
`Antimony_atom_flow`()	Method to calculate and return the mole flow that is Antimony, [mol/s]
`Antimony_atom_fraction`()	Method to calculate and return the mole fraction that is Antimony element, [-]
`Antimony_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Antimony element, [kg/s]
`Antimony_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Antimony element, [-]
`Argon_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Argon, [atoms/s]
`Argon_atom_flow`()	Method to calculate and return the mole flow that is Argon, [mol/s]
`Argon_atom_fraction`()	Method to calculate and return the mole fraction that is Argon element, [-]
`Argon_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Argon element, [kg/s]
`Argon_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Argon element, [-]
`Arsenic_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Arsenic, [atoms/s]
`Arsenic_atom_flow`()	Method to calculate and return the mole flow that is Arsenic, [mol/s]
`Arsenic_atom_fraction`()	Method to calculate and return the mole fraction that is Arsenic element, [-]
`Arsenic_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Arsenic element, [kg/s]
`Arsenic_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Arsenic element, [-]
`Astatine_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Astatine, [atoms/s]
`Astatine_atom_flow`()	Method to calculate and return the mole flow that is Astatine, [mol/s]
`Astatine_atom_fraction`()	Method to calculate and return the mole fraction that is Astatine element, [-]
`Astatine_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Astatine element, [kg/s]
`Astatine_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Astatine element, [-]
`Barium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Barium, [atoms/s]
`Barium_atom_flow`()	Method to calculate and return the mole flow that is Barium, [mol/s]
`Barium_atom_fraction`()	Method to calculate and return the mole fraction that is Barium element, [-]
`Barium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Barium element, [kg/s]
`Barium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Barium element, [-]
`Berkelium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Berkelium, [atoms/s]
`Berkelium_atom_flow`()	Method to calculate and return the mole flow that is Berkelium, [mol/s]
`Berkelium_atom_fraction`()	Method to calculate and return the mole fraction that is Berkelium element, [-]
`Berkelium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Berkelium element, [kg/s]
`Berkelium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Berkelium element, [-]
`Beryllium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Beryllium, [atoms/s]
`Beryllium_atom_flow`()	Method to calculate and return the mole flow that is Beryllium, [mol/s]
`Beryllium_atom_fraction`()	Method to calculate and return the mole fraction that is Beryllium element, [-]
`Beryllium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Beryllium element, [kg/s]
`Beryllium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Beryllium element, [-]
`Bismuth_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Bismuth, [atoms/s]
`Bismuth_atom_flow`()	Method to calculate and return the mole flow that is Bismuth, [mol/s]
`Bismuth_atom_fraction`()	Method to calculate and return the mole fraction that is Bismuth element, [-]
`Bismuth_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Bismuth element, [kg/s]
`Bismuth_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Bismuth element, [-]
`Bohrium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Bohrium, [atoms/s]
`Bohrium_atom_flow`()	Method to calculate and return the mole flow that is Bohrium, [mol/s]
`Bohrium_atom_fraction`()	Method to calculate and return the mole fraction that is Bohrium element, [-]
`Bohrium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Bohrium element, [kg/s]
`Bohrium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Bohrium element, [-]
`Boron_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Boron, [atoms/s]
`Boron_atom_flow`()	Method to calculate and return the mole flow that is Boron, [mol/s]
`Boron_atom_fraction`()	Method to calculate and return the mole fraction that is Boron element, [-]
`Boron_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Boron element, [kg/s]
`Boron_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Boron element, [-]
`Bromine_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Bromine, [atoms/s]
`Bromine_atom_flow`()	Method to calculate and return the mole flow that is Bromine, [mol/s]
`Bromine_atom_fraction`()	Method to calculate and return the mole fraction that is Bromine element, [-]
`Bromine_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Bromine element, [kg/s]
`Bromine_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Bromine element, [-]
`Bvirial`()	Method to calculate and return the B virial coefficient of the phase at its current conditions.
`Cadmium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Cadmium, [atoms/s]
`Cadmium_atom_flow`()	Method to calculate and return the mole flow that is Cadmium, [mol/s]
`Cadmium_atom_fraction`()	Method to calculate and return the mole fraction that is Cadmium element, [-]
`Cadmium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Cadmium element, [kg/s]
`Cadmium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Cadmium element, [-]
`Caesium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Caesium, [atoms/s]
`Caesium_atom_flow`()	Method to calculate and return the mole flow that is Caesium, [mol/s]
`Caesium_atom_fraction`()	Method to calculate and return the mole fraction that is Caesium element, [-]
`Caesium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Caesium element, [kg/s]
`Caesium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Caesium element, [-]
`Calcium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Calcium, [atoms/s]
`Calcium_atom_flow`()	Method to calculate and return the mole flow that is Calcium, [mol/s]
`Calcium_atom_fraction`()	Method to calculate and return the mole fraction that is Calcium element, [-]
`Calcium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Calcium element, [kg/s]
`Calcium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Calcium element, [-]
`Californium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Californium, [atoms/s]
`Californium_atom_flow`()	Method to calculate and return the mole flow that is Californium, [mol/s]
`Californium_atom_fraction`()	Method to calculate and return the mole fraction that is Californium element, [-]
`Californium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Californium element, [kg/s]
`Californium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Californium element, [-]
`Carbon_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Carbon, [atoms/s]
`Carbon_atom_flow`()	Method to calculate and return the mole flow that is Carbon, [mol/s]
`Carbon_atom_fraction`()	Method to calculate and return the mole fraction that is Carbon element, [-]
`Carbon_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Carbon element, [kg/s]
`Carbon_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Carbon element, [-]
`Cerium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Cerium, [atoms/s]
`Cerium_atom_flow`()	Method to calculate and return the mole flow that is Cerium, [mol/s]
`Cerium_atom_fraction`()	Method to calculate and return the mole fraction that is Cerium element, [-]
`Cerium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Cerium element, [kg/s]
`Cerium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Cerium element, [-]
`Chlorine_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Chlorine, [atoms/s]
`Chlorine_atom_flow`()	Method to calculate and return the mole flow that is Chlorine, [mol/s]
`Chlorine_atom_fraction`()	Method to calculate and return the mole fraction that is Chlorine element, [-]
`Chlorine_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Chlorine element, [kg/s]
`Chlorine_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Chlorine element, [-]
`Chromium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Chromium, [atoms/s]
`Chromium_atom_flow`()	Method to calculate and return the mole flow that is Chromium, [mol/s]
`Chromium_atom_fraction`()	Method to calculate and return the mole fraction that is Chromium element, [-]
`Chromium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Chromium element, [kg/s]
`Chromium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Chromium element, [-]
`Cobalt_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Cobalt, [atoms/s]
`Cobalt_atom_flow`()	Method to calculate and return the mole flow that is Cobalt, [mol/s]
`Cobalt_atom_fraction`()	Method to calculate and return the mole fraction that is Cobalt element, [-]
`Cobalt_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Cobalt element, [kg/s]
`Cobalt_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Cobalt element, [-]
`Copernicium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Copernicium, [atoms/s]
`Copernicium_atom_flow`()	Method to calculate and return the mole flow that is Copernicium, [mol/s]
`Copernicium_atom_fraction`()	Method to calculate and return the mole fraction that is Copernicium element, [-]
`Copernicium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Copernicium element, [kg/s]
`Copernicium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Copernicium element, [-]
`Copper_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Copper, [atoms/s]
`Copper_atom_flow`()	Method to calculate and return the mole flow that is Copper, [mol/s]
`Copper_atom_fraction`()	Method to calculate and return the mole fraction that is Copper element, [-]
`Copper_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Copper element, [kg/s]
`Copper_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Copper element, [-]
`Cp`()	Method to calculate and return the constant-pressure heat capacity of the phase.
`Cp_Cv_ratio`()	Method to calculate and return the Cp/Cv ratio of the phase.
`Cp_Cv_ratio_ideal_gas`()	Method to calculate and return the ratio of the ideal-gas heat capacity to its constant-volume heat capacity.
`Cp_dep_mass`()	Method to calculate and return mass constant pressure departure heat capacity of the phase.
`Cp_ideal_gas`()	Method to calculate and return the ideal-gas heat capacity of the phase.
`Cp_ideal_gas_mass`()	Method to calculate and return mass constant pressure departure heat capacity of the phase.
`Cp_mass`()	Method to calculate and return mass constant pressure heat capacity of the phase.
`Cpgs`()	Method to calculate and return the pure-component ideal gas heat capacities of each species from the `thermo.heat_capacity.HeatCapacityGas` objects.
`Cpig_integrals_over_T_pure`()	Method to calculate and return the integrals of the ideal-gas heat capacities divided by temperature of every component in the phase from a temperature of `Phase.T_REF_IG` to the system temperature.
`Cpig_integrals_pure`()	Method to calculate and return the integrals of the ideal-gas heat capacities of every component in the phase from a temperature of `Phase.T_REF_IG` to the system temperature.
`Cpigs_pure`()	Method to calculate and return the ideal-gas heat capacities of every component in the phase.
`Cpls`()	Method to calculate and return the pure-component liquid temperature-dependent heat capacities of each species from the `thermo.heat_capacity.HeatCapacityLiquid` objects.
`Cpss`()	Method to calculate and return the pure-component solid heat capacities of each species from the `thermo.heat_capacity.HeatCapacitySolid` objects.
`Curium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Curium, [atoms/s]
`Curium_atom_flow`()	Method to calculate and return the mole flow that is Curium, [mol/s]
`Curium_atom_fraction`()	Method to calculate and return the mole fraction that is Curium element, [-]
`Curium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Curium element, [kg/s]
`Curium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Curium element, [-]
`Cv`()	Method to calculate and return the constant-volume heat capacity Cv of the phase.
`Cv_dep`()	Method to calculate and return the difference between the actual Cv and the ideal-gas constant volume heat capacity $C_v^{ig}$ of the phase.
`Cv_dep_mass`()	Method to calculate and return mass constant pressure departure heat capacity of the phase.
`Cv_ideal_gas`()	Method to calculate and return the ideal-gas constant volume heat capacity of the phase.
`Cv_mass`()	Method to calculate and return mass constant volume heat capacity of the phase.
`Darmstadtium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Darmstadtium, [atoms/s]
`Darmstadtium_atom_flow`()	Method to calculate and return the mole flow that is Darmstadtium, [mol/s]
`Darmstadtium_atom_fraction`()	Method to calculate and return the mole fraction that is Darmstadtium element, [-]
`Darmstadtium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Darmstadtium element, [kg/s]
`Darmstadtium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Darmstadtium element, [-]
`Dubnium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Dubnium, [atoms/s]
`Dubnium_atom_flow`()	Method to calculate and return the mole flow that is Dubnium, [mol/s]
`Dubnium_atom_fraction`()	Method to calculate and return the mole fraction that is Dubnium element, [-]
`Dubnium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Dubnium element, [kg/s]
`Dubnium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Dubnium element, [-]
`Dysprosium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Dysprosium, [atoms/s]
`Dysprosium_atom_flow`()	Method to calculate and return the mole flow that is Dysprosium, [mol/s]
`Dysprosium_atom_fraction`()	Method to calculate and return the mole fraction that is Dysprosium element, [-]
`Dysprosium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Dysprosium element, [kg/s]
`Dysprosium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Dysprosium element, [-]
`Einsteinium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Einsteinium, [atoms/s]
`Einsteinium_atom_flow`()	Method to calculate and return the mole flow that is Einsteinium, [mol/s]
`Einsteinium_atom_fraction`()	Method to calculate and return the mole fraction that is Einsteinium element, [-]
`Einsteinium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Einsteinium element, [kg/s]
`Einsteinium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Einsteinium element, [-]
`Erbium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Erbium, [atoms/s]
`Erbium_atom_flow`()	Method to calculate and return the mole flow that is Erbium, [mol/s]
`Erbium_atom_fraction`()	Method to calculate and return the mole fraction that is Erbium element, [-]
`Erbium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Erbium element, [kg/s]
`Erbium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Erbium element, [-]
`Europium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Europium, [atoms/s]
`Europium_atom_flow`()	Method to calculate and return the mole flow that is Europium, [mol/s]
`Europium_atom_fraction`()	Method to calculate and return the mole fraction that is Europium element, [-]
`Europium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Europium element, [kg/s]
`Europium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Europium element, [-]
`Fermium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Fermium, [atoms/s]
`Fermium_atom_flow`()	Method to calculate and return the mole flow that is Fermium, [mol/s]
`Fermium_atom_fraction`()	Method to calculate and return the mole fraction that is Fermium element, [-]
`Fermium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Fermium element, [kg/s]
`Fermium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Fermium element, [-]
`Flerovium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Flerovium, [atoms/s]
`Flerovium_atom_flow`()	Method to calculate and return the mole flow that is Flerovium, [mol/s]
`Flerovium_atom_fraction`()	Method to calculate and return the mole fraction that is Flerovium element, [-]
`Flerovium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Flerovium element, [kg/s]
`Flerovium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Flerovium element, [-]
`Fluorine_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Fluorine, [atoms/s]
`Fluorine_atom_flow`()	Method to calculate and return the mole flow that is Fluorine, [mol/s]
`Fluorine_atom_fraction`()	Method to calculate and return the mole fraction that is Fluorine element, [-]
`Fluorine_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Fluorine element, [kg/s]
`Fluorine_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Fluorine element, [-]
`Francium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Francium, [atoms/s]
`Francium_atom_flow`()	Method to calculate and return the mole flow that is Francium, [mol/s]
`Francium_atom_fraction`()	Method to calculate and return the mole fraction that is Francium element, [-]
`Francium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Francium element, [kg/s]
`Francium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Francium element, [-]
`G`()	Method to calculate and return the Gibbs free energy of the phase.
`G_dep`()	Method to calculate and return the departure Gibbs free energy of the phase.
`G_dep_flow`()	Method to return the flow rate of the difference between the ideal-gas Gibbs free energy of this phase and the actual Gibbs free energy of the phase This method is only available when the phase is linked to an EquilibriumStream.
`G_dep_mass`()	Method to calculate and return the mass departure Gibbs free energy of the phase.
`G_dep_phi_consistency`()	Method to calculate and return a consistency check between departure Gibbs free energy, and the fugacity coefficients.
`G_flow`()	Method to return the flow rate of Gibbs free energy of this phase.
`G_formation_ideal_gas`()	Method to calculate and return the ideal-gas Gibbs free energy of formation of the phase (as if the phase was an ideal gas).
`G_formation_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas formation Gibbs free energy of the phase.
`G_ideal_gas`()	Method to calculate and return the ideal-gas Gibbs free energy of the phase.
`G_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas Gibbs free energy of the phase.
`G_mass`()	Method to calculate and return mass Gibbs energy of the phase.
`G_min`()	Method to calculate and return the Gibbs free energy of the phase.
`G_min_criteria`()	Method to calculate and return the Gibbs energy criteria required for comparing phase stability.
`G_reactive`()	Method to calculate and return the Gibbs free energy of the phase on a reactive basis.
`G_reactive_mass`()	Method to calculate and return mass Gibbs free energy on a reactive basis of the phase.
`Gadolinium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Gadolinium, [atoms/s]
`Gadolinium_atom_flow`()	Method to calculate and return the mole flow that is Gadolinium, [mol/s]
`Gadolinium_atom_fraction`()	Method to calculate and return the mole fraction that is Gadolinium element, [-]
`Gadolinium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Gadolinium element, [kg/s]
`Gadolinium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Gadolinium element, [-]
`Gallium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Gallium, [atoms/s]
`Gallium_atom_flow`()	Method to calculate and return the mole flow that is Gallium, [mol/s]
`Gallium_atom_fraction`()	Method to calculate and return the mole fraction that is Gallium element, [-]
`Gallium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Gallium element, [kg/s]
`Gallium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Gallium element, [-]
`Germanium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Germanium, [atoms/s]
`Germanium_atom_flow`()	Method to calculate and return the mole flow that is Germanium, [mol/s]
`Germanium_atom_fraction`()	Method to calculate and return the mole fraction that is Germanium element, [-]
`Germanium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Germanium element, [kg/s]
`Germanium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Germanium element, [-]
`Gold_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Gold, [atoms/s]
`Gold_atom_flow`()	Method to calculate and return the mole flow that is Gold, [mol/s]
`Gold_atom_fraction`()	Method to calculate and return the mole fraction that is Gold element, [-]
`Gold_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Gold element, [kg/s]
`Gold_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Gold element, [-]
`H`()	Method to calculate and return the enthalpy of the phase.
`H_C_ratio`()	Method to calculate and return the atomic ratio of hydrogen atoms to carbon atoms, based on the current composition of the phase.
`H_C_ratio_mass`()	Method to calculate and return the mass ratio of hydrogen atoms to carbon atoms, based on the current composition of the phase.
`H_dep_flow`()	Method to return the flow rate of the difference between the ideal-gas energy of this phase and the actual energy of the phase This method is only available when the phase is linked to an EquilibriumStream.
`H_dep_mass`()	Method to calculate and return the mass departure enthalpy of the phase.
`H_dep_phi_consistency`()	Method to calculate and return a consistency check between departure enthalpy, and the fugacity coefficients' temperature derivatives.
`H_flow`()	Method to return the flow rate of enthalpy of this phase.
`H_formation_ideal_gas`()	Method to calculate and return the ideal-gas enthalpy of formation of the phase (as if the phase was an ideal gas).
`H_formation_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas formation enthalpy of the phase.
`H_from_phi`()	Method to calculate and return the enthalpy of the fluid as calculated from the ideal-gas enthalpy and the the fugacity coefficients' temperature derivatives.
`H_ideal_gas`()	Method to calculate and return the ideal-gas enthalpy of the phase.
`H_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas enthalpy of the phase.
`H_mass`()	Method to calculate and return mass enthalpy of the phase.
`H_phi_consistency`()	Method to calculate and return a consistency check between ideal gas enthalpy behavior, and the fugacity coefficients and their temperature derivatives.
`H_reactive`()	Method to calculate and return the enthalpy of the phase on a reactive basis, using the Hfs values of the phase.
`H_reactive_mass`()	Method to calculate and return mass enthalpy on a reactive basis of the phase.
`Hafnium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Hafnium, [atoms/s]
`Hafnium_atom_flow`()	Method to calculate and return the mole flow that is Hafnium, [mol/s]
`Hafnium_atom_fraction`()	Method to calculate and return the mole fraction that is Hafnium element, [-]
`Hafnium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Hafnium element, [kg/s]
`Hafnium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Hafnium element, [-]
`Hassium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Hassium, [atoms/s]
`Hassium_atom_flow`()	Method to calculate and return the mole flow that is Hassium, [mol/s]
`Hassium_atom_fraction`()	Method to calculate and return the mole fraction that is Hassium element, [-]
`Hassium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Hassium element, [kg/s]
`Hassium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Hassium element, [-]
`Hc`()	Method to calculate and return the molar ideal-gas higher heat of combustion of the object, [J/mol]
`Hc_lower`()	Method to calculate and return the molar ideal-gas lower heat of combustion of the object, [J/mol]
`Hc_lower_mass`()	Method to calculate and return the mass ideal-gas lower heat of combustion of the object, [J/mol]
`Hc_lower_normal`()	Method to calculate and return the volumetric ideal-gas lower heat of combustion of the object using the normal gas volume, [J/m^3]
`Hc_lower_standard`()	Method to calculate and return the volumetric ideal-gas lower heat of combustion of the object using the standard gas volume, [J/m^3]
`Hc_mass`()	Method to calculate and return the mass ideal-gas higher heat of combustion of the object, [J/mol]
`Hc_normal`()	Method to calculate and return the volumetric ideal-gas higher heat of combustion of the object using the normal gas volume, [J/m^3]
`Hc_standard`()	Method to calculate and return the volumetric ideal-gas higher heat of combustion of the object using the standard gas volume, [J/m^3]
`Helium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Helium, [atoms/s]
`Helium_atom_flow`()	Method to calculate and return the mole flow that is Helium, [mol/s]
`Helium_atom_fraction`()	Method to calculate and return the mole fraction that is Helium element, [-]
`Helium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Helium element, [kg/s]
`Helium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Helium element, [-]
`Holmium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Holmium, [atoms/s]
`Holmium_atom_flow`()	Method to calculate and return the mole flow that is Holmium, [mol/s]
`Holmium_atom_fraction`()	Method to calculate and return the mole fraction that is Holmium element, [-]
`Holmium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Holmium element, [kg/s]
`Holmium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Holmium element, [-]
`Hsubs`()	Method to calculate and return the pure-component enthalpy of sublimation of each species from the `thermo.phase_change.EnthalpySublimation` objects.
`Hvaps`()	Method to calculate and return the pure-component enthalpy of vaporization of each species from the `thermo.phase_change.EnthalpyVaporization` objects.
`Hydrogen_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Hydrogen, [atoms/s]
`Hydrogen_atom_flow`()	Method to calculate and return the mole flow that is Hydrogen, [mol/s]
`Hydrogen_atom_fraction`()	Method to calculate and return the mole fraction that is Hydrogen element, [-]
`Hydrogen_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Hydrogen element, [kg/s]
`Hydrogen_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Hydrogen element, [-]
`Indium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Indium, [atoms/s]
`Indium_atom_flow`()	Method to calculate and return the mole flow that is Indium, [mol/s]
`Indium_atom_fraction`()	Method to calculate and return the mole fraction that is Indium element, [-]
`Indium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Indium element, [kg/s]
`Indium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Indium element, [-]
`Iodine_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Iodine, [atoms/s]
`Iodine_atom_flow`()	Method to calculate and return the mole flow that is Iodine, [mol/s]
`Iodine_atom_fraction`()	Method to calculate and return the mole fraction that is Iodine element, [-]
`Iodine_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Iodine element, [kg/s]
`Iodine_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Iodine element, [-]
`Iridium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Iridium, [atoms/s]
`Iridium_atom_flow`()	Method to calculate and return the mole flow that is Iridium, [mol/s]
`Iridium_atom_fraction`()	Method to calculate and return the mole fraction that is Iridium element, [-]
`Iridium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Iridium element, [kg/s]
`Iridium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Iridium element, [-]
`Iron_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Iron, [atoms/s]
`Iron_atom_flow`()	Method to calculate and return the mole flow that is Iron, [mol/s]
`Iron_atom_fraction`()	Method to calculate and return the mole fraction that is Iron element, [-]
`Iron_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Iron element, [kg/s]
`Iron_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Iron element, [-]
`Joule_Thomson`()	Method to calculate and return the Joule-Thomson coefficient of the phase.
`Krypton_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Krypton, [atoms/s]
`Krypton_atom_flow`()	Method to calculate and return the mole flow that is Krypton, [mol/s]
`Krypton_atom_fraction`()	Method to calculate and return the mole fraction that is Krypton element, [-]
`Krypton_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Krypton element, [kg/s]
`Krypton_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Krypton element, [-]
`Lanthanum_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Lanthanum, [atoms/s]
`Lanthanum_atom_flow`()	Method to calculate and return the mole flow that is Lanthanum, [mol/s]
`Lanthanum_atom_fraction`()	Method to calculate and return the mole fraction that is Lanthanum element, [-]
`Lanthanum_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Lanthanum element, [kg/s]
`Lanthanum_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Lanthanum element, [-]
`Lawrencium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Lawrencium, [atoms/s]
`Lawrencium_atom_flow`()	Method to calculate and return the mole flow that is Lawrencium, [mol/s]
`Lawrencium_atom_fraction`()	Method to calculate and return the mole fraction that is Lawrencium element, [-]
`Lawrencium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Lawrencium element, [kg/s]
`Lawrencium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Lawrencium element, [-]
`Lead_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Lead, [atoms/s]
`Lead_atom_flow`()	Method to calculate and return the mole flow that is Lead, [mol/s]
`Lead_atom_fraction`()	Method to calculate and return the mole fraction that is Lead element, [-]
`Lead_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Lead element, [kg/s]
`Lead_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Lead element, [-]
`Lithium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Lithium, [atoms/s]
`Lithium_atom_flow`()	Method to calculate and return the mole flow that is Lithium, [mol/s]
`Lithium_atom_fraction`()	Method to calculate and return the mole fraction that is Lithium element, [-]
`Lithium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Lithium element, [kg/s]
`Lithium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Lithium element, [-]
`Livermorium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Livermorium, [atoms/s]
`Livermorium_atom_flow`()	Method to calculate and return the mole flow that is Livermorium, [mol/s]
`Livermorium_atom_fraction`()	Method to calculate and return the mole fraction that is Livermorium element, [-]
`Livermorium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Livermorium element, [kg/s]
`Livermorium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Livermorium element, [-]
`Lutetium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Lutetium, [atoms/s]
`Lutetium_atom_flow`()	Method to calculate and return the mole flow that is Lutetium, [mol/s]
`Lutetium_atom_fraction`()	Method to calculate and return the mole fraction that is Lutetium element, [-]
`Lutetium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Lutetium element, [kg/s]
`Lutetium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Lutetium element, [-]
`MW`()	Method to calculate and return molecular weight of the phase.
`MW_inv`()	Method to calculate and return inverse of molecular weight of the phase.
`Magnesium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Magnesium, [atoms/s]
`Magnesium_atom_flow`()	Method to calculate and return the mole flow that is Magnesium, [mol/s]
`Magnesium_atom_fraction`()	Method to calculate and return the mole fraction that is Magnesium element, [-]
`Magnesium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Magnesium element, [kg/s]
`Magnesium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Magnesium element, [-]
`Manganese_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Manganese, [atoms/s]
`Manganese_atom_flow`()	Method to calculate and return the mole flow that is Manganese, [mol/s]
`Manganese_atom_fraction`()	Method to calculate and return the mole fraction that is Manganese element, [-]
`Manganese_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Manganese element, [kg/s]
`Manganese_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Manganese element, [-]
`Meitnerium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Meitnerium, [atoms/s]
`Meitnerium_atom_flow`()	Method to calculate and return the mole flow that is Meitnerium, [mol/s]
`Meitnerium_atom_fraction`()	Method to calculate and return the mole fraction that is Meitnerium element, [-]
`Meitnerium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Meitnerium element, [kg/s]
`Meitnerium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Meitnerium element, [-]
`Mendelevium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Mendelevium, [atoms/s]
`Mendelevium_atom_flow`()	Method to calculate and return the mole flow that is Mendelevium, [mol/s]
`Mendelevium_atom_fraction`()	Method to calculate and return the mole fraction that is Mendelevium element, [-]
`Mendelevium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Mendelevium element, [kg/s]
`Mendelevium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Mendelevium element, [-]
`Mercury_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Mercury, [atoms/s]
`Mercury_atom_flow`()	Method to calculate and return the mole flow that is Mercury, [mol/s]
`Mercury_atom_fraction`()	Method to calculate and return the mole fraction that is Mercury element, [-]
`Mercury_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Mercury element, [kg/s]
`Mercury_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Mercury element, [-]
`Molybdenum_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Molybdenum, [atoms/s]
`Molybdenum_atom_flow`()	Method to calculate and return the mole flow that is Molybdenum, [mol/s]
`Molybdenum_atom_fraction`()	Method to calculate and return the mole fraction that is Molybdenum element, [-]
`Molybdenum_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Molybdenum element, [kg/s]
`Molybdenum_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Molybdenum element, [-]
`Moscovium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Moscovium, [atoms/s]
`Moscovium_atom_flow`()	Method to calculate and return the mole flow that is Moscovium, [mol/s]
`Moscovium_atom_fraction`()	Method to calculate and return the mole fraction that is Moscovium element, [-]
`Moscovium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Moscovium element, [kg/s]
`Moscovium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Moscovium element, [-]
`Neodymium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Neodymium, [atoms/s]
`Neodymium_atom_flow`()	Method to calculate and return the mole flow that is Neodymium, [mol/s]
`Neodymium_atom_fraction`()	Method to calculate and return the mole fraction that is Neodymium element, [-]
`Neodymium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Neodymium element, [kg/s]
`Neodymium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Neodymium element, [-]
`Neon_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Neon, [atoms/s]
`Neon_atom_flow`()	Method to calculate and return the mole flow that is Neon, [mol/s]
`Neon_atom_fraction`()	Method to calculate and return the mole fraction that is Neon element, [-]
`Neon_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Neon element, [kg/s]
`Neon_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Neon element, [-]
`Neptunium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Neptunium, [atoms/s]
`Neptunium_atom_flow`()	Method to calculate and return the mole flow that is Neptunium, [mol/s]
`Neptunium_atom_fraction`()	Method to calculate and return the mole fraction that is Neptunium element, [-]
`Neptunium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Neptunium element, [kg/s]
`Neptunium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Neptunium element, [-]
`Nickel_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Nickel, [atoms/s]
`Nickel_atom_flow`()	Method to calculate and return the mole flow that is Nickel, [mol/s]
`Nickel_atom_fraction`()	Method to calculate and return the mole fraction that is Nickel element, [-]
`Nickel_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Nickel element, [kg/s]
`Nickel_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Nickel element, [-]
`Nihonium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Nihonium, [atoms/s]
`Nihonium_atom_flow`()	Method to calculate and return the mole flow that is Nihonium, [mol/s]
`Nihonium_atom_fraction`()	Method to calculate and return the mole fraction that is Nihonium element, [-]
`Nihonium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Nihonium element, [kg/s]
`Nihonium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Nihonium element, [-]
`Niobium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Niobium, [atoms/s]
`Niobium_atom_flow`()	Method to calculate and return the mole flow that is Niobium, [mol/s]
`Niobium_atom_fraction`()	Method to calculate and return the mole fraction that is Niobium element, [-]
`Niobium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Niobium element, [kg/s]
`Niobium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Niobium element, [-]
`Nitrogen_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Nitrogen, [atoms/s]
`Nitrogen_atom_flow`()	Method to calculate and return the mole flow that is Nitrogen, [mol/s]
`Nitrogen_atom_fraction`()	Method to calculate and return the mole fraction that is Nitrogen element, [-]
`Nitrogen_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Nitrogen element, [kg/s]
`Nitrogen_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Nitrogen element, [-]
`Nobelium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Nobelium, [atoms/s]
`Nobelium_atom_flow`()	Method to calculate and return the mole flow that is Nobelium, [mol/s]
`Nobelium_atom_fraction`()	Method to calculate and return the mole fraction that is Nobelium element, [-]
`Nobelium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Nobelium element, [kg/s]
`Nobelium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Nobelium element, [-]
`Oganesson_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Oganesson, [atoms/s]
`Oganesson_atom_flow`()	Method to calculate and return the mole flow that is Oganesson, [mol/s]
`Oganesson_atom_fraction`()	Method to calculate and return the mole fraction that is Oganesson element, [-]
`Oganesson_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Oganesson element, [kg/s]
`Oganesson_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Oganesson element, [-]
`Osmium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Osmium, [atoms/s]
`Osmium_atom_flow`()	Method to calculate and return the mole flow that is Osmium, [mol/s]
`Osmium_atom_fraction`()	Method to calculate and return the mole fraction that is Osmium element, [-]
`Osmium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Osmium element, [kg/s]
`Osmium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Osmium element, [-]
`Oxygen_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Oxygen, [atoms/s]
`Oxygen_atom_flow`()	Method to calculate and return the mole flow that is Oxygen, [mol/s]
`Oxygen_atom_fraction`()	Method to calculate and return the mole fraction that is Oxygen element, [-]
`Oxygen_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Oxygen element, [kg/s]
`Oxygen_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Oxygen element, [-]
`PIP`()	Method to calculate and return the phase identification parameter of the phase.
`P_max_at_V`(V)	Dummy method.
`P_transitions`()	Dummy method.
`Palladium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Palladium, [atoms/s]
`Palladium_atom_flow`()	Method to calculate and return the mole flow that is Palladium, [mol/s]
`Palladium_atom_fraction`()	Method to calculate and return the mole fraction that is Palladium element, [-]
`Palladium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Palladium element, [kg/s]
`Palladium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Palladium element, [-]
`Phosphorus_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Phosphorus, [atoms/s]
`Phosphorus_atom_flow`()	Method to calculate and return the mole flow that is Phosphorus, [mol/s]
`Phosphorus_atom_fraction`()	Method to calculate and return the mole fraction that is Phosphorus element, [-]
`Phosphorus_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Phosphorus element, [kg/s]
`Phosphorus_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Phosphorus element, [-]
`Platinum_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Platinum, [atoms/s]
`Platinum_atom_flow`()	Method to calculate and return the mole flow that is Platinum, [mol/s]
`Platinum_atom_fraction`()	Method to calculate and return the mole fraction that is Platinum element, [-]
`Platinum_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Platinum element, [kg/s]
`Platinum_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Platinum element, [-]
`Plutonium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Plutonium, [atoms/s]
`Plutonium_atom_flow`()	Method to calculate and return the mole flow that is Plutonium, [mol/s]
`Plutonium_atom_fraction`()	Method to calculate and return the mole fraction that is Plutonium element, [-]
`Plutonium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Plutonium element, [kg/s]
`Plutonium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Plutonium element, [-]
`Pmc`()	Method to calculate and return the mechanical critical pressure of the phase.
`Polonium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Polonium, [atoms/s]
`Polonium_atom_flow`()	Method to calculate and return the mole flow that is Polonium, [mol/s]
`Polonium_atom_fraction`()	Method to calculate and return the mole fraction that is Polonium element, [-]
`Polonium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Polonium element, [kg/s]
`Polonium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Polonium element, [-]
`Potassium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Potassium, [atoms/s]
`Potassium_atom_flow`()	Method to calculate and return the mole flow that is Potassium, [mol/s]
`Potassium_atom_fraction`()	Method to calculate and return the mole fraction that is Potassium element, [-]
`Potassium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Potassium element, [kg/s]
`Potassium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Potassium element, [-]
`Prandtl`()	Method to calculate and return the Prandtl number of the phase
`Praseodymium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Praseodymium, [atoms/s]
`Praseodymium_atom_flow`()	Method to calculate and return the mole flow that is Praseodymium, [mol/s]
`Praseodymium_atom_fraction`()	Method to calculate and return the mole fraction that is Praseodymium element, [-]
`Praseodymium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Praseodymium element, [kg/s]
`Praseodymium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Praseodymium element, [-]
`Promethium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Promethium, [atoms/s]
`Promethium_atom_flow`()	Method to calculate and return the mole flow that is Promethium, [mol/s]
`Promethium_atom_fraction`()	Method to calculate and return the mole fraction that is Promethium element, [-]
`Promethium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Promethium element, [kg/s]
`Promethium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Promethium element, [-]
`Protactinium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Protactinium, [atoms/s]
`Protactinium_atom_flow`()	Method to calculate and return the mole flow that is Protactinium, [mol/s]
`Protactinium_atom_fraction`()	Method to calculate and return the mole fraction that is Protactinium element, [-]
`Protactinium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Protactinium element, [kg/s]
`Protactinium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Protactinium element, [-]
`Psats`()	Method to calculate and return the pure-component vapor pressures of each species from the `thermo.vapor_pressure.VaporPressure` objects.
`Psubs`()	Method to calculate and return the pure-component sublimation of each species from the `thermo.vapor_pressure.SublimationPressure` objects.
`Radium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Radium, [atoms/s]
`Radium_atom_flow`()	Method to calculate and return the mole flow that is Radium, [mol/s]
`Radium_atom_fraction`()	Method to calculate and return the mole fraction that is Radium element, [-]
`Radium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Radium element, [kg/s]
`Radium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Radium element, [-]
`Radon_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Radon, [atoms/s]
`Radon_atom_flow`()	Method to calculate and return the mole flow that is Radon, [mol/s]
`Radon_atom_fraction`()	Method to calculate and return the mole fraction that is Radon element, [-]
`Radon_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Radon element, [kg/s]
`Radon_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Radon element, [-]
`Rhenium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Rhenium, [atoms/s]
`Rhenium_atom_flow`()	Method to calculate and return the mole flow that is Rhenium, [mol/s]
`Rhenium_atom_fraction`()	Method to calculate and return the mole fraction that is Rhenium element, [-]
`Rhenium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Rhenium element, [kg/s]
`Rhenium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Rhenium element, [-]
`Rhodium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Rhodium, [atoms/s]
`Rhodium_atom_flow`()	Method to calculate and return the mole flow that is Rhodium, [mol/s]
`Rhodium_atom_fraction`()	Method to calculate and return the mole fraction that is Rhodium element, [-]
`Rhodium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Rhodium element, [kg/s]
`Rhodium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Rhodium element, [-]
`Roentgenium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Roentgenium, [atoms/s]
`Roentgenium_atom_flow`()	Method to calculate and return the mole flow that is Roentgenium, [mol/s]
`Roentgenium_atom_fraction`()	Method to calculate and return the mole fraction that is Roentgenium element, [-]
`Roentgenium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Roentgenium element, [kg/s]
`Roentgenium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Roentgenium element, [-]
`Rubidium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Rubidium, [atoms/s]
`Rubidium_atom_flow`()	Method to calculate and return the mole flow that is Rubidium, [mol/s]
`Rubidium_atom_fraction`()	Method to calculate and return the mole fraction that is Rubidium element, [-]
`Rubidium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Rubidium element, [kg/s]
`Rubidium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Rubidium element, [-]
`Ruthenium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Ruthenium, [atoms/s]
`Ruthenium_atom_flow`()	Method to calculate and return the mole flow that is Ruthenium, [mol/s]
`Ruthenium_atom_fraction`()	Method to calculate and return the mole fraction that is Ruthenium element, [-]
`Ruthenium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Ruthenium element, [kg/s]
`Ruthenium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Ruthenium element, [-]
`Rutherfordium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Rutherfordium, [atoms/s]
`Rutherfordium_atom_flow`()	Method to calculate and return the mole flow that is Rutherfordium, [mol/s]
`Rutherfordium_atom_fraction`()	Method to calculate and return the mole fraction that is Rutherfordium element, [-]
`Rutherfordium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Rutherfordium element, [kg/s]
`Rutherfordium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Rutherfordium element, [-]
`S`()	Method to calculate and return the entropy of the phase.
`SG`()	Method to calculate and return the standard liquid specific gravity of the phase, using constant liquid pure component densities not calculated by the phase object, at 60 °F.
`SG_gas`()	Method to calculate and return the specific gravity of the phase with respect to a gas reference density.
`S_dep_flow`()	Method to return the flow rate of the difference between the ideal-gas entropy of this phase and the actual entropy of the phase This method is only available when the phase is linked to an EquilibriumStream.
`S_dep_mass`()	Method to calculate and return the mass departure entropy of the phase.
`S_dep_phi_consistency`()	Method to calculate and return a consistency check between ideal gas entropy behavior, and the fugacity coefficients and their temperature derivatives.
`S_flow`()	Method to return the flow rate of entropy of this phase.
`S_formation_ideal_gas`()	Method to calculate and return the ideal-gas entropy of formation of the phase (as if the phase was an ideal gas).
`S_formation_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas formation entropy of the phase.
`S_from_phi`()	Method to calculate and return the entropy of the fluid as calculated from the ideal-gas entropy and the the fugacity coefficients' temperature derivatives.
`S_ideal_gas`()	Method to calculate and return the ideal-gas entropy of the phase.
`S_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas entropy of the phase.
`S_mass`()	Method to calculate and return mass entropy of the phase.
`S_phi_consistency`()	Method to calculate and return a consistency check between ideal gas entropy behavior, and the fugacity coefficients and their temperature derivatives.
`S_reactive`()	Method to calculate and return the entropy of the phase on a reactive basis, using the Sfs values of the phase.
`S_reactive_mass`()	Method to calculate and return mass entropy on a reactive basis of the phase.
`Samarium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Samarium, [atoms/s]
`Samarium_atom_flow`()	Method to calculate and return the mole flow that is Samarium, [mol/s]
`Samarium_atom_fraction`()	Method to calculate and return the mole fraction that is Samarium element, [-]
`Samarium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Samarium element, [kg/s]
`Samarium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Samarium element, [-]
`Scandium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Scandium, [atoms/s]
`Scandium_atom_flow`()	Method to calculate and return the mole flow that is Scandium, [mol/s]
`Scandium_atom_fraction`()	Method to calculate and return the mole fraction that is Scandium element, [-]
`Scandium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Scandium element, [kg/s]
`Scandium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Scandium element, [-]
`Seaborgium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Seaborgium, [atoms/s]
`Seaborgium_atom_flow`()	Method to calculate and return the mole flow that is Seaborgium, [mol/s]
`Seaborgium_atom_fraction`()	Method to calculate and return the mole fraction that is Seaborgium element, [-]
`Seaborgium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Seaborgium element, [kg/s]
`Seaborgium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Seaborgium element, [-]
`Selenium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Selenium, [atoms/s]
`Selenium_atom_flow`()	Method to calculate and return the mole flow that is Selenium, [mol/s]
`Selenium_atom_fraction`()	Method to calculate and return the mole fraction that is Selenium element, [-]
`Selenium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Selenium element, [kg/s]
`Selenium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Selenium element, [-]
`Silicon_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Silicon, [atoms/s]
`Silicon_atom_flow`()	Method to calculate and return the mole flow that is Silicon, [mol/s]
`Silicon_atom_fraction`()	Method to calculate and return the mole fraction that is Silicon element, [-]
`Silicon_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Silicon element, [kg/s]
`Silicon_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Silicon element, [-]
`Silver_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Silver, [atoms/s]
`Silver_atom_flow`()	Method to calculate and return the mole flow that is Silver, [mol/s]
`Silver_atom_fraction`()	Method to calculate and return the mole fraction that is Silver element, [-]
`Silver_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Silver element, [kg/s]
`Silver_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Silver element, [-]
`Sodium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Sodium, [atoms/s]
`Sodium_atom_flow`()	Method to calculate and return the mole flow that is Sodium, [mol/s]
`Sodium_atom_fraction`()	Method to calculate and return the mole fraction that is Sodium element, [-]
`Sodium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Sodium element, [kg/s]
`Sodium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Sodium element, [-]
`Strontium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Strontium, [atoms/s]
`Strontium_atom_flow`()	Method to calculate and return the mole flow that is Strontium, [mol/s]
`Strontium_atom_fraction`()	Method to calculate and return the mole fraction that is Strontium element, [-]
`Strontium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Strontium element, [kg/s]
`Strontium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Strontium element, [-]
`Sulfur_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Sulfur, [atoms/s]
`Sulfur_atom_flow`()	Method to calculate and return the mole flow that is Sulfur, [mol/s]
`Sulfur_atom_fraction`()	Method to calculate and return the mole fraction that is Sulfur element, [-]
`Sulfur_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Sulfur element, [kg/s]
`Sulfur_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Sulfur element, [-]
`T_max_at_V`(V)	Method to calculate the maximum temperature the phase can create at a constant volume, if one exists; returns None otherwise.
`Tantalum_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Tantalum, [atoms/s]
`Tantalum_atom_flow`()	Method to calculate and return the mole flow that is Tantalum, [mol/s]
`Tantalum_atom_fraction`()	Method to calculate and return the mole fraction that is Tantalum element, [-]
`Tantalum_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Tantalum element, [kg/s]
`Tantalum_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Tantalum element, [-]
`Technetium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Technetium, [atoms/s]
`Technetium_atom_flow`()	Method to calculate and return the mole flow that is Technetium, [mol/s]
`Technetium_atom_fraction`()	Method to calculate and return the mole fraction that is Technetium element, [-]
`Technetium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Technetium element, [kg/s]
`Technetium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Technetium element, [-]
`Tellurium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Tellurium, [atoms/s]
`Tellurium_atom_flow`()	Method to calculate and return the mole flow that is Tellurium, [mol/s]
`Tellurium_atom_fraction`()	Method to calculate and return the mole fraction that is Tellurium element, [-]
`Tellurium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Tellurium element, [kg/s]
`Tellurium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Tellurium element, [-]
`Tennessine_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Tennessine, [atoms/s]
`Tennessine_atom_flow`()	Method to calculate and return the mole flow that is Tennessine, [mol/s]
`Tennessine_atom_fraction`()	Method to calculate and return the mole fraction that is Tennessine element, [-]
`Tennessine_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Tennessine element, [kg/s]
`Tennessine_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Tennessine element, [-]
`Terbium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Terbium, [atoms/s]
`Terbium_atom_flow`()	Method to calculate and return the mole flow that is Terbium, [mol/s]
`Terbium_atom_fraction`()	Method to calculate and return the mole fraction that is Terbium element, [-]
`Terbium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Terbium element, [kg/s]
`Terbium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Terbium element, [-]
`Thallium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Thallium, [atoms/s]
`Thallium_atom_flow`()	Method to calculate and return the mole flow that is Thallium, [mol/s]
`Thallium_atom_fraction`()	Method to calculate and return the mole fraction that is Thallium element, [-]
`Thallium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Thallium element, [kg/s]
`Thallium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Thallium element, [-]
`Thorium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Thorium, [atoms/s]
`Thorium_atom_flow`()	Method to calculate and return the mole flow that is Thorium, [mol/s]
`Thorium_atom_fraction`()	Method to calculate and return the mole fraction that is Thorium element, [-]
`Thorium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Thorium element, [kg/s]
`Thorium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Thorium element, [-]
`Thulium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Thulium, [atoms/s]
`Thulium_atom_flow`()	Method to calculate and return the mole flow that is Thulium, [mol/s]
`Thulium_atom_fraction`()	Method to calculate and return the mole fraction that is Thulium element, [-]
`Thulium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Thulium element, [kg/s]
`Thulium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Thulium element, [-]
`Tin_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Tin, [atoms/s]
`Tin_atom_flow`()	Method to calculate and return the mole flow that is Tin, [mol/s]
`Tin_atom_fraction`()	Method to calculate and return the mole fraction that is Tin element, [-]
`Tin_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Tin element, [kg/s]
`Tin_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Tin element, [-]
`Titanium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Titanium, [atoms/s]
`Titanium_atom_flow`()	Method to calculate and return the mole flow that is Titanium, [mol/s]
`Titanium_atom_fraction`()	Method to calculate and return the mole fraction that is Titanium element, [-]
`Titanium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Titanium element, [kg/s]
`Titanium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Titanium element, [-]
`Tmc`()	Method to calculate and return the mechanical critical temperature of the phase.
`Tungsten_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Tungsten, [atoms/s]
`Tungsten_atom_flow`()	Method to calculate and return the mole flow that is Tungsten, [mol/s]
`Tungsten_atom_fraction`()	Method to calculate and return the mole fraction that is Tungsten element, [-]
`Tungsten_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Tungsten element, [kg/s]
`Tungsten_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Tungsten element, [-]
`U`()	Method to calculate and return the internal energy of the phase.
`U_dep`()	Method to calculate and return the departure internal energy of the phase.
`U_dep_flow`()	Method to return the flow rate of the difference between the ideal-gas internal energy of this phase and the actual internal energy of the phase This method is only available when the phase is linked to an EquilibriumStream.
`U_dep_mass`()	Method to calculate and return the departure mass internal energy of the phase.
`U_flow`()	Method to return the flow rate of internal energy of this phase.
`U_formation_ideal_gas`()	Method to calculate and return the ideal-gas internal energy of formation of the phase (as if the phase was an ideal gas).
`U_formation_ideal_gas_mass`()	Method to calculate and return the ideal-gas formation mass internal energy of the phase.
`U_ideal_gas`()	Method to calculate and return the ideal-gas internal energy of the phase.
`U_ideal_gas_mass`()	Method to calculate and return the mass ideal-gas internal energy of the phase.
`U_mass`()	Method to calculate and return mass internal energy of the phase.
`U_reactive`()	Method to calculate and return the internal energy of the phase on a reactive basis.
`U_reactive_mass`()	Method to calculate and return mass internal energy on a reactive basis of the phase.
`Uranium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Uranium, [atoms/s]
`Uranium_atom_flow`()	Method to calculate and return the mole flow that is Uranium, [mol/s]
`Uranium_atom_fraction`()	Method to calculate and return the mole fraction that is Uranium element, [-]
`Uranium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Uranium element, [kg/s]
`Uranium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Uranium element, [-]
`V`()	Method to return the molar volume of the phase.
`V_dep`()	Method to calculate and return the departure (from ideal gas behavior) molar volume of the phase.
`V_from_phi`()	Method to calculate and return the molar volume of the fluid as calculated from the pressure derivatives of fugacity coefficients.
`V_gas`()	Method to calculate and return the ideal-gas molar volume of the phase at the chosen reference temperature and pressure, according to the temperature variable T_gas_ref and pressure variable P_gas_ref of the `thermo.bulk.BulkSettings`.
`V_gas_normal`()	Method to calculate and return the ideal-gas molar volume of the phase at the normal temperature and pressure, according to the temperature variable T_normal and pressure variable P_normal of the `thermo.bulk.BulkSettings`.
`V_gas_standard`()	Method to calculate and return the ideal-gas molar volume of the phase at the standard temperature and pressure, according to the temperature variable T_standard and pressure variable P_standard of the `thermo.bulk.BulkSettings`.
`V_ideal_gas`()	Method to calculate and return the ideal-gas molar volume of the phase.
`V_iter`([force])	Method to calculate and return the volume of the phase in a way suitable for a TV resolution to converge on the same pressure.
`V_liquid_ref`()	Method to calculate and return the liquid reference molar volume according to the temperature variable T_liquid_volume_ref of `thermo.bulk.BulkSettings` and the composition of the phase.
`V_mass`()	Method to calculate and return the specific volume of the phase.
`V_phi_consistency`()	Method to calculate and return a consistency check between molar volume, and the fugacity coefficients' pressures derivatives.
`Vanadium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Vanadium, [atoms/s]
`Vanadium_atom_flow`()	Method to calculate and return the mole flow that is Vanadium, [mol/s]
`Vanadium_atom_fraction`()	Method to calculate and return the mole fraction that is Vanadium element, [-]
`Vanadium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Vanadium element, [kg/s]
`Vanadium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Vanadium element, [-]
`Vfgs`()	Method to calculate and return the ideal-gas volume fractions of the components of the phase.
`Vfls`()	Method to calculate and return the ideal-liquid volume fractions of the components of the phase, using the standard liquid densities at the temperature variable T_liquid_volume_ref of `thermo.bulk.BulkSettings` and the composition of the phase.
`Vls`()	Method to calculate and return the pure-component liquid temperature-dependent molar volume of each species from the `thermo.volume.VolumeLiquid` objects.
`Vmc`()	Method to calculate and return the mechanical critical volume of the phase.
`Vss`()	Method to calculate and return the pure-component solid temperature-dependent molar volume of each species from the `thermo.volume.VolumeSolid` objects.
`Wobbe_index`()	Method to calculate and return the molar Wobbe index of the object, [J/mol].
`Wobbe_index_lower`()	Method to calculate and return the molar lower Wobbe index of the
`Wobbe_index_lower_mass`()	Method to calculate and return the lower mass Wobbe index of the object, [J/kg].
`Wobbe_index_lower_normal`()	Method to calculate and return the volumetric normal lower Wobbe index of the object, [J/m^3].
`Wobbe_index_lower_standard`()	Method to calculate and return the volumetric standard lower Wobbe index of the object, [J/m^3].
`Wobbe_index_mass`()	Method to calculate and return the mass Wobbe index of the object, [J/kg].
`Wobbe_index_normal`()	Method to calculate and return the volumetric normal Wobbe index of the object, [J/m^3].
`Wobbe_index_standard`()	Method to calculate and return the volumetric standard Wobbe index of the object, [J/m^3].
`Xenon_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Xenon, [atoms/s]
`Xenon_atom_flow`()	Method to calculate and return the mole flow that is Xenon, [mol/s]
`Xenon_atom_fraction`()	Method to calculate and return the mole fraction that is Xenon element, [-]
`Xenon_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Xenon element, [kg/s]
`Xenon_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Xenon element, [-]
`Ytterbium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Ytterbium, [atoms/s]
`Ytterbium_atom_flow`()	Method to calculate and return the mole flow that is Ytterbium, [mol/s]
`Ytterbium_atom_fraction`()	Method to calculate and return the mole fraction that is Ytterbium element, [-]
`Ytterbium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Ytterbium element, [kg/s]
`Ytterbium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Ytterbium element, [-]
`Yttrium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Yttrium, [atoms/s]
`Yttrium_atom_flow`()	Method to calculate and return the mole flow that is Yttrium, [mol/s]
`Yttrium_atom_fraction`()	Method to calculate and return the mole fraction that is Yttrium element, [-]
`Yttrium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Yttrium element, [kg/s]
`Yttrium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Yttrium element, [-]
`Z`()	Method to calculate and return the compressibility factor of the phase.
`Zinc_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Zinc, [atoms/s]
`Zinc_atom_flow`()	Method to calculate and return the mole flow that is Zinc, [mol/s]
`Zinc_atom_fraction`()	Method to calculate and return the mole fraction that is Zinc element, [-]
`Zinc_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Zinc element, [kg/s]
`Zinc_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Zinc element, [-]
`Zirconium_atom_count_flow`()	Method to calculate and return the number of atoms in the flow which are Zirconium, [atoms/s]
`Zirconium_atom_flow`()	Method to calculate and return the mole flow that is Zirconium, [mol/s]
`Zirconium_atom_fraction`()	Method to calculate and return the mole fraction that is Zirconium element, [-]
`Zirconium_atom_mass_flow`()	Method to calculate and return the mass flow of atoms that are Zirconium element, [kg/s]
`Zirconium_atom_mass_fraction`()	Method to calculate and return the mass fraction of the phase that is Zirconium element, [-]
`Zmc`()	Method to calculate and return the mechanical critical compressibility of the phase.
`activities`()	Method to calculate and return the activities of each component in the phase [-].
`alpha`()	Method to calculate and return the thermal diffusivity of the phase.
`ammonia_molar_weight`()	Method to calculate and return the effective quantiy of ammonia in the phase as a molar weight, [g/mol].
`ammonia_partial_pressure`()	Method to calculate and return the ideal partial pressure of ammonia, [Pa]
`argon_molar_weight`()	Method to calculate and return the effective quantiy of argon in the phase as a molar weight, [g/mol].
`argon_partial_pressure`()	Method to calculate and return the ideal partial pressure of argon, [Pa]
`as_json`()	Method to create a JSON-friendly serialization of the phase which can be stored, and reloaded later.
`atom_content`()	Method to calculate and return the number of moles of each atom in the phase per mole of the phase; returns a dictionary of atom counts, containing only those elements who are present.
`atom_count_flows`()	Method to calculate and return the atom count flow rates of the phase; returns a dictionary of atom count flows, containing only those elements who are present.
`atom_flows`()	Method to calculate and return the atomic flow rates of the phase; returns a dictionary of atom flows, containing only those elements who are present.
`atom_fractions`()	Method to calculate and return the atomic composition of the phase; returns a dictionary of atom fraction (by count), containing only those elements who are present.
`atom_mass_flows`()	Method to calculate and return the atomic mass flow rates of the phase; returns a dictionary of atom mass flows, containing only those elements who are present.
`atom_mass_fractions`()	Method to calculate and return the atomic mass fractions of the phase; returns a dictionary of atom fraction (by mass), containing only those elements who arxe present.
`carbon_dioxide_molar_weight`()	Method to calculate and return the effective quantiy of carbon_dioxide in the phase as a molar weight, [g/mol].
`carbon_dioxide_partial_pressure`()	Method to calculate and return the ideal partial pressure of carbon_dioxide, [Pa]
`chemical_potential`()	Method to calculate and return the chemical potentials of each component in the phase [-].
`concentrations`()	Method to return the molar concentrations of each component in the phase in units of mol/m^3.
`concentrations_gas`()	Method to return the molar concentrations of each component in the phase in units of mol/m^3, using the ideal-gas molar volume of the phase at the chosen reference temperature and pressure.
`concentrations_gas_normal`()	Method to return the molar concentrations of each component in the phase in units of mol/m^3, using the ideal-gas molar volume of the phase at the normal temperature and pressure.
`concentrations_gas_standard`()	Method to return the molar concentrations of each component in the phase in units of mol/m^3, using the ideal-gas molar volume of the phase at the standard temperature and pressure.
`concentrations_mass`()	Method to return the mass concentrations of each component in the phase in units of kg/m^3.
`concentrations_mass_gas`()	Method to return the mass concentrations of each component in the phase in units of kg/m^3, using the ideal-gas molar volume of the phase at the chosen reference temperature and pressure.
`concentrations_mass_gas_normal`()	Method to return the mass concentrations of each component in the phase in units of kg/m^3, using the ideal-gas molar volume of the phase at the normal temperature and pressure.
`concentrations_mass_gas_standard`()	Method to return the mass concentrations of each component in the phase in units of kg/m^3, using the ideal-gas molar volume of the phase at the standard temperature and pressure.
`d2P_dT2`()	Method to calculate and return the second temperature derivative of pressure of the phase.
`d2P_dTdV`()	Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.
`d2P_dTdrho`()	Method to calculate and return the temperature derivative and then molar density derivative of the pressure of the phase.
`d2P_dV2`()	Method to calculate and return the second volume derivative of pressure of the phase.
`d2P_dVdT`()	Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.
`d2P_drho2`()	Method to calculate and return the second molar density derivative of pressure of the phase.
`d2T_dP2`()	Method to calculate and return the constant-volume second pressure derivative of temperature of the phase.
`d2T_dP2_V`()	Method to calculate and return the constant-volume second pressure derivative of temperature of the phase.
`d2T_dPdV`()	Method to calculate and return the derivative of pressure and then the derivative of volume of temperature of the phase.
`d2T_dPdrho`()	Method to calculate and return the pressure derivative and then molar density derivative of the temperature of the phase.
`d2T_dV2`()	Method to calculate and return the constant-pressure second volume derivative of temperature of the phase.
`d2T_dV2_P`()	Method to calculate and return the constant-pressure second volume derivative of temperature of the phase.
`d2T_dVdP`()	Method to calculate and return the derivative of pressure and then the derivative of volume of temperature of the phase.
`d2T_drho2`()	Method to calculate and return the second molar density derivative of temperature of the phase.
`d2V_dP2`()	Method to calculate and return the constant-temperature pressure derivative of volume of the phase.
`d2V_dP2_T`()	Method to calculate and return the constant-temperature pressure derivative of volume of the phase.
`d2V_dPdT`()	Method to calculate and return the derivative of pressure and then the derivative of temperature of volume of the phase.
`d2V_dT2`()	Method to calculate and return the constant-pressure second temperature derivative of volume of the phase.
`d2V_dT2_P`()	Method to calculate and return the constant-pressure second temperature derivative of volume of the phase.
`d2V_dTdP`()	Method to calculate and return the derivative of pressure and then the derivative of temperature of volume of the phase.
`d2rho_dP2`()	Method to calculate and return the second pressure derivative of molar density of the phase.
`d2rho_dPdT`()	Method to calculate and return the pressure derivative and then temperature derivative of the molar density of the phase.
`d2rho_dT2`()	Method to calculate and return the second temperature derivative of molar density of the phase.
`dA_dP`()	Method to calculate and return the constant-temperature pressure derivative of Helmholtz energy.
`dA_dP_T`()	Method to calculate and return the constant-temperature pressure derivative of Helmholtz energy.
`dA_dP_V`()	Method to calculate and return the constant-volume pressure derivative of Helmholtz energy.
`dA_dT`()	Method to calculate and return the constant-pressure temperature derivative of Helmholtz energy.
`dA_dT_P`()	Method to calculate and return the constant-pressure temperature derivative of Helmholtz energy.
`dA_dT_V`()	Method to calculate and return the constant-volume temperature derivative of Helmholtz energy.
`dA_dV_P`()	Method to calculate and return the constant-pressure volume derivative of Helmholtz energy.
`dA_dV_T`()	Method to calculate and return the constant-temperature volume derivative of Helmholtz energy.
`dA_mass_dP`([prop])	Method to calculate and return the pressure derivative of mass Helmholtz energy of the phase at constant temperature.
`dA_mass_dP_T`([prop])	Method to calculate and return the pressure derivative of mass Helmholtz energy of the phase at constant temperature.
`dA_mass_dP_V`([prop])	Method to calculate and return the pressure derivative of mass Helmholtz energy of the phase at constant volume.
`dA_mass_dT`([prop])	Method to calculate and return the temperature derivative of mass Helmholtz energy of the phase at constant pressure.
`dA_mass_dT_P`([prop])	Method to calculate and return the temperature derivative of mass Helmholtz energy of the phase at constant pressure.
`dA_mass_dT_V`([prop])	Method to calculate and return the temperature derivative of mass Helmholtz energy of the phase at constant volume.
`dA_mass_dV_P`([prop])	Method to calculate and return the volume derivative of mass Helmholtz energy of the phase at constant pressure.
`dA_mass_dV_T`([prop])	Method to calculate and return the volume derivative of mass Helmholtz energy of the phase at constant temperature.
`dCpigs_dT_pure`()	Method to calculate and return the first temperature derivative of ideal-gas heat capacities of every component in the phase.
`dCv_dP_T`()	Method to calculate the pressure derivative of Cv, constant volume heat capacity, at constant temperature.
`dCv_dT_P`()	Method to calculate the temperature derivative of Cv, constant volume heat capacity, at constant pressure.
`dCv_mass_dP_T`([prop])	Method to calculate and return the pressure derivative of mass Constant-volume heat capacity of the phase at constant temperature.
`dCv_mass_dT_P`([prop])	Method to calculate and return the temperature derivative of mass Constant-volume heat capacity of the phase at constant pressure.
`dG_dP`()	Method to calculate and return the constant-temperature pressure derivative of Gibbs free energy.
`dG_dP_T`()	Method to calculate and return the constant-temperature pressure derivative of Gibbs free energy.
`dG_dP_V`()	Method to calculate and return the constant-volume pressure derivative of Gibbs free energy.
`dG_dT`()	Method to calculate and return the constant-pressure temperature derivative of Gibbs free energy.
`dG_dT_P`()	Method to calculate and return the constant-pressure temperature derivative of Gibbs free energy.
`dG_dT_V`()	Method to calculate and return the constant-volume temperature derivative of Gibbs free energy.
`dG_dV_P`()	Method to calculate and return the constant-pressure volume derivative of Gibbs free energy.
`dG_dV_T`()	Method to calculate and return the constant-temperature volume derivative of Gibbs free energy.
`dG_mass_dP`([prop])	Method to calculate and return the pressure derivative of mass Gibbs free energy of the phase at constant temperature.
`dG_mass_dP_T`([prop])	Method to calculate and return the pressure derivative of mass Gibbs free energy of the phase at constant temperature.
`dG_mass_dP_V`([prop])	Method to calculate and return the pressure derivative of mass Gibbs free energy of the phase at constant volume.
`dG_mass_dT`([prop])	Method to calculate and return the temperature derivative of mass Gibbs free energy of the phase at constant pressure.
`dG_mass_dT_P`([prop])	Method to calculate and return the temperature derivative of mass Gibbs free energy of the phase at constant pressure.
`dG_mass_dT_V`([prop])	Method to calculate and return the temperature derivative of mass Gibbs free energy of the phase at constant volume.
`dG_mass_dV_P`([prop])	Method to calculate and return the volume derivative of mass Gibbs free energy of the phase at constant pressure.
`dG_mass_dV_T`([prop])	Method to calculate and return the volume derivative of mass Gibbs free energy of the phase at constant temperature.
`dH_dP_T`()	Method to calculate and return the pressure derivative of enthalpy of the phase at constant pressure.
`dH_dT_P`()	Method to calculate and return the temperature derivative of enthalpy of the phase at constant pressure.
`dH_dns`()	Method to calculate and return the mole number derivative of the enthalpy of the phase.
`dH_mass_dP`([prop])	Method to calculate and return the pressure derivative of mass enthalpy of the phase at constant temperature.
`dH_mass_dP_T`([prop])	Method to calculate and return the pressure derivative of mass enthalpy of the phase at constant temperature.
`dH_mass_dP_V`([prop])	Method to calculate and return the pressure derivative of mass enthalpy of the phase at constant volume.
`dH_mass_dT`([prop])	Method to calculate and return the temperature derivative of mass enthalpy of the phase at constant pressure.
`dH_mass_dT_P`([prop])	Method to calculate and return the temperature derivative of mass enthalpy of the phase at constant pressure.
`dH_mass_dT_V`([prop])	Method to calculate and return the temperature derivative of mass enthalpy of the phase at constant volume.
`dH_mass_dV_P`([prop])	Method to calculate and return the volume derivative of mass enthalpy of the phase at constant pressure.
`dH_mass_dV_T`([prop])	Method to calculate and return the volume derivative of mass enthalpy of the phase at constant temperature.
`dP_dP_A`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of pressure of the phase at constant Helmholtz energy.
`dP_dP_G`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of pressure of the phase at constant Gibbs energy.
`dP_dP_H`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of pressure of the phase at constant enthalpy.
`dP_dP_S`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of pressure of the phase at constant entropy.
`dP_dP_T`()	Method to calculate and return the pressure derivative of pressure of the phase at constant temperature.
`dP_dP_U`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of pressure of the phase at constant internal energy.
`dP_dP_V`()	Method to calculate and return the pressure derivative of pressure of the phase at constant volume.
`dP_dT`()	Method to calculate and return the first temperature derivative of pressure of the phase.
`dP_dT_A`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of pressure of the phase at constant Helmholtz energy.
`dP_dT_G`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of pressure of the phase at constant Gibbs energy.
`dP_dT_H`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of pressure of the phase at constant enthalpy.
`dP_dT_P`()	Method to calculate and return the temperature derivative of temperature of the phase at constant pressure.
`dP_dT_S`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of pressure of the phase at constant entropy.
`dP_dT_U`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of pressure of the phase at constant internal energy.
`dP_dV`()	Method to calculate and return the first volume derivative of pressure of the phase.
`dP_dV_A`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of pressure of the phase at constant Helmholtz energy.
`dP_dV_G`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of pressure of the phase at constant Gibbs energy.
`dP_dV_H`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of pressure of the phase at constant enthalpy.
`dP_dV_P`()	Method to calculate and return the volume derivative of pressure of the phase at constant pressure.
`dP_dV_S`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of pressure of the phase at constant entropy.
`dP_dV_U`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of pressure of the phase at constant internal energy.
`dP_drho`()	Method to calculate and return the molar density derivative of pressure of the phase.
`dP_drho_A`([property, differentiate_by, ...])	Method to calculate and return the density derivative of pressure of the phase at constant Helmholtz energy.
`dP_drho_G`([property, differentiate_by, ...])	Method to calculate and return the density derivative of pressure of the phase at constant Gibbs energy.
`dP_drho_H`([property, differentiate_by, ...])	Method to calculate and return the density derivative of pressure of the phase at constant enthalpy.
`dP_drho_S`([property, differentiate_by, ...])	Method to calculate and return the density derivative of pressure of the phase at constant entropy.
`dP_drho_U`([property, differentiate_by, ...])	Method to calculate and return the density derivative of pressure of the phase at constant internal energy.
`dS_dP_T`()	Method to calculate and return the pressure derivative of entropy of the phase at constant pressure.
`dS_dV_P`()	Method to calculate and return the volume derivative of entropy of the phase at constant pressure.
`dS_dV_T`()	Method to calculate and return the volume derivative of entropy of the phase at constant temperature.
`dS_dns`()	Method to calculate and return the mole number derivative of the entropy of the phase.
`dS_mass_dP`([prop])	Method to calculate and return the pressure derivative of mass entropy of the phase at constant temperature.
`dS_mass_dP_T`([prop])	Method to calculate and return the pressure derivative of mass entropy of the phase at constant temperature.
`dS_mass_dP_V`([prop])	Method to calculate and return the pressure derivative of mass entropy of the phase at constant volume.
`dS_mass_dT`([prop])	Method to calculate and return the temperature derivative of mass entropy of the phase at constant pressure.
`dS_mass_dT_P`([prop])	Method to calculate and return the temperature derivative of mass entropy of the phase at constant pressure.
`dS_mass_dT_V`([prop])	Method to calculate and return the temperature derivative of mass entropy of the phase at constant volume.
`dS_mass_dV_P`([prop])	Method to calculate and return the volume derivative of mass entropy of the phase at constant pressure.
`dS_mass_dV_T`([prop])	Method to calculate and return the volume derivative of mass entropy of the phase at constant temperature.
`dT_dP`()	Method to calculate and return the constant-volume pressure derivative of temperature of the phase.
`dT_dP_A`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of temperature of the phase at constant Helmholtz energy.
`dT_dP_G`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of temperature of the phase at constant Gibbs energy.
`dT_dP_H`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of temperature of the phase at constant enthalpy.
`dT_dP_S`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of temperature of the phase at constant entropy.
`dT_dP_T`()	Method to calculate and return the pressure derivative of temperature of the phase at constant temperature.
`dT_dP_U`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of temperature of the phase at constant internal energy.
`dT_dP_V`()	Method to calculate and return the constant-volume pressure derivative of temperature of the phase.
`dT_dT_A`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of temperature of the phase at constant Helmholtz energy.
`dT_dT_G`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of temperature of the phase at constant Gibbs energy.
`dT_dT_H`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of temperature of the phase at constant enthalpy.
`dT_dT_P`()	Method to calculate and return the temperature derivative of temperature of the phase at constant pressure.
`dT_dT_S`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of temperature of the phase at constant entropy.
`dT_dT_U`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of temperature of the phase at constant internal energy.
`dT_dT_V`()	Method to calculate and return the temperature derivative of temperature of the phase at constant volume.
`dT_dV`()	Method to calculate and return the constant-pressure volume derivative of temperature of the phase.
`dT_dV_A`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of temperature of the phase at constant Helmholtz energy.
`dT_dV_G`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of temperature of the phase at constant Gibbs energy.
`dT_dV_H`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of temperature of the phase at constant enthalpy.
`dT_dV_P`()	Method to calculate and return the constant-pressure volume derivative of temperature of the phase.
`dT_dV_S`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of temperature of the phase at constant entropy.
`dT_dV_T`()	Method to calculate and return the volume derivative of temperature of the phase at constant temperature.
`dT_dV_U`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of temperature of the phase at constant internal energy.
`dT_drho`()	Method to calculate and return the molar density derivative of temperature of the phase.
`dT_drho_A`([property, differentiate_by, ...])	Method to calculate and return the density derivative of temperature of the phase at constant Helmholtz energy.
`dT_drho_G`([property, differentiate_by, ...])	Method to calculate and return the density derivative of temperature of the phase at constant Gibbs energy.
`dT_drho_H`([property, differentiate_by, ...])	Method to calculate and return the density derivative of temperature of the phase at constant enthalpy.
`dT_drho_S`([property, differentiate_by, ...])	Method to calculate and return the density derivative of temperature of the phase at constant entropy.
`dT_drho_U`([property, differentiate_by, ...])	Method to calculate and return the density derivative of temperature of the phase at constant internal energy.
`dU_dP`()	Method to calculate and return the constant-temperature pressure derivative of internal energy.
`dU_dP_T`()	Method to calculate and return the constant-temperature pressure derivative of internal energy.
`dU_dP_V`()	Method to calculate and return the constant-volume pressure derivative of internal energy.
`dU_dT`()	Method to calculate and return the constant-pressure temperature derivative of internal energy.
`dU_dT_P`()	Method to calculate and return the constant-pressure temperature derivative of internal energy.
`dU_dT_V`()	Method to calculate and return the constant-volume temperature derivative of internal energy.
`dU_dV_P`()	Method to calculate and return the constant-pressure volume derivative of internal energy.
`dU_dV_T`()	Method to calculate and return the constant-temperature volume derivative of internal energy.
`dU_mass_dP`([prop])	Method to calculate and return the pressure derivative of mass internal energy of the phase at constant temperature.
`dU_mass_dP_T`([prop])	Method to calculate and return the pressure derivative of mass internal energy of the phase at constant temperature.
`dU_mass_dP_V`([prop])	Method to calculate and return the pressure derivative of mass internal energy of the phase at constant volume.
`dU_mass_dT`([prop])	Method to calculate and return the temperature derivative of mass internal energy of the phase at constant pressure.
`dU_mass_dT_P`([prop])	Method to calculate and return the temperature derivative of mass internal energy of the phase at constant pressure.
`dU_mass_dT_V`([prop])	Method to calculate and return the temperature derivative of mass internal energy of the phase at constant volume.
`dU_mass_dV_P`([prop])	Method to calculate and return the volume derivative of mass internal energy of the phase at constant pressure.
`dU_mass_dV_T`([prop])	Method to calculate and return the volume derivative of mass internal energy of the phase at constant temperature.
`dV_dP`()	Method to calculate and return the constant-temperature pressure derivative of volume of the phase.
`dV_dP_A`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of volume of the phase at constant Helmholtz energy.
`dV_dP_G`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of volume of the phase at constant Gibbs energy.
`dV_dP_H`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of volume of the phase at constant enthalpy.
`dV_dP_S`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of volume of the phase at constant entropy.
`dV_dP_T`()	Method to calculate and return the constant-temperature pressure derivative of volume of the phase.
`dV_dP_U`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of volume of the phase at constant internal energy.
`dV_dP_V`()	Method to calculate and return the volume derivative of pressure of the phase at constant volume.
`dV_dT`()	Method to calculate and return the constant-pressure temperature derivative of volume of the phase.
`dV_dT_A`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of volume of the phase at constant Helmholtz energy.
`dV_dT_G`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of volume of the phase at constant Gibbs energy.
`dV_dT_H`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of volume of the phase at constant enthalpy.
`dV_dT_P`()	Method to calculate and return the constant-pressure temperature derivative of volume of the phase.
`dV_dT_S`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of volume of the phase at constant entropy.
`dV_dT_U`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of volume of the phase at constant internal energy.
`dV_dT_V`()	Method to calculate and return the temperature derivative of volume of the phase at constant volume.
`dV_dV_A`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of volume of the phase at constant Helmholtz energy.
`dV_dV_G`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of volume of the phase at constant Gibbs energy.
`dV_dV_H`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of volume of the phase at constant enthalpy.
`dV_dV_P`()	Method to calculate and return the volume derivative of volume of the phase at constant pressure.
`dV_dV_S`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of volume of the phase at constant entropy.
`dV_dV_T`()	Method to calculate and return the volume derivative of volume of the phase at constant temperature.
`dV_dV_U`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of volume of the phase at constant internal energy.
`dV_dns`()	Method to calculate and return the mole number derivatives of the molar volume V of the phase.
`dV_drho_A`([property, differentiate_by, ...])	Method to calculate and return the density derivative of volume of the phase at constant Helmholtz energy.
`dV_drho_G`([property, differentiate_by, ...])	Method to calculate and return the density derivative of volume of the phase at constant Gibbs energy.
`dV_drho_H`([property, differentiate_by, ...])	Method to calculate and return the density derivative of volume of the phase at constant enthalpy.
`dV_drho_S`([property, differentiate_by, ...])	Method to calculate and return the density derivative of volume of the phase at constant entropy.
`dV_drho_U`([property, differentiate_by, ...])	Method to calculate and return the density derivative of volume of the phase at constant internal energy.
`dV_dzs`()	Method to calculate and return the mole fraction derivatives of the molar volume V of the phase.
`dZ_dP`()	Method to calculate and return the pressure derivative of compressibility of the phase.
`dZ_dT`()	Method to calculate and return the temperature derivative of compressibility of the phase.
`dZ_dV`()	Method to calculate and return the volume derivative of compressibility of the phase.
`dZ_dns`()	Method to calculate and return the mole number derivatives of the compressibility factor Z of the phase.
`dZ_dzs`()	Method to calculate and return the mole fraction derivatives of the compressibility factor Z of the phase.
`dfugacities_dP`()	Method to calculate and return the pressure derivative of the fugacities of the components in the phase.
`dfugacities_dT`()	Method to calculate and return the temperature derivative of fugacities of the phase.
`dfugacities_dns`()	Method to calculate and return the mole number derivative of the fugacities of the components in the phase.
`dfugacity_dP`()	Method to calculate and return the pressure derivative of fugacity of the phase; provided the phase is 1 component.
`dfugacity_dT`()	Method to calculate and return the temperature derivative of fugacity of the phase; provided the phase is 1 component.
`disobaric_expansion_dP`()	Method to calculate and return the pressure derivative of isobatic expansion coefficient of the phase.
`disobaric_expansion_dT`()	Method to calculate and return the temperature derivative of isobatic expansion coefficient of the phase.
`disothermal_compressibility_dT`()	Method to calculate and return the temperature derivative of isothermal compressibility of the phase.
`dkappa_dT`()	Method to calculate and return the temperature derivative of isothermal compressibility of the phase.
`dlnfugacities_dns`()	Method to calculate and return the mole number derivative of the log of fugacities of the components in the phase.
`dlnfugacities_dzs`()	Method to calculate and return the mole fraction derivative of the log of fugacities of the components in the phase.
`dlnphis_dP`()	Method to calculate and return the pressure derivative of the log of fugacity coefficients of each component in the phase.
`dlnphis_dT`()	Method to calculate and return the temperature derivative of the log of fugacity coefficients of each component in the phase.
`dnV_dns`()	Method to calculate and return the partial mole number derivatives of the molar volume V of the phase.
`dphis_dP`()	Method to calculate and return the pressure derivative of fugacity coefficients of the phase.
`dphis_dT`()	Method to calculate and return the temperature derivative of fugacity coefficients of the phase.
`dphis_dzs`()	Method to calculate and return the molar composition derivative of fugacity coefficients of the phase.
`drho_dP`()	Method to calculate and return the pressure derivative of molar density of the phase.
`drho_dP_A`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of density of the phase at constant Helmholtz energy.
`drho_dP_G`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of density of the phase at constant Gibbs energy.
`drho_dP_H`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of density of the phase at constant enthalpy.
`drho_dP_S`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of density of the phase at constant entropy.
`drho_dP_U`([property, differentiate_by, ...])	Method to calculate and return the pressure derivative of density of the phase at constant internal energy.
`drho_dT`()	Method to calculate and return the temperature derivative of molar density of the phase.
`drho_dT_A`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of density of the phase at constant Helmholtz energy.
`drho_dT_G`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of density of the phase at constant Gibbs energy.
`drho_dT_H`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of density of the phase at constant enthalpy.
`drho_dT_S`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of density of the phase at constant entropy.
`drho_dT_U`([property, differentiate_by, ...])	Method to calculate and return the temperature derivative of density of the phase at constant internal energy.
`drho_dT_V`()	Method to calculate and return the temperature derivative of molar density of the phase at constant volume.
`drho_dV_A`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of density of the phase at constant Helmholtz energy.
`drho_dV_G`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of density of the phase at constant Gibbs energy.
`drho_dV_H`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of density of the phase at constant enthalpy.
`drho_dV_S`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of density of the phase at constant entropy.
`drho_dV_T`()	Method to calculate and return the volume derivative of molar density of the phase.
`drho_dV_U`([property, differentiate_by, ...])	Method to calculate and return the volume derivative of density of the phase at constant internal energy.
`drho_drho_A`([property, differentiate_by, ...])	Method to calculate and return the density derivative of density of the phase at constant Helmholtz energy.
`drho_drho_G`([property, differentiate_by, ...])	Method to calculate and return the density derivative of density of the phase at constant Gibbs energy.
`drho_drho_H`([property, differentiate_by, ...])	Method to calculate and return the density derivative of density of the phase at constant enthalpy.
`drho_drho_S`([property, differentiate_by, ...])	Method to calculate and return the density derivative of density of the phase at constant entropy.
`drho_drho_U`([property, differentiate_by, ...])	Method to calculate and return the density derivative of density of the phase at constant internal energy.
`drho_mass_dP`()	Method to calculate the mass density derivative with respect to pressure, at constant temperature.
`drho_mass_dT`()	Method to calculate the mass density derivative with respect to temperature, at constant pressure.
`dspeed_of_sound_dP_T`()	Method to calculate the pressure derivative of speed of sound at constant temperature in molar units.
`dspeed_of_sound_dT_P`()	Method to calculate the temperature derivative of speed of sound at constant pressure in molar units.
`from_json`(json_repr)	Method to create a phase from a JSON serialization of another phase.
`fugacities`()	Method to calculate and return the fugacities of the phase.
`fugacities_at_zs`(zs[, most_stable])	Method to directly calculate the figacities at a different composition than the current phase.
`fugacities_lowest_Gibbs`()	Method to calculate and return the fugacities of the phase.
`fugacity`()	Method to calculate and return the fugacity of the phase; provided the phase is 1 component.
`gammas`()	Method to calculate and return the activity coefficients of the phase, [-].
`gammas_infinite_dilution`()	Calculate and return the infinite dilution activity coefficients of each component.
`helium_molar_weight`()	Method to calculate and return the effective quantiy of helium in the phase as a molar weight, [g/mol].
`helium_partial_pressure`()	Method to calculate and return the ideal partial pressure of helium, [Pa]
`humidity_ratio`()	Method to calculate and return the humidity ratio of the phase; normally defined as the kg water/kg dry air, the definition here is kg water/(kg rest of the phase) [-]
`hydrogen_molar_weight`()	Method to calculate and return the effective quantiy of hydrogen in the phase as a molar weight, [g/mol].
`hydrogen_partial_pressure`()	Method to calculate and return the ideal partial pressure of hydrogen, [Pa]
`hydrogen_sulfide_molar_weight`()	Method to calculate and return the effective quantiy of hydrogen_sulfide in the phase as a molar weight, [g/mol].
`hydrogen_sulfide_partial_pressure`()	Method to calculate and return the ideal partial pressure of hydrogen_sulfide, [Pa]
`is_same_model`(other_phase[, ignore_phase])	Method to check whether or not a model is the exact same as another.
`isentropic_exponent`()	Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $PV^k = \text{const}$ .
`isentropic_exponent_PT`()	Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $P^{(1-k)}T^k = \text{const}$ .
`isentropic_exponent_PV`()	Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $PV^k = \text{const}$ .
`isentropic_exponent_TV`()	Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $TV^{k-1} = \text{const}$ .
`isobaric_expansion`()	Method to calculate and return the isobatic expansion coefficient of the phase.
`isothermal_bulk_modulus`()	Method to calculate and return the isothermal bulk modulus of the phase.
`isothermal_compressibility`()	Method to calculate and return the isothermal compressibility of the phase.
`kappa`()	Method to calculate and return the isothermal compressibility of the phase.
`kgs`()	Method to calculate and return the pure-component gas temperature-dependent thermal conductivity of each species from the `thermo.thermal_conductivity.ThermalConductivityGas` objects.
`kinematic_viscosity`()	Method to calculate and return the kinematic viscosity of the phase, [m^2/s]
`kls`()	Method to calculate and return the pure-component liquid temperature-dependent thermal conductivity of each species from the `thermo.thermal_conductivity.ThermalConductivityLiquid` objects.
`lnfugacities`()	Method to calculate and return the log of fugacities of the phase.
`lnphi`()	Method to calculate and return the log of fugacity coefficient of the phase; provided the phase is 1 component.
`lnphis`()	Method to calculate and return the log of fugacity coefficients of each component in the phase.
`lnphis_G_min`()	Method to calculate and return the log fugacity coefficients of the phase.
`lnphis_at_zs`(zs[, most_stable])	Method to directly calculate the log fugacity coefficients at a different composition than the current phase.
`log_zs`()	Method to calculate and return the log of mole fractions specified.
`methane_molar_weight`()	Method to calculate and return the effective quantiy of methane in the phase as a molar weight, [g/mol].
`methane_partial_pressure`()	Method to calculate and return the ideal partial pressure of methane, [Pa]
`model_hash`([ignore_phase])	Method to compute a hash of a phase.
`mu`()
`mugs`()	Method to calculate and return the pure-component gas temperature-dependent viscosity of each species from the `thermo.viscosity.ViscosityGas` objects.
`muls`()	Method to calculate and return the pure-component liquid temperature-dependent viscosity of each species from the `thermo.viscosity.ViscosityLiquid` objects.
`nitrogen_molar_weight`()	Method to calculate and return the effective quantiy of nitrogen in the phase as a molar weight, [g/mol].
`nitrogen_partial_pressure`()	Method to calculate and return the ideal partial pressure of nitrogen, [Pa]
`nu`()	Method to calculate and return the kinematic viscosity of the phase, [m^2/s]
`oxygen_molar_weight`()	Method to calculate and return the effective quantiy of oxygen in the phase as a molar weight, [g/mol].
`oxygen_partial_pressure`()	Method to calculate and return the ideal partial pressure of oxygen, [Pa]
`partial_pressures`()	Method to return the partial pressures of each component in the phase.
`phi`()	Method to calculate and return the fugacity coefficient of the phase; provided the phase is 1 component.
`phis`()	Method to calculate and return the fugacity coefficients of the phase.
`pseudo_Pc`()	Method to calculate and return the pseudocritical pressure calculated using Kay's rule (linear mole fractions):
`pseudo_Tc`()	Method to calculate and return the pseudocritical temperature calculated using Kay's rule (linear mole fractions):
`pseudo_Vc`()	Method to calculate and return the pseudocritical volume calculated using Kay's rule (linear mole fractions):
`pseudo_Zc`()	Method to calculate and return the pseudocritical compressibility calculated using Kay's rule (linear mole fractions):
`pseudo_omega`()	Method to calculate and return the pseudocritical acentric factor calculated using Kay's rule (linear mole fractions):
`rho`()	Method to calculate and return the molar density of the phase.
`rho_gas`()	Method to calculate and return the ideal-gas molar density of the phase at the chosen reference temperature and pressure, according to the temperature variable T_gas_ref and pressure variable P_gas_ref of the `thermo.bulk.BulkSettings`.
`rho_gas_normal`()	Method to calculate and return the ideal-gas molar density of the phase at the normal temperature and pressure, according to the temperature variable T_normal and pressure variable P_normal of the `thermo.bulk.BulkSettings`.
`rho_gas_standard`()	Method to calculate and return the ideal-gas molar density of the phase at the standard temperature and pressure, according to the temperature variable T_standard and pressure variable P_standard of the `thermo.bulk.BulkSettings`.
`rho_mass`()	Method to calculate and return mass density of the phase.
`rho_mass_gas`()	Method to calculate and return the ideal-gas mass density of the phase at the chosen reference temperature and pressure, according to the temperature variable T_gas_ref and pressure variable P_gas_ref of the `thermo.bulk.BulkSettings`.
`rho_mass_gas_normal`()	Method to calculate and return the ideal-gas mass density of the phase at the normal temperature and pressure, according to the temperature variable T_normal and pressure variable P_normal of the `thermo.bulk.BulkSettings`.
`rho_mass_gas_standard`()	Method to calculate and return the ideal-gas mass density of the phase at the standard temperature and pressure, according to the temperature variable T_standard and pressure variable P_standard of the `thermo.bulk.BulkSettings`.
`rho_mass_liquid_ref`()	Method to calculate and return the liquid reference mass density according to the temperature variable T_liquid_volume_ref of `thermo.bulk.BulkSettings` and the composition of the phase.
`sigma`()	Calculate and return the surface tension of the phase.
`sigmas`()	Method to calculate and return the pure-component surface tensions of each species from the `thermo.interface.SurfaceTension` objects.
`speed_of_sound`()	Method to calculate and return the molar speed of sound of the phase.
`speed_of_sound_ideal_gas`()	Method to calculate and return the molar speed of sound of an ideal gas phase at the current conditions.
`speed_of_sound_ideal_gas_mass`()	Method to calculate and return the mass speed of sound of an ideal gas phase at the current conditions.
`speed_of_sound_mass`()	Method to calculate and return the speed of sound of the phase.
`state_hash`()	Basic method to calculate a hash of the state of the phase and its model parameters.
`thermal_diffusivity`()	Method to calculate and return the thermal diffusivity of the phase.
`to`(zs[, T, P, V])	Method to create a new Phase object with the same constants as the existing Phase but at different conditions.
`to_TP_zs`(T, P, zs)	Method to create a new Phase object with the same constants as the existing Phase but at a different T and P.
`value`(name)	Method to retrieve a property from a string.
`water_molar_weight`()	Method to calculate and return the effective quantiy of water in the phase as a molar weight, [g/mol].
`water_partial_pressure`()	Method to calculate and return the ideal partial pressure of water, [Pa]
`ws`()	Method to calculate and return the mass fractions of the phase, [-]
`ws_no_water`()	Method to calculate and return the mass fractions of all species in the phase, normalized to a water-free basis (the mass fraction of water returned is zero).
`zs_no_water`()	Method to calculate and return the mole fractions of all species in the phase, normalized to a water-free basis (the mole fraction of water returned is zero).

G_ideal_gas_standard_state
Gs_ideal_gas_standard_state
H_ideal_gas_standard_state
Hs_ideal_gas_standard_state
S_ideal_gas_standard_state
Ss_ideal_gas_standard_state
as_EquilibriumState
as_EquilibriumStream
d2G_mass_dP2
d2G_mass_dPdT
d2G_mass_dT2
d2G_mass_dTdP
lnphis_lowest_Gibbs
molar_water_content

A()[source]¶

Method to calculate and return the Helmholtz energy of the phase.

A = U - TS

Returns

Afloat: Helmholtz energy, [J/mol]

API()¶

Method to calculate and return the API of the phase.

\text{API gravity} = \frac{141.5}{\text{SG}} - 131.5

Returns

APIfloat: API of the fluid [-]

A_dep()[source]¶

Method to calculate and return the departure Helmholtz energy of the phase.

A_{dep} = U_{dep} - TS_{dep}

Returns

A_depfloat: Departure Helmholtz energy, [J/mol]

A_dep_flow()¶

Method to return the flow rate of the difference between the ideal-gas Helmholtz energy of this phase and the Helmholtz energy of the phase This method is only available when the phase is linked to an EquilibriumStream.

Returns

A_dep_flowfloat: Flow rate of departure Helmholtz energy, [J/s]

A_dep_mass()[source]¶

Method to calculate and return the departure mass Helmholtz energy of the phase.

Returns

A_dep_massfloat: Departure mass Helmholtz energy, [J/kg]

A_flow()¶

Method to return the flow rate of Helmholtz energy of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

A_flowfloat: Flow rate of Helmholtz energy, [J/s]

A_formation_ideal_gas()[source]¶

Method to calculate and return the ideal-gas Helmholtz energy of formation of the phase (as if the phase was an ideal gas).

A_{formation}^{ig} = U_{formation}^{ig} - T_{ref}^{ig} S_{formation}^{ig}

Returns

A_formation_ideal_gasfloat: Helmholtz energy of formation of the phase on a formation basis as an ideal gas, [J/(mol)]

A_formation_ideal_gas_mass()[source]¶

Method to calculate and return the ideal-gas formation mass Helmholtz energy of the phase.

Returns

A_formation_ideal_gas_massfloat: Formation mass Helmholtz energy, [J/kg]

A_ideal_gas()[source]¶

Method to calculate and return the ideal-gas Helmholtz energy of the phase.

A^{ig} = U^{ig} - T S^{ig}

Returns

A_ideal_gasfloat: Ideal gas Helmholtz free energy, [J/(mol)]

A_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas Helmholtz energy of the phase.

Returns

A_ideal_gas_massfloat: Ideal gas mass Helmholtz free energy, [J/(kg)]

A_mass()[source]¶

Method to calculate and return mass Helmholtz energy of the phase.

A_{mass} = \frac{1000 A_{molar}}{MW}

Returns

A_massfloat: Mass Helmholtz energy, [J/(kg)]

A_reactive()[source]¶

Method to calculate and return the Helmholtz free energy of the phase on a reactive basis.

A_{reactive} = U_{reactive} - TS_{reactive}

Returns

A_reactivefloat: Helmholtz free energy of the phase on a reactive basis, [J/(mol)]

A_reactive_mass()[source]¶

Method to calculate and return mass Helmholtz energy on a reactive basis of the phase.

A_{reactive,mass} = \frac{1000 A_{reactive, molar}}{MW}

Returns

A_reactive_massfloat: Mass Helmholtz energy on a reactive basis, [J/kg]

Actinium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Actinium, [atoms/s]

Actinium_atom_flow()¶: Method to calculate and return the mole flow that is Actinium, [mol/s]

Actinium_atom_fraction()¶: Method to calculate and return the mole fraction that is Actinium element, [-]

Actinium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Actinium element, [kg/s]

Actinium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Actinium element, [-]

Aluminium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Aluminium, [atoms/s]

Aluminium_atom_flow()¶: Method to calculate and return the mole flow that is Aluminium, [mol/s]

Aluminium_atom_fraction()¶: Method to calculate and return the mole fraction that is Aluminium element, [-]

Aluminium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Aluminium element, [kg/s]

Aluminium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Aluminium element, [-]

Americium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Americium, [atoms/s]

Americium_atom_flow()¶: Method to calculate and return the mole flow that is Americium, [mol/s]

Americium_atom_fraction()¶: Method to calculate and return the mole fraction that is Americium element, [-]

Americium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Americium element, [kg/s]

Americium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Americium element, [-]

Antimony_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Antimony, [atoms/s]

Antimony_atom_flow()¶: Method to calculate and return the mole flow that is Antimony, [mol/s]

Antimony_atom_fraction()¶: Method to calculate and return the mole fraction that is Antimony element, [-]

Antimony_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Antimony element, [kg/s]

Antimony_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Antimony element, [-]

Argon_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Argon, [atoms/s]

Argon_atom_flow()¶: Method to calculate and return the mole flow that is Argon, [mol/s]

Argon_atom_fraction()¶: Method to calculate and return the mole fraction that is Argon element, [-]

Argon_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Argon element, [kg/s]

Argon_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Argon element, [-]

Arsenic_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Arsenic, [atoms/s]

Arsenic_atom_flow()¶: Method to calculate and return the mole flow that is Arsenic, [mol/s]

Arsenic_atom_fraction()¶: Method to calculate and return the mole fraction that is Arsenic element, [-]

Arsenic_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Arsenic element, [kg/s]

Arsenic_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Arsenic element, [-]

Astatine_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Astatine, [atoms/s]

Astatine_atom_flow()¶: Method to calculate and return the mole flow that is Astatine, [mol/s]

Astatine_atom_fraction()¶: Method to calculate and return the mole fraction that is Astatine element, [-]

Astatine_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Astatine element, [kg/s]

Astatine_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Astatine element, [-]

Barium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Barium, [atoms/s]

Barium_atom_flow()¶: Method to calculate and return the mole flow that is Barium, [mol/s]

Barium_atom_fraction()¶: Method to calculate and return the mole fraction that is Barium element, [-]

Barium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Barium element, [kg/s]

Barium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Barium element, [-]

Berkelium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Berkelium, [atoms/s]

Berkelium_atom_flow()¶: Method to calculate and return the mole flow that is Berkelium, [mol/s]

Berkelium_atom_fraction()¶: Method to calculate and return the mole fraction that is Berkelium element, [-]

Berkelium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Berkelium element, [kg/s]

Berkelium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Berkelium element, [-]

Beryllium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Beryllium, [atoms/s]

Beryllium_atom_flow()¶: Method to calculate and return the mole flow that is Beryllium, [mol/s]

Beryllium_atom_fraction()¶: Method to calculate and return the mole fraction that is Beryllium element, [-]

Beryllium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Beryllium element, [kg/s]

Beryllium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Beryllium element, [-]

Bismuth_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Bismuth, [atoms/s]

Bismuth_atom_flow()¶: Method to calculate and return the mole flow that is Bismuth, [mol/s]

Bismuth_atom_fraction()¶: Method to calculate and return the mole fraction that is Bismuth element, [-]

Bismuth_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Bismuth element, [kg/s]

Bismuth_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Bismuth element, [-]

Bohrium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Bohrium, [atoms/s]

Bohrium_atom_flow()¶: Method to calculate and return the mole flow that is Bohrium, [mol/s]

Bohrium_atom_fraction()¶: Method to calculate and return the mole fraction that is Bohrium element, [-]

Bohrium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Bohrium element, [kg/s]

Bohrium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Bohrium element, [-]

Boron_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Boron, [atoms/s]

Boron_atom_flow()¶: Method to calculate and return the mole flow that is Boron, [mol/s]

Boron_atom_fraction()¶: Method to calculate and return the mole fraction that is Boron element, [-]

Boron_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Boron element, [kg/s]

Boron_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Boron element, [-]

Bromine_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Bromine, [atoms/s]

Bromine_atom_flow()¶: Method to calculate and return the mole flow that is Bromine, [mol/s]

Bromine_atom_fraction()¶: Method to calculate and return the mole fraction that is Bromine element, [-]

Bromine_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Bromine element, [kg/s]

Bromine_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Bromine element, [-]

Bvirial()[source]¶

Method to calculate and return the B virial coefficient of the phase at its current conditions.

Returns

Bvirialfloat: Virial coefficient, [m^3/mol]

property CASs¶

CAS registration numbers for each component, [-].

Returns

CASslist[str]: CAS registration numbers for each component, [-].

Cadmium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Cadmium, [atoms/s]

Cadmium_atom_flow()¶: Method to calculate and return the mole flow that is Cadmium, [mol/s]

Cadmium_atom_fraction()¶: Method to calculate and return the mole fraction that is Cadmium element, [-]

Cadmium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Cadmium element, [kg/s]

Cadmium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Cadmium element, [-]

Caesium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Caesium, [atoms/s]

Caesium_atom_flow()¶: Method to calculate and return the mole flow that is Caesium, [mol/s]

Caesium_atom_fraction()¶: Method to calculate and return the mole fraction that is Caesium element, [-]

Caesium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Caesium element, [kg/s]

Caesium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Caesium element, [-]

Calcium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Calcium, [atoms/s]

Calcium_atom_flow()¶: Method to calculate and return the mole flow that is Calcium, [mol/s]

Calcium_atom_fraction()¶: Method to calculate and return the mole fraction that is Calcium element, [-]

Calcium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Calcium element, [kg/s]

Calcium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Calcium element, [-]

Californium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Californium, [atoms/s]

Californium_atom_flow()¶: Method to calculate and return the mole flow that is Californium, [mol/s]

Californium_atom_fraction()¶: Method to calculate and return the mole fraction that is Californium element, [-]

Californium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Californium element, [kg/s]

Californium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Californium element, [-]

Carbon_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Carbon, [atoms/s]

Carbon_atom_flow()¶: Method to calculate and return the mole flow that is Carbon, [mol/s]

Carbon_atom_fraction()¶: Method to calculate and return the mole fraction that is Carbon element, [-]

Carbon_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Carbon element, [kg/s]

Carbon_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Carbon element, [-]

property Carcinogens¶

Status of each component in cancer causing registries, [-].

Returns

Carcinogenslist[dict]: Status of each component in cancer causing registries, [-].

property Ceilings¶

Ceiling exposure limits to chemicals (and their units; ppm or mg/m^3), [various].

Returns

Ceilingslist[tuple[(float, str)]]: Ceiling exposure limits to chemicals (and their units; ppm or mg/m^3), [various].

Cerium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Cerium, [atoms/s]

Cerium_atom_flow()¶: Method to calculate and return the mole flow that is Cerium, [mol/s]

Cerium_atom_fraction()¶: Method to calculate and return the mole fraction that is Cerium element, [-]

Cerium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Cerium element, [kg/s]

Cerium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Cerium element, [-]

Chlorine_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Chlorine, [atoms/s]

Chlorine_atom_flow()¶: Method to calculate and return the mole flow that is Chlorine, [mol/s]

Chlorine_atom_fraction()¶: Method to calculate and return the mole fraction that is Chlorine element, [-]

Chlorine_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Chlorine element, [kg/s]

Chlorine_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Chlorine element, [-]

Chromium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Chromium, [atoms/s]

Chromium_atom_flow()¶: Method to calculate and return the mole flow that is Chromium, [mol/s]

Chromium_atom_fraction()¶: Method to calculate and return the mole fraction that is Chromium element, [-]

Chromium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Chromium element, [kg/s]

Chromium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Chromium element, [-]

Cobalt_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Cobalt, [atoms/s]

Cobalt_atom_flow()¶: Method to calculate and return the mole flow that is Cobalt, [mol/s]

Cobalt_atom_fraction()¶: Method to calculate and return the mole fraction that is Cobalt element, [-]

Cobalt_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Cobalt element, [kg/s]

Cobalt_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Cobalt element, [-]

Copernicium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Copernicium, [atoms/s]

Copernicium_atom_flow()¶: Method to calculate and return the mole flow that is Copernicium, [mol/s]

Copernicium_atom_fraction()¶: Method to calculate and return the mole fraction that is Copernicium element, [-]

Copernicium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Copernicium element, [kg/s]

Copernicium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Copernicium element, [-]

Copper_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Copper, [atoms/s]

Copper_atom_flow()¶: Method to calculate and return the mole flow that is Copper, [mol/s]

Copper_atom_fraction()¶: Method to calculate and return the mole fraction that is Copper element, [-]

Copper_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Copper element, [kg/s]

Copper_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Copper element, [-]

Cp()[source]¶

Method to calculate and return the constant-pressure heat capacity of the phase.

Returns

Cpfloat: Molar heat capacity, [J/(mol*K)]

Cp_Cv_ratio()[source]¶

Method to calculate and return the Cp/Cv ratio of the phase.

\frac{C_p}{C_v}

Returns

Cp_Cv_ratiofloat: Cp/Cv ratio, [-]

Cp_Cv_ratio_ideal_gas()[source]¶

Method to calculate and return the ratio of the ideal-gas heat capacity to its constant-volume heat capacity.

\frac{C_p^{ig}}{C_v^{ig}}

Returns

Cp_Cv_ratio_ideal_gasfloat: Cp/Cv for the phase as an ideal gas, [-]

Cp_dep_mass()[source]¶

Method to calculate and return mass constant pressure departure heat capacity of the phase.

Cp_{dep, mass} = \frac{1000 Cp_{dep, molar}}{MW}

Returns

Cp_dep_massfloat: Mass departure heat capacity, [J/(kg*K)]

Cp_ideal_gas()[source]¶

Method to calculate and return the ideal-gas heat capacity of the phase.

C_p^{ig} = \sum_i z_i {C_{p,i}^{ig}}

Returns

Cpfloat: Ideal gas heat capacity, [J/(mol*K)]

Cp_ideal_gas_mass()[source]¶

Method to calculate and return mass constant pressure departure heat capacity of the phase.

Cp_{ideal, mass} = \frac{1000 Cp_{ideal, molar}}{MW}

Returns

Cp_ideal_gas_massfloat: Mass departure heat capacity, [J/(kg*K)]

Cp_mass()[source]¶

Method to calculate and return mass constant pressure heat capacity of the phase.

Cp_{mass} = \frac{1000 Cp_{molar}}{MW}

Returns

Cp_massfloat: Mass heat capacity, [J/(kg*K)]

Cpgs()¶

Method to calculate and return the pure-component ideal gas heat capacities of each species from the thermo.heat_capacity.HeatCapacityGas objects.

Returns

Cpgslist[float]: Ideal gas pure component heat capacities, [J/(mol*K)]

Cpgs_poly_fit = False¶

Cpig_integrals_over_T_pure()[source]¶

Method to calculate and return the integrals of the ideal-gas heat capacities divided by temperature of every component in the phase from a temperature of Phase.T_REF_IG to the system temperature. This method is powered by the HeatCapacityGases objects, except when all components have the same heat capacity form and a fast implementation has been written for it (currently only polynomials).

\Delta S^{ig} = \int^T_{T_{ref}} \frac{C_p^{ig}}{T} dT

Returns

dS_iglist[float]: Integrals of ideal gas heat capacity over temperature from the reference temperature to the system temperature, [J/(mol)]

Cpig_integrals_pure()[source]¶

Method to calculate and return the integrals of the ideal-gas heat capacities of every component in the phase from a temperature of Phase.T_REF_IG to the system temperature. This method is powered by the HeatCapacityGases objects, except when all components have the same heat capacity form and a fast implementation has been written for it (currently only polynomials).

\Delta H^{ig} = \int^T_{T_{ref}} C_p^{ig} dT

Returns

dH_iglist[float]: Integrals of ideal gas heat capacity from the reference temperature to the system temperature, [J/(mol)]

Cpigs_pure()[source]¶

Method to calculate and return the ideal-gas heat capacities of every component in the phase. This method is powered by the HeatCapacityGases objects, except when all components have the same heat capacity form and a fast implementation has been written for it (currently only polynomials).

Returns

Cp_iglist[float]: Molar ideal gas heat capacities, [J/(mol*K)]

Cpls()¶

Method to calculate and return the pure-component liquid temperature-dependent heat capacities of each species from the thermo.heat_capacity.HeatCapacityLiquid objects.

Note that some correlation methods for liquid heat capacity are at low pressure, and others are along the saturation line. There is a large difference in values.

Returns

Cplslist[float]: Pure component liquid heat capacities, [J/(mol*K)]

Cpss()¶

Method to calculate and return the pure-component solid heat capacities of each species from the thermo.heat_capacity.HeatCapacitySolid objects.

Returns

Cpsslist[float]: Pure component solid heat capacities, [J/(mol*K)]

Curium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Curium, [atoms/s]

Curium_atom_flow()¶: Method to calculate and return the mole flow that is Curium, [mol/s]

Curium_atom_fraction()¶: Method to calculate and return the mole fraction that is Curium element, [-]

Curium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Curium element, [kg/s]

Curium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Curium element, [-]

Cv()[source]¶

Method to calculate and return the constant-volume heat capacity Cv of the phase.

C_v = T\left(\frac{\partial P}{\partial T}\right)_V^2/ \left(\frac{\partial P}{\partial V}\right)_T + Cp

Returns

Cvfloat: Constant volume molar heat capacity, [J/(mol*K)]

Cv_dep()[source]¶

Method to calculate and return the difference between the actual Cv and the ideal-gas constant volume heat capacity $C_v^{ig}$ of the phase.

C_v^{dep} = C_v - C_v^{ig}

Returns

Cv_depfloat: Departure ideal gas constant volume heat capacity, [J/(mol*K)]

Cv_dep_mass()[source]¶

Method to calculate and return mass constant pressure departure heat capacity of the phase.

Cv_{dep, mass} = \frac{1000 Cv_{dep, molar}}{MW}

Returns

Cv_dep_massfloat: Mass departure heat capacity, [J/(kg*K)]

Cv_ideal_gas()[source]¶

Method to calculate and return the ideal-gas constant volume heat capacity of the phase.

C_v^{ig} = \sum_i z_i {C_{p,i}^{ig}} - R

Returns

Cvfloat: Ideal gas constant volume heat capacity, [J/(mol*K)]

Cv_mass()[source]¶

Method to calculate and return mass constant volume heat capacity of the phase.

Cv_{mass} = \frac{1000 Cv_{molar}}{MW}

Returns

Cv_massfloat: Mass constant volume heat capacity, [J/(kg*K)]

Darmstadtium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Darmstadtium, [atoms/s]

Darmstadtium_atom_flow()¶: Method to calculate and return the mole flow that is Darmstadtium, [mol/s]

Darmstadtium_atom_fraction()¶: Method to calculate and return the mole fraction that is Darmstadtium element, [-]

Darmstadtium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Darmstadtium element, [kg/s]

Darmstadtium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Darmstadtium element, [-]

Dubnium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Dubnium, [atoms/s]

Dubnium_atom_flow()¶: Method to calculate and return the mole flow that is Dubnium, [mol/s]

Dubnium_atom_fraction()¶: Method to calculate and return the mole fraction that is Dubnium element, [-]

Dubnium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Dubnium element, [kg/s]

Dubnium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Dubnium element, [-]

Dysprosium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Dysprosium, [atoms/s]

Dysprosium_atom_flow()¶: Method to calculate and return the mole flow that is Dysprosium, [mol/s]

Dysprosium_atom_fraction()¶: Method to calculate and return the mole fraction that is Dysprosium element, [-]

Dysprosium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Dysprosium element, [kg/s]

Dysprosium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Dysprosium element, [-]

Einsteinium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Einsteinium, [atoms/s]

Einsteinium_atom_flow()¶: Method to calculate and return the mole flow that is Einsteinium, [mol/s]

Einsteinium_atom_fraction()¶: Method to calculate and return the mole fraction that is Einsteinium element, [-]

Einsteinium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Einsteinium element, [kg/s]

Einsteinium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Einsteinium element, [-]

Erbium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Erbium, [atoms/s]

Erbium_atom_flow()¶: Method to calculate and return the mole flow that is Erbium, [mol/s]

Erbium_atom_fraction()¶: Method to calculate and return the mole fraction that is Erbium element, [-]

Erbium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Erbium element, [kg/s]

Erbium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Erbium element, [-]

Europium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Europium, [atoms/s]

Europium_atom_flow()¶: Method to calculate and return the mole flow that is Europium, [mol/s]

Europium_atom_fraction()¶: Method to calculate and return the mole fraction that is Europium element, [-]

Europium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Europium element, [kg/s]

Europium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Europium element, [-]

Fermium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Fermium, [atoms/s]

Fermium_atom_flow()¶: Method to calculate and return the mole flow that is Fermium, [mol/s]

Fermium_atom_fraction()¶: Method to calculate and return the mole fraction that is Fermium element, [-]

Fermium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Fermium element, [kg/s]

Fermium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Fermium element, [-]

Flerovium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Flerovium, [atoms/s]

Flerovium_atom_flow()¶: Method to calculate and return the mole flow that is Flerovium, [mol/s]

Flerovium_atom_fraction()¶: Method to calculate and return the mole fraction that is Flerovium element, [-]

Flerovium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Flerovium element, [kg/s]

Flerovium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Flerovium element, [-]

Fluorine_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Fluorine, [atoms/s]

Fluorine_atom_flow()¶: Method to calculate and return the mole flow that is Fluorine, [mol/s]

Fluorine_atom_fraction()¶: Method to calculate and return the mole fraction that is Fluorine element, [-]

Fluorine_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Fluorine element, [kg/s]

Fluorine_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Fluorine element, [-]

Francium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Francium, [atoms/s]

Francium_atom_flow()¶: Method to calculate and return the mole flow that is Francium, [mol/s]

Francium_atom_fraction()¶: Method to calculate and return the mole fraction that is Francium element, [-]

Francium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Francium element, [kg/s]

Francium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Francium element, [-]

G()[source]¶

Method to calculate and return the Gibbs free energy of the phase.

G = H - TS

Returns

Gfloat: Gibbs free energy, [J/mol]

property GWPs¶

Global Warming Potentials for each component (impact/mass chemical)/(impact/mass CO2), [-].

Returns

GWPslist[float]: Global Warming Potentials for each component (impact/mass chemical)/(impact/mass CO2), [-].

G_dep()[source]¶

Method to calculate and return the departure Gibbs free energy of the phase.

G_{dep} = H_{dep} - TS_{dep}

Returns

G_depfloat: Departure Gibbs free energy, [J/mol]

G_dep_flow()¶

Method to return the flow rate of the difference between the ideal-gas Gibbs free energy of this phase and the actual Gibbs free energy of the phase This method is only available when the phase is linked to an EquilibriumStream.

Returns

G_dep_flowfloat: Flow rate of departure Gibbs energy, [J/s]

G_dep_mass()[source]¶

Method to calculate and return the mass departure Gibbs free energy of the phase.

Returns

G_dep_massfloat: Departure mass Gibbs free energy, [J/kg]

G_dep_phi_consistency()[source]¶

Method to calculate and return a consistency check between departure Gibbs free energy, and the fugacity coefficients.

G^{\text{from phi}}_{dep} = RT\sum_i z_i \phi_i

Returns

errorfloat: Relative consistency error $|1 - G^{\text{from phi}}_{dep}/G^\text{implemented}_{dep}|$ , [-]

G_flow()¶

Method to return the flow rate of Gibbs free energy of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

G_flowfloat: Flow rate of Gibbs energy, [J/s]

G_formation_ideal_gas()[source]¶

Method to calculate and return the ideal-gas Gibbs free energy of formation of the phase (as if the phase was an ideal gas).

G_{formation}^{ig} = H_{formation}^{ig} - T_{ref}^{ig} S_{formation}^{ig}

Returns

G_formation_ideal_gasfloat: Gibbs free energy of formation of the phase on a formation basis as an ideal gas, [J/(mol)]

G_formation_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas formation Gibbs free energy of the phase.

Returns

G_formation_ideal_gas_massfloat: Formation mass Gibbs free energy, [J/kg]

G_ideal_gas()[source]¶

Method to calculate and return the ideal-gas Gibbs free energy of the phase.

G^{ig} = H^{ig} - T S^{ig}

Returns

G_ideal_gasfloat: Ideal gas free energy, [J/(mol)]

G_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas Gibbs free energy of the phase.

Returns

G_ideal_gas_massfloat: Ideal gas mass free energy, [J/(kg)]

G_ideal_gas_standard_state()[source]¶

G_mass()[source]¶

Method to calculate and return mass Gibbs energy of the phase.

G_{mass} = \frac{1000 G_{molar}}{MW}

Returns

G_massfloat: Mass Gibbs energy, [J/(kg)]

G_min()¶

Method to calculate and return the Gibbs free energy of the phase.

G = H - TS

Returns

Gfloat: Gibbs free energy, [J/mol]

G_min_criteria()[source]¶

Method to calculate and return the Gibbs energy criteria required for comparing phase stability. This calculation can be faster than calculating the full Gibbs energy. For this comparison to work, all phases must use the ideal gas basis.

G^{\text{criteria}} = G^{dep} + RT\sum_i z_i \ln z_i

Returns

G_critfloat: Gibbs free energy like criteria [J/mol]

G_reactive()[source]¶

Method to calculate and return the Gibbs free energy of the phase on a reactive basis.

G_{reactive} = H_{reactive} - TS_{reactive}

Returns

G_reactivefloat: Gibbs free energy of the phase on a reactive basis, [J/(mol)]

G_reactive_mass()[source]¶

Method to calculate and return mass Gibbs free energy on a reactive basis of the phase.

G_{reactive,mass} = \frac{1000 G_{reactive, molar}}{MW}

Returns

G_reactive_massfloat: Gibbs free energy on a reactive basis, [J/kg]

Gadolinium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Gadolinium, [atoms/s]

Gadolinium_atom_flow()¶: Method to calculate and return the mole flow that is Gadolinium, [mol/s]

Gadolinium_atom_fraction()¶: Method to calculate and return the mole fraction that is Gadolinium element, [-]

Gadolinium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Gadolinium element, [kg/s]

Gadolinium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Gadolinium element, [-]

Gallium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Gallium, [atoms/s]

Gallium_atom_flow()¶: Method to calculate and return the mole flow that is Gallium, [mol/s]

Gallium_atom_fraction()¶: Method to calculate and return the mole fraction that is Gallium element, [-]

Gallium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Gallium element, [kg/s]

Gallium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Gallium element, [-]

Germanium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Germanium, [atoms/s]

Germanium_atom_flow()¶: Method to calculate and return the mole flow that is Germanium, [mol/s]

Germanium_atom_fraction()¶: Method to calculate and return the mole fraction that is Germanium element, [-]

Germanium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Germanium element, [kg/s]

Germanium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Germanium element, [-]

property Gfgs¶

Ideal gas standard molar Gibbs free energy of formation for each component, [J/mol].

Returns

Gfgslist[float]: Ideal gas standard molar Gibbs free energy of formation for each component, [J/mol].

property Gfgs_mass¶

Ideal gas standard Gibbs free energy of formation for each component, [J/kg].

Returns

Gfgs_masslist[float]: Ideal gas standard Gibbs free energy of formation for each component, [J/kg].

Gold_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Gold, [atoms/s]

Gold_atom_flow()¶: Method to calculate and return the mole flow that is Gold, [mol/s]

Gold_atom_fraction()¶: Method to calculate and return the mole fraction that is Gold element, [-]

Gold_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Gold element, [kg/s]

Gold_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Gold element, [-]

Gs_ideal_gas_standard_state()[source]¶

H()[source]¶

Method to calculate and return the enthalpy of the phase. The reference state for most subclasses is an ideal-gas enthalpy of zero at 298.15 K and 101325 Pa.

Returns

Hfloat: Molar enthalpy, [J/(mol)]

H_C_ratio()¶

Method to calculate and return the atomic ratio of hydrogen atoms to carbon atoms, based on the current composition of the phase.

Returns

H_C_ratiofloat: H/C ratio on a molar basis, [-]

Notes

None is returned if no species are present that have carbon atoms.

H_C_ratio_mass()¶

Method to calculate and return the mass ratio of hydrogen atoms to carbon atoms, based on the current composition of the phase.

Returns

H_C_ratio_massfloat: H/C ratio on a mass basis, [-]

Notes

None is returned if no species are present that have carbon atoms.

property H_calc¶

H_dep_flow()¶

Method to return the flow rate of the difference between the ideal-gas energy of this phase and the actual energy of the phase This method is only available when the phase is linked to an EquilibriumStream.

Returns

H_dep_flowfloat: Flow rate of departure energy, [J/s]

H_dep_mass()[source]¶

Method to calculate and return the mass departure enthalpy of the phase.

Returns

H_dep_massfloat: Departure mass enthalpy free energy, [J/kg]

H_dep_phi_consistency()[source]¶

Method to calculate and return a consistency check between departure enthalpy, and the fugacity coefficients’ temperature derivatives.

H^{\text{from phi}}_{dep} = -RT^2\sum_i z_i \frac{\partial \ln \phi_i}{\partial T}

Returns

errorfloat: Relative consistency error $|1 - H^{\text{from phi}}_{dep}/H^\text{implemented}_{dep}|$ , [-]

H_flow()¶

Method to return the flow rate of enthalpy of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

H_flowfloat: Flow rate of energy, [J/s]

H_formation_ideal_gas()[source]¶

Method to calculate and return the ideal-gas enthalpy of formation of the phase (as if the phase was an ideal gas).

H_{formation}^{ig} = \sum_i z_i {H_{f,i}}

Returns

H_formation_ideal_gasfloat: Enthalpy of formation of the phase on a formation basis as an ideal gas, [J/mol]

H_formation_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas formation enthalpy of the phase.

Returns

H_formation_ideal_gas_massfloat: Formation mass enthalpy, [J/kg]

H_from_phi()[source]¶

Method to calculate and return the enthalpy of the fluid as calculated from the ideal-gas enthalpy and the the fugacity coefficients’ temperature derivatives.

H^{\text{from phi}} = H^{ig} - RT^2\sum_i z_i \frac{\partial \ln \phi_i}{\partial T}

Returns

Hfloat: Enthalpy as calculated from fugacity coefficient temperature derivatives [J/mol]

H_ideal_gas()[source]¶

Method to calculate and return the ideal-gas enthalpy of the phase.

H^{ig} = \sum_i z_i {H_{i}^{ig}}

Returns

Hfloat: Ideal gas enthalpy, [J/(mol)]

H_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas enthalpy of the phase.

Returns

H_ideal_gas_massfloat: Ideal gas mass enthalpy, [J/(kg)]

H_ideal_gas_standard_state()[source]¶

H_mass()[source]¶

Method to calculate and return mass enthalpy of the phase.

H_{mass} = \frac{1000 H_{molar}}{MW}

Returns

H_massfloat: Mass enthalpy, [J/kg]

H_phi_consistency()[source]¶

Method to calculate and return a consistency check between ideal gas enthalpy behavior, and the fugacity coefficients and their temperature derivatives.

H^{\text{from phi}} = H^{ig} - RT^2\sum_i z_i \frac{\partial \ln \phi_i}{\partial T}

Returns

errorfloat: Relative consistency error $|1 - H^{\text{from phi}}/H^\text{implemented}|$ , [-]

H_reactive()[source]¶

Method to calculate and return the enthalpy of the phase on a reactive basis, using the Hfs values of the phase.

H_{reactive} = H + \sum_i z_i {H_{f,i}}

Returns

H_reactivefloat: Enthalpy of the phase on a reactive basis, [J/mol]

H_reactive_mass()[source]¶

Method to calculate and return mass enthalpy on a reactive basis of the phase.

H_{reactive,mass} = \frac{1000 H_{reactive, molar}}{MW}

Returns

H_reactive_massfloat: Mass enthalpy on a reactive basis, [J/kg]

Hafnium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Hafnium, [atoms/s]

Hafnium_atom_flow()¶: Method to calculate and return the mole flow that is Hafnium, [mol/s]

Hafnium_atom_fraction()¶: Method to calculate and return the mole fraction that is Hafnium element, [-]

Hafnium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Hafnium element, [kg/s]

Hafnium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Hafnium element, [-]

Hassium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Hassium, [atoms/s]

Hassium_atom_flow()¶: Method to calculate and return the mole flow that is Hassium, [mol/s]

Hassium_atom_fraction()¶: Method to calculate and return the mole fraction that is Hassium element, [-]

Hassium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Hassium element, [kg/s]

Hassium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Hassium element, [-]

Hc()¶

Method to calculate and return the molar ideal-gas higher heat of combustion of the object, [J/mol]

Returns

Hcfloat: Molar higher heat of combustion, [J/(mol)]

Hc_lower()¶

Method to calculate and return the molar ideal-gas lower heat of combustion of the object, [J/mol]

Returns

Hc_lowerfloat: Molar lower heat of combustion, [J/(mol)]

Hc_lower_mass()¶

Method to calculate and return the mass ideal-gas lower heat of combustion of the object, [J/mol]

Returns

Hc_lower_massfloat: Mass lower heat of combustion, [J/(kg)]

Hc_lower_normal()¶

Method to calculate and return the volumetric ideal-gas lower heat of combustion of the object using the normal gas volume, [J/m^3]

Returns

Hc_lower_normalfloat: Volumetric (normal) lower heat of combustion, [J/(m^3)]

Hc_lower_standard()¶

Method to calculate and return the volumetric ideal-gas lower heat of combustion of the object using the standard gas volume, [J/m^3]

Returns

Hc_lower_standardfloat: Volumetric (standard) lower heat of combustion, [J/(m^3)]

Hc_mass()¶

Method to calculate and return the mass ideal-gas higher heat of combustion of the object, [J/mol]

Returns

Hc_massfloat: Mass higher heat of combustion, [J/(kg)]

Hc_normal()¶

Method to calculate and return the volumetric ideal-gas higher heat of combustion of the object using the normal gas volume, [J/m^3]

Returns

Hc_normalfloat: Volumetric (normal) higher heat of combustion, [J/(m^3)]

Hc_standard()¶

Method to calculate and return the volumetric ideal-gas higher heat of combustion of the object using the standard gas volume, [J/m^3]

Returns

Hc_normalfloat: Volumetric (standard) higher heat of combustion, [J/(m^3)]

property Hcs¶

Higher standard molar heats of combustion for each component, [J/mol].

Returns

Hcslist[float]: Higher standard molar heats of combustion for each component, [J/mol].

property Hcs_lower¶

Lower standard molar heats of combustion for each component, [J/mol].

Returns

Hcs_lowerlist[float]: Lower standard molar heats of combustion for each component, [J/mol].

property Hcs_lower_mass¶

Lower standard heats of combustion for each component, [J/kg].

Returns

Hcs_lower_masslist[float]: Lower standard heats of combustion for each component, [J/kg].

property Hcs_mass¶

Higher standard heats of combustion for each component, [J/kg].

Returns

Hcs_masslist[float]: Higher standard heats of combustion for each component, [J/kg].

Helium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Helium, [atoms/s]

Helium_atom_flow()¶: Method to calculate and return the mole flow that is Helium, [mol/s]

Helium_atom_fraction()¶: Method to calculate and return the mole fraction that is Helium element, [-]

Helium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Helium element, [kg/s]

Helium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Helium element, [-]

property Hf_STPs¶

Standard state molar enthalpies of formation for each component, [J/mol].

Returns

Hf_STPslist[float]: Standard state molar enthalpies of formation for each component, [J/mol].

property Hf_STPs_mass¶

Standard state mass enthalpies of formation for each component, [J/kg].

Returns

Hf_STPs_masslist[float]: Standard state mass enthalpies of formation for each component, [J/kg].

property Hfgs¶

Ideal gas standard molar enthalpies of formation for each component, [J/mol].

Returns

Hfgslist[float]: Ideal gas standard molar enthalpies of formation for each component, [J/mol].

property Hfgs_mass¶

Ideal gas standard enthalpies of formation for each component, [J/kg].

Returns

Hfgs_masslist[float]: Ideal gas standard enthalpies of formation for each component, [J/kg].

property Hfus_Tms¶

Molar heats of fusion for each component at their respective melting points, [J/mol].

Returns

Hfus_Tmslist[float]: Molar heats of fusion for each component at their respective melting points, [J/mol].

property Hfus_Tms_mass¶

Heats of fusion for each component at their respective melting points, [J/kg].

Returns

Hfus_Tms_masslist[float]: Heats of fusion for each component at their respective melting points, [J/kg].

Holmium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Holmium, [atoms/s]

Holmium_atom_flow()¶: Method to calculate and return the mole flow that is Holmium, [mol/s]

Holmium_atom_fraction()¶: Method to calculate and return the mole fraction that is Holmium element, [-]

Holmium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Holmium element, [kg/s]

Holmium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Holmium element, [-]

Hs_ideal_gas_standard_state()[source]¶

property Hsub_Tts¶

Heats of sublimation for each component at their respective triple points, [J/mol].

Returns

Hsub_Ttslist[float]: Heats of sublimation for each component at their respective triple points, [J/mol].

property Hsub_Tts_mass¶

Heats of sublimation for each component at their respective triple points, [J/kg].

Returns

Hsub_Tts_masslist[float]: Heats of sublimation for each component at their respective triple points, [J/kg].

Hsubs()¶

Method to calculate and return the pure-component enthalpy of sublimation of each species from the thermo.phase_change.EnthalpySublimation objects.

Returns

Hsubslist[float]: Sublimation enthalpies, [J/mol]

Notes

Warning

This is not necessarily consistent with the saturation enthalpy change calculated by a flash algorithm.

property Hvap_298s¶

Molar heats of vaporization for each component at 298.15 K, [J/mol].

Returns

Hvap_298slist[float]: Molar heats of vaporization for each component at 298.15 K, [J/mol].

property Hvap_298s_mass¶

Heats of vaporization for each component at 298.15 K, [J/kg].

Returns

Hvap_298s_masslist[float]: Heats of vaporization for each component at 298.15 K, [J/kg].

property Hvap_Tbs¶

Molar heats of vaporization for each component at their respective normal boiling points, [J/mol].

Returns

Hvap_Tbslist[float]: Molar heats of vaporization for each component at their respective normal boiling points, [J/mol].

property Hvap_Tbs_mass¶

Heats of vaporization for each component at their respective normal boiling points, [J/kg].

Returns

Hvap_Tbs_masslist[float]: Heats of vaporization for each component at their respective normal boiling points, [J/kg].

Hvaps()¶

Method to calculate and return the pure-component enthalpy of vaporization of each species from the thermo.phase_change.EnthalpyVaporization objects.

Returns

Hvapslist[float]: Enthalpies of vaporization, [J/mol]

Notes

Warning

This is not necessarily consistent with the saturation enthalpy change calculated by a flash algorithm.

Hydrogen_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Hydrogen, [atoms/s]

Hydrogen_atom_flow()¶: Method to calculate and return the mole flow that is Hydrogen, [mol/s]

Hydrogen_atom_fraction()¶: Method to calculate and return the mole fraction that is Hydrogen element, [-]

Hydrogen_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Hydrogen element, [kg/s]

Hydrogen_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Hydrogen element, [-]

INCOMPRESSIBLE_CONST = 1e+30¶

property InChI_Keys¶

InChI Keys for each component, [-].

Returns

InChI_Keyslist[str]: InChI Keys for each component, [-].

property InChIs¶

InChI strings for each component, [-].

Returns

InChIslist[str]: InChI strings for each component, [-].

Indium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Indium, [atoms/s]

Indium_atom_flow()¶: Method to calculate and return the mole flow that is Indium, [mol/s]

Indium_atom_fraction()¶: Method to calculate and return the mole fraction that is Indium element, [-]

Indium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Indium element, [kg/s]

Indium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Indium element, [-]

Iodine_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Iodine, [atoms/s]

Iodine_atom_flow()¶: Method to calculate and return the mole flow that is Iodine, [mol/s]

Iodine_atom_fraction()¶: Method to calculate and return the mole fraction that is Iodine element, [-]

Iodine_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Iodine element, [kg/s]

Iodine_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Iodine element, [-]

Iridium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Iridium, [atoms/s]

Iridium_atom_flow()¶: Method to calculate and return the mole flow that is Iridium, [mol/s]

Iridium_atom_fraction()¶: Method to calculate and return the mole fraction that is Iridium element, [-]

Iridium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Iridium element, [kg/s]

Iridium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Iridium element, [-]

Iron_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Iron, [atoms/s]

Iron_atom_flow()¶: Method to calculate and return the mole flow that is Iron, [mol/s]

Iron_atom_fraction()¶: Method to calculate and return the mole fraction that is Iron element, [-]

Iron_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Iron element, [kg/s]

Iron_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Iron element, [-]

Joule_Thomson()[source]¶

Method to calculate and return the Joule-Thomson coefficient of the phase.

\mu_{JT} = \left(\frac{\partial T}{\partial P}\right)_H = \frac{1}{C_p} \left[T \left(\frac{\partial V}{\partial T}\right)_P - V\right] = \frac{V}{C_p}\left(\beta T-1\right)

Returns

mu_JTfloat: Joule-Thomson coefficient [K/Pa]

Krypton_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Krypton, [atoms/s]

Krypton_atom_flow()¶: Method to calculate and return the mole flow that is Krypton, [mol/s]

Krypton_atom_fraction()¶: Method to calculate and return the mole fraction that is Krypton element, [-]

Krypton_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Krypton element, [kg/s]

Krypton_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Krypton element, [-]

property LFLs¶

Lower flammability limits for each component, [-].

Returns

LFLslist[float]: Lower flammability limits for each component, [-].

LOG_P_REF_IG = 11.52608845149651¶

Lanthanum_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Lanthanum, [atoms/s]

Lanthanum_atom_flow()¶: Method to calculate and return the mole flow that is Lanthanum, [mol/s]

Lanthanum_atom_fraction()¶: Method to calculate and return the mole fraction that is Lanthanum element, [-]

Lanthanum_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Lanthanum element, [kg/s]

Lanthanum_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Lanthanum element, [-]

Lawrencium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Lawrencium, [atoms/s]

Lawrencium_atom_flow()¶: Method to calculate and return the mole flow that is Lawrencium, [mol/s]

Lawrencium_atom_fraction()¶: Method to calculate and return the mole fraction that is Lawrencium element, [-]

Lawrencium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Lawrencium element, [kg/s]

Lawrencium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Lawrencium element, [-]

Lead_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Lead, [atoms/s]

Lead_atom_flow()¶: Method to calculate and return the mole flow that is Lead, [mol/s]

Lead_atom_fraction()¶: Method to calculate and return the mole fraction that is Lead element, [-]

Lead_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Lead element, [kg/s]

Lead_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Lead element, [-]

Lithium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Lithium, [atoms/s]

Lithium_atom_flow()¶: Method to calculate and return the mole flow that is Lithium, [mol/s]

Lithium_atom_fraction()¶: Method to calculate and return the mole fraction that is Lithium element, [-]

Lithium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Lithium element, [kg/s]

Lithium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Lithium element, [-]

Livermorium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Livermorium, [atoms/s]

Livermorium_atom_flow()¶: Method to calculate and return the mole flow that is Livermorium, [mol/s]

Livermorium_atom_fraction()¶: Method to calculate and return the mole fraction that is Livermorium element, [-]

Livermorium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Livermorium element, [kg/s]

Livermorium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Livermorium element, [-]

Lutetium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Lutetium, [atoms/s]

Lutetium_atom_flow()¶: Method to calculate and return the mole flow that is Lutetium, [mol/s]

Lutetium_atom_fraction()¶: Method to calculate and return the mole fraction that is Lutetium element, [-]

Lutetium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Lutetium element, [kg/s]

Lutetium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Lutetium element, [-]

MW()[source]¶

Method to calculate and return molecular weight of the phase.

\text{MW} = \sum_i z_i \text{MW}_i

Returns

MWfloat: Molecular weight, [g/mol]

MW_inv()[source]¶

Method to calculate and return inverse of molecular weight of the phase.

\frac{1}{\text{MW}} = \frac{1}{\sum_i z_i \text{MW}_i}

Returns

MW_invfloat: Inverse of molecular weight, [mol/g]

property MWs¶

Molecular weights for each component, [g/mol].

Returns

MWslist[float]: Molecular weights for each component, [g/mol].

Magnesium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Magnesium, [atoms/s]

Magnesium_atom_flow()¶: Method to calculate and return the mole flow that is Magnesium, [mol/s]

Magnesium_atom_fraction()¶: Method to calculate and return the mole fraction that is Magnesium element, [-]

Magnesium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Magnesium element, [kg/s]

Magnesium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Magnesium element, [-]

Manganese_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Manganese, [atoms/s]

Manganese_atom_flow()¶: Method to calculate and return the mole flow that is Manganese, [mol/s]

Manganese_atom_fraction()¶: Method to calculate and return the mole fraction that is Manganese element, [-]

Manganese_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Manganese element, [kg/s]

Manganese_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Manganese element, [-]

Meitnerium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Meitnerium, [atoms/s]

Meitnerium_atom_flow()¶: Method to calculate and return the mole flow that is Meitnerium, [mol/s]

Meitnerium_atom_fraction()¶: Method to calculate and return the mole fraction that is Meitnerium element, [-]

Meitnerium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Meitnerium element, [kg/s]

Meitnerium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Meitnerium element, [-]

Mendelevium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Mendelevium, [atoms/s]

Mendelevium_atom_flow()¶: Method to calculate and return the mole flow that is Mendelevium, [mol/s]

Mendelevium_atom_fraction()¶: Method to calculate and return the mole fraction that is Mendelevium element, [-]

Mendelevium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Mendelevium element, [kg/s]

Mendelevium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Mendelevium element, [-]

Mercury_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Mercury, [atoms/s]

Mercury_atom_flow()¶: Method to calculate and return the mole flow that is Mercury, [mol/s]

Mercury_atom_fraction()¶: Method to calculate and return the mole fraction that is Mercury element, [-]

Mercury_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Mercury element, [kg/s]

Mercury_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Mercury element, [-]

Molybdenum_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Molybdenum, [atoms/s]

Molybdenum_atom_flow()¶: Method to calculate and return the mole flow that is Molybdenum, [mol/s]

Molybdenum_atom_fraction()¶: Method to calculate and return the mole fraction that is Molybdenum element, [-]

Molybdenum_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Molybdenum element, [kg/s]

Molybdenum_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Molybdenum element, [-]

Moscovium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Moscovium, [atoms/s]

Moscovium_atom_flow()¶: Method to calculate and return the mole flow that is Moscovium, [mol/s]

Moscovium_atom_fraction()¶: Method to calculate and return the mole fraction that is Moscovium element, [-]

Moscovium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Moscovium element, [kg/s]

Moscovium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Moscovium element, [-]

Neodymium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Neodymium, [atoms/s]

Neodymium_atom_flow()¶: Method to calculate and return the mole flow that is Neodymium, [mol/s]

Neodymium_atom_fraction()¶: Method to calculate and return the mole fraction that is Neodymium element, [-]

Neodymium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Neodymium element, [kg/s]

Neodymium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Neodymium element, [-]

Neon_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Neon, [atoms/s]

Neon_atom_flow()¶: Method to calculate and return the mole flow that is Neon, [mol/s]

Neon_atom_fraction()¶: Method to calculate and return the mole fraction that is Neon element, [-]

Neon_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Neon element, [kg/s]

Neon_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Neon element, [-]

Neptunium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Neptunium, [atoms/s]

Neptunium_atom_flow()¶: Method to calculate and return the mole flow that is Neptunium, [mol/s]

Neptunium_atom_fraction()¶: Method to calculate and return the mole fraction that is Neptunium element, [-]

Neptunium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Neptunium element, [kg/s]

Neptunium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Neptunium element, [-]

Nickel_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Nickel, [atoms/s]

Nickel_atom_flow()¶: Method to calculate and return the mole flow that is Nickel, [mol/s]

Nickel_atom_fraction()¶: Method to calculate and return the mole fraction that is Nickel element, [-]

Nickel_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Nickel element, [kg/s]

Nickel_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Nickel element, [-]

Nihonium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Nihonium, [atoms/s]

Nihonium_atom_flow()¶: Method to calculate and return the mole flow that is Nihonium, [mol/s]

Nihonium_atom_fraction()¶: Method to calculate and return the mole fraction that is Nihonium element, [-]

Nihonium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Nihonium element, [kg/s]

Nihonium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Nihonium element, [-]

Niobium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Niobium, [atoms/s]

Niobium_atom_flow()¶: Method to calculate and return the mole flow that is Niobium, [mol/s]

Niobium_atom_fraction()¶: Method to calculate and return the mole fraction that is Niobium element, [-]

Niobium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Niobium element, [kg/s]

Niobium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Niobium element, [-]

Nitrogen_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Nitrogen, [atoms/s]

Nitrogen_atom_flow()¶: Method to calculate and return the mole flow that is Nitrogen, [mol/s]

Nitrogen_atom_fraction()¶: Method to calculate and return the mole fraction that is Nitrogen element, [-]

Nitrogen_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Nitrogen element, [kg/s]

Nitrogen_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Nitrogen element, [-]

Nobelium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Nobelium, [atoms/s]

Nobelium_atom_flow()¶: Method to calculate and return the mole flow that is Nobelium, [mol/s]

Nobelium_atom_fraction()¶: Method to calculate and return the mole fraction that is Nobelium element, [-]

Nobelium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Nobelium element, [kg/s]

Nobelium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Nobelium element, [-]

property ODPs¶

Ozone Depletion Potentials for each component (impact/mass chemical)/(impact/mass CFC-11), [-].

Returns

ODPslist[float]: Ozone Depletion Potentials for each component (impact/mass chemical)/(impact/mass CFC-11), [-].

Oganesson_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Oganesson, [atoms/s]

Oganesson_atom_flow()¶: Method to calculate and return the mole flow that is Oganesson, [mol/s]

Oganesson_atom_fraction()¶: Method to calculate and return the mole fraction that is Oganesson element, [-]

Oganesson_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Oganesson element, [kg/s]

Oganesson_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Oganesson element, [-]

Osmium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Osmium, [atoms/s]

Osmium_atom_flow()¶: Method to calculate and return the mole flow that is Osmium, [mol/s]

Osmium_atom_fraction()¶: Method to calculate and return the mole fraction that is Osmium element, [-]

Osmium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Osmium element, [kg/s]

Osmium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Osmium element, [-]

Oxygen_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Oxygen, [atoms/s]

Oxygen_atom_flow()¶: Method to calculate and return the mole flow that is Oxygen, [mol/s]

Oxygen_atom_fraction()¶: Method to calculate and return the mole fraction that is Oxygen element, [-]

Oxygen_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Oxygen element, [kg/s]

Oxygen_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Oxygen element, [-]

PIP()[source]¶

Method to calculate and return the phase identification parameter of the phase.

\Pi = V \left[\frac{\frac{\partial^2 P}{\partial V \partial T}} {\frac{\partial P }{\partial T}}- \frac{\frac{\partial^2 P}{\partial V^2}}{\frac{\partial P}{\partial V}} \right]

Returns

PIPfloat: Phase identification parameter, [-]

property PSRK_groups¶

PSRK subgroup: count groups for each component, [-].

Returns

PSRK_groupslist[dict]: PSRK subgroup: count groups for each component, [-].

P_MAX_FIXED = 1000000000.0¶

P_MIN_FIXED = 0.01¶

P_REF_IG = 101325.0¶

P_REF_IG_INV = 9.869232667160129e-06¶

property P_calc¶

P_max_at_V(V)[source]¶

Dummy method. The idea behind this method, which is implemented by some subclasses, is to calculate the maximum pressure the phase can create at a constant volume, if one exists; returns None otherwise. This method, as a dummy method, always returns None.

Parameters

Vfloat: Constant molar volume, [m^3/mol]

Returns

Pfloat: Maximum possible isochoric pressure, [Pa]

P_transitions()[source]¶

Dummy method. The idea behind this method is to calculate any pressures (at constant temperature) which cause the phase properties to become discontinuous.

Returns

P_transitionslist[float]: Transition pressures, [Pa]

Palladium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Palladium, [atoms/s]

Palladium_atom_flow()¶: Method to calculate and return the mole flow that is Palladium, [mol/s]

Palladium_atom_fraction()¶: Method to calculate and return the mole fraction that is Palladium element, [-]

Palladium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Palladium element, [kg/s]

Palladium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Palladium element, [-]

property Parachors¶

Parachors for each component, [N^0.25*m^2.75/mol].

Returns

Parachorslist[float]: Parachors for each component, [N^0.25*m^2.75/mol].

property Pcs¶

Critical pressures for each component, [Pa].

Returns

Pcslist[float]: Critical pressures for each component, [Pa].

Phosphorus_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Phosphorus, [atoms/s]

Phosphorus_atom_flow()¶: Method to calculate and return the mole flow that is Phosphorus, [mol/s]

Phosphorus_atom_fraction()¶: Method to calculate and return the mole fraction that is Phosphorus element, [-]

Phosphorus_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Phosphorus element, [kg/s]

Phosphorus_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Phosphorus element, [-]

Platinum_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Platinum, [atoms/s]

Platinum_atom_flow()¶: Method to calculate and return the mole flow that is Platinum, [mol/s]

Platinum_atom_fraction()¶: Method to calculate and return the mole fraction that is Platinum element, [-]

Platinum_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Platinum element, [kg/s]

Platinum_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Platinum element, [-]

Plutonium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Plutonium, [atoms/s]

Plutonium_atom_flow()¶: Method to calculate and return the mole flow that is Plutonium, [mol/s]

Plutonium_atom_fraction()¶: Method to calculate and return the mole fraction that is Plutonium element, [-]

Plutonium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Plutonium element, [kg/s]

Plutonium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Plutonium element, [-]

Pmc()[source]¶

Method to calculate and return the mechanical critical pressure of the phase.

Returns

Pmcfloat: Mechanical critical pressure, [Pa]

Polonium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Polonium, [atoms/s]

Polonium_atom_flow()¶: Method to calculate and return the mole flow that is Polonium, [mol/s]

Polonium_atom_fraction()¶: Method to calculate and return the mole fraction that is Polonium element, [-]

Polonium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Polonium element, [kg/s]

Polonium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Polonium element, [-]

Potassium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Potassium, [atoms/s]

Potassium_atom_flow()¶: Method to calculate and return the mole flow that is Potassium, [mol/s]

Potassium_atom_fraction()¶: Method to calculate and return the mole fraction that is Potassium element, [-]

Potassium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Potassium element, [kg/s]

Potassium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Potassium element, [-]

Prandtl()[source]¶

Method to calculate and return the Prandtl number of the phase

Pr = \frac{C_p \mu}{k} = \frac{\nu}{\alpha} = \frac{C_p \rho \nu}{k}

Returns

Prfloat: Prandtl number []

Praseodymium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Praseodymium, [atoms/s]

Praseodymium_atom_flow()¶: Method to calculate and return the mole flow that is Praseodymium, [mol/s]

Praseodymium_atom_fraction()¶: Method to calculate and return the mole fraction that is Praseodymium element, [-]

Praseodymium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Praseodymium element, [kg/s]

Praseodymium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Praseodymium element, [-]

Promethium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Promethium, [atoms/s]

Promethium_atom_flow()¶: Method to calculate and return the mole flow that is Promethium, [mol/s]

Promethium_atom_fraction()¶: Method to calculate and return the mole fraction that is Promethium element, [-]

Promethium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Promethium element, [kg/s]

Promethium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Promethium element, [-]

Protactinium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Protactinium, [atoms/s]

Protactinium_atom_flow()¶: Method to calculate and return the mole flow that is Protactinium, [mol/s]

Protactinium_atom_fraction()¶: Method to calculate and return the mole fraction that is Protactinium element, [-]

Protactinium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Protactinium element, [kg/s]

Protactinium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Protactinium element, [-]

property Psat_298s¶

Vapor pressures for each component at 298.15 K, [Pa].

Returns

Psat_298slist[float]: Vapor pressures for each component at 298.15 K, [Pa].

Psats()¶

Method to calculate and return the pure-component vapor pressures of each species from the thermo.vapor_pressure.VaporPressure objects.

Returns

Psatslist[float]: Vapor pressures, [Pa]

Notes

Warning

This is not necessarily consistent with the saturation pressure calculated by a flash algorithm.

Psats_poly_fit = False¶

Psubs()¶

Method to calculate and return the pure-component sublimation of each species from the thermo.vapor_pressure.SublimationPressure objects.

Returns

Psubslist[float]: Sublimation pressures, [Pa]

Notes

Warning

This is not necessarily consistent with the saturation pressure calculated by a flash algorithm.

property Pts¶

Triple point pressures for each component, [Pa].

Returns

Ptslist[float]: Triple point pressures for each component, [Pa].

property PubChems¶

Pubchem IDs for each component, [-].

Returns

PubChemslist[int]: Pubchem IDs for each component, [-].

property Q¶

Method to return the actual volumetric flow rate of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

Qfloat: Volume flow of the phase, [m^3/s]

property Q_calc¶

Method to return the actual volumetric flow rate of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

Qfloat: Volume flow of the phase, [m^3/s]

property Qg¶

Method to return the volume flow rate of this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qgfloat: Ideal gas flow rate of the phase, [m^3/s]

property Qg_calc¶

Method to return the volume flow rate of this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qgfloat: Ideal gas flow rate of the phase, [m^3/s]

property Qgs¶

Method to return the volume flow rate of each component in this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qgsfloat: Ideal gas flow rates of the components in the phase, [m^3/s]

property Qgs_calc¶

Method to return the volume flow rate of each component in this phase as an ideal gas, using the configured temperature T_gas_ref and pressure P_gas_ref. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qgsfloat: Ideal gas flow rates of the components in the phase, [m^3/s]

property Ql¶

Method to return the volume flow rate of this phase as an ideal liquid, using the configured standard molar volumes Vml_STPs. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qlfloat: Ideal liquid flow rate of the phase, [m^3/s]

property Ql_calc¶

Method to return the volume flow rate of this phase as an ideal liquid, using the configured standard molar volumes Vml_STPs. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qlfloat: Ideal liquid flow rate of the phase, [m^3/s]

property Qls¶

Method to return the volume flow rate of each component in this phase as an ideal liquid, using the configured V_liquids_ref. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qlsfloat: Ideal liquid flow rates of the components in the phase, [m^3/s]

property Qls_calc¶

Method to return the volume flow rate of each component in this phase as an ideal liquid, using the configured V_liquids_ref. This method is only available when the phase is linked to an EquilibriumStream. This method totally ignores phase equilibrium.

Returns

Qlsfloat: Ideal liquid flow rates of the components in the phase, [m^3/s]

R = 8.31446261815324¶

R2 = 69.13028862866763¶

property RI_Ts¶

Temperatures at which the refractive indexes were reported for each component, [K].

Returns

RI_Tslist[float]: Temperatures at which the refractive indexes were reported for each component, [K].

property RIs¶

Refractive indexes for each component, [-].

Returns

RIslist[float]: Refractive indexes for each component, [-].

R_inv = 0.12027235504272604¶

Radium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Radium, [atoms/s]

Radium_atom_flow()¶: Method to calculate and return the mole flow that is Radium, [mol/s]

Radium_atom_fraction()¶: Method to calculate and return the mole fraction that is Radium element, [-]

Radium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Radium element, [kg/s]

Radium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Radium element, [-]

Radon_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Radon, [atoms/s]

Radon_atom_flow()¶: Method to calculate and return the mole flow that is Radon, [mol/s]

Radon_atom_fraction()¶: Method to calculate and return the mole fraction that is Radon element, [-]

Radon_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Radon element, [kg/s]

Radon_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Radon element, [-]

Rhenium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Rhenium, [atoms/s]

Rhenium_atom_flow()¶: Method to calculate and return the mole flow that is Rhenium, [mol/s]

Rhenium_atom_fraction()¶: Method to calculate and return the mole fraction that is Rhenium element, [-]

Rhenium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Rhenium element, [kg/s]

Rhenium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Rhenium element, [-]

Rhodium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Rhodium, [atoms/s]

Rhodium_atom_flow()¶: Method to calculate and return the mole flow that is Rhodium, [mol/s]

Rhodium_atom_fraction()¶: Method to calculate and return the mole fraction that is Rhodium element, [-]

Rhodium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Rhodium element, [kg/s]

Rhodium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Rhodium element, [-]

Roentgenium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Roentgenium, [atoms/s]

Roentgenium_atom_flow()¶: Method to calculate and return the mole flow that is Roentgenium, [mol/s]

Roentgenium_atom_fraction()¶: Method to calculate and return the mole fraction that is Roentgenium element, [-]

Roentgenium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Roentgenium element, [kg/s]

Roentgenium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Roentgenium element, [-]

Rubidium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Rubidium, [atoms/s]

Rubidium_atom_flow()¶: Method to calculate and return the mole flow that is Rubidium, [mol/s]

Rubidium_atom_fraction()¶: Method to calculate and return the mole fraction that is Rubidium element, [-]

Rubidium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Rubidium element, [kg/s]

Rubidium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Rubidium element, [-]

Ruthenium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Ruthenium, [atoms/s]

Ruthenium_atom_flow()¶: Method to calculate and return the mole flow that is Ruthenium, [mol/s]

Ruthenium_atom_fraction()¶: Method to calculate and return the mole fraction that is Ruthenium element, [-]

Ruthenium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Ruthenium element, [kg/s]

Ruthenium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Ruthenium element, [-]

Rutherfordium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Rutherfordium, [atoms/s]

Rutherfordium_atom_flow()¶: Method to calculate and return the mole flow that is Rutherfordium, [mol/s]

Rutherfordium_atom_fraction()¶: Method to calculate and return the mole fraction that is Rutherfordium element, [-]

Rutherfordium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Rutherfordium element, [kg/s]

Rutherfordium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Rutherfordium element, [-]

S()[source]¶

Method to calculate and return the entropy of the phase. The reference state for most subclasses is an ideal-gas entropy of zero at 298.15 K and 101325 Pa.

Returns

Sfloat: Molar entropy, [J/(mol*K)]

property S0gs¶

Ideal gas absolute molar entropies at 298.15 K at 1 atm for each component, [J/(mol*K)].

Returns

S0gslist[float]: Ideal gas absolute molar entropies at 298.15 K at 1 atm for each component, [J/(mol*K)].

property S0gs_mass¶

Ideal gas absolute entropies at 298.15 K at 1 atm for each component, [J/(kg*K)].

Returns

S0gs_masslist[float]: Ideal gas absolute entropies at 298.15 K at 1 atm for each component, [J/(kg*K)].

SG()¶

Method to calculate and return the standard liquid specific gravity of the phase, using constant liquid pure component densities not calculated by the phase object, at 60 °F.

Returns

SGfloat: Specific gravity of the liquid, [-]

Notes

The reference density of water is from the IAPWS-95 standard - 999.0170824078306 kg/m^3.

SG_gas()¶

Method to calculate and return the specific gravity of the phase with respect to a gas reference density.

Returns

SG_gasfloat: Specific gravity of the gas, [-]

Notes

The reference molecular weight of air used is 28.9586 g/mol.

property STELs¶

Short term exposure limits to chemicals (and their units; ppm or mg/m^3), [various].

Returns

STELslist[tuple[(float, str)]]: Short term exposure limits to chemicals (and their units; ppm or mg/m^3), [various].

S_dep_flow()¶

Method to return the flow rate of the difference between the ideal-gas entropy of this phase and the actual entropy of the phase This method is only available when the phase is linked to an EquilibriumStream.

Returns

S_dep_flowfloat: Flow rate of departure entropy, [J/(K*s)]

S_dep_mass()[source]¶

Method to calculate and return the mass departure entropy of the phase.

Returns

S_dep_massfloat: Departure mass entropy free energy, [J/(kg*K)]

S_dep_phi_consistency()[source]¶

Method to calculate and return a consistency check between ideal gas entropy behavior, and the fugacity coefficients and their temperature derivatives.

S_{dep}^{\text{from phi}} = - \sum_{i} z_i R\left(\ln \phi_i + T \frac{\partial \ln \phi_i}{\partial T}\right)

Returns

errorfloat: Relative consistency error $|1 - S^{\text{from phi}}_{dep}/S^\text{implemented}_{dep}|$ , [-]

S_flow()¶

Method to return the flow rate of entropy of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

S_flowfloat: Flow rate of entropy, [J/(K*s)]

S_formation_ideal_gas()[source]¶

Method to calculate and return the ideal-gas entropy of formation of the phase (as if the phase was an ideal gas).

S_{formation}^{ig} = \sum_i z_i {S_{f,i}}

Returns

S_formation_ideal_gasfloat: Entropy of formation of the phase on a formation basis as an ideal gas, [J/(mol*K)]

S_formation_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas formation entropy of the phase.

Returns

S_formation_ideal_gas_massfloat: Formation mass entropy, [J/(kg*K)]

S_from_phi()[source]¶

Method to calculate and return the entropy of the fluid as calculated from the ideal-gas entropy and the the fugacity coefficients’ temperature derivatives.

S = S^{ig} - \sum_{i} z_i R\left(\ln \phi_i + T \frac{\partial \ln \phi_i}{\partial T}\right)

Returns

Sfloat: Entropy as calculated from fugacity coefficient temperature derivatives [J/(mol*K)]

S_ideal_gas()[source]¶

Method to calculate and return the ideal-gas entropy of the phase.

S^{ig} = \sum_i z_i S_{i}^{ig} - R\ln\left(\frac{P}{P_{ref}}\right) - R\sum_i z_i \ln(z_i)

Returns

Sfloat: Ideal gas molar entropy, [J/(mol*K)]

S_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas entropy of the phase.

Returns

S_ideal_gas_massfloat: Ideal gas mass entropy, [J/(kg*K)]

S_ideal_gas_standard_state()[source]¶

S_mass()[source]¶

Method to calculate and return mass entropy of the phase.

S_{mass} = \frac{1000 S_{molar}}{MW}

Returns

S_massfloat: Mass enthalpy, [J/(kg*K)]

S_phi_consistency()[source]¶

Method to calculate and return a consistency check between ideal gas entropy behavior, and the fugacity coefficients and their temperature derivatives.

S = S^{ig} - \sum_{i} z_i R\left(\ln \phi_i + T \frac{\partial \ln \phi_i}{\partial T}\right)

Returns

errorfloat: Relative consistency error $|1 - S^{\text{from phi}}/S^\text{implemented}|$ , [-]

S_reactive()[source]¶

Method to calculate and return the entropy of the phase on a reactive basis, using the Sfs values of the phase.

S_{reactive} = S + \sum_i z_i {S_{f,i}}

Returns

S_reactivefloat: Entropy of the phase on a reactive basis, [J/(mol*K)]

S_reactive_mass()[source]¶

Method to calculate and return mass entropy on a reactive basis of the phase.

S_{reactive,mass} = \frac{1000 S_{reactive, molar}}{MW}

Returns

S_reactive_massfloat: Mass entropy on a reactive basis, [J/(kg*K)]

Samarium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Samarium, [atoms/s]

Samarium_atom_flow()¶: Method to calculate and return the mole flow that is Samarium, [mol/s]

Samarium_atom_fraction()¶: Method to calculate and return the mole fraction that is Samarium element, [-]

Samarium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Samarium element, [kg/s]

Samarium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Samarium element, [-]

Scandium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Scandium, [atoms/s]

Scandium_atom_flow()¶: Method to calculate and return the mole flow that is Scandium, [mol/s]

Scandium_atom_fraction()¶: Method to calculate and return the mole fraction that is Scandium element, [-]

Scandium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Scandium element, [kg/s]

Scandium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Scandium element, [-]

Seaborgium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Seaborgium, [atoms/s]

Seaborgium_atom_flow()¶: Method to calculate and return the mole flow that is Seaborgium, [mol/s]

Seaborgium_atom_fraction()¶: Method to calculate and return the mole fraction that is Seaborgium element, [-]

Seaborgium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Seaborgium element, [kg/s]

Seaborgium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Seaborgium element, [-]

Selenium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Selenium, [atoms/s]

Selenium_atom_flow()¶: Method to calculate and return the mole flow that is Selenium, [mol/s]

Selenium_atom_fraction()¶: Method to calculate and return the mole fraction that is Selenium element, [-]

Selenium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Selenium element, [kg/s]

Selenium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Selenium element, [-]

property Sfgs¶

Ideal gas standard molar entropies of formation for each component, [J/(mol*K)].

Returns

Sfgslist[float]: Ideal gas standard molar entropies of formation for each component, [J/(mol*K)].

property Sfgs_mass¶

Ideal gas standard entropies of formation for each component, [J/(kg*K)].

Returns

Sfgs_masslist[float]: Ideal gas standard entropies of formation for each component, [J/(kg*K)].

Silicon_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Silicon, [atoms/s]

Silicon_atom_flow()¶: Method to calculate and return the mole flow that is Silicon, [mol/s]

Silicon_atom_fraction()¶: Method to calculate and return the mole fraction that is Silicon element, [-]

Silicon_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Silicon element, [kg/s]

Silicon_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Silicon element, [-]

Silver_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Silver, [atoms/s]

Silver_atom_flow()¶: Method to calculate and return the mole flow that is Silver, [mol/s]

Silver_atom_fraction()¶: Method to calculate and return the mole fraction that is Silver element, [-]

Silver_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Silver element, [kg/s]

Silver_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Silver element, [-]

property Skins¶

Whether each compound can be absorbed through the skin or not, [-].

Returns

Skinslist[bool]: Whether each compound can be absorbed through the skin or not, [-].

Sodium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Sodium, [atoms/s]

Sodium_atom_flow()¶: Method to calculate and return the mole flow that is Sodium, [mol/s]

Sodium_atom_fraction()¶: Method to calculate and return the mole fraction that is Sodium element, [-]

Sodium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Sodium element, [kg/s]

Sodium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Sodium element, [-]

Ss_ideal_gas_standard_state()[source]¶

property StielPolars¶

Stiel polar factors for each component, [-].

Returns

StielPolarslist[float]: Stiel polar factors for each component, [-].

property Stockmayers¶

Lennard-Jones Stockmayer parameters (depth of potential-energy minimum over k) for each component, [K].

Returns

Stockmayerslist[float]: Lennard-Jones Stockmayer parameters (depth of potential-energy minimum over k) for each component, [K].

Strontium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Strontium, [atoms/s]

Strontium_atom_flow()¶: Method to calculate and return the mole flow that is Strontium, [mol/s]

Strontium_atom_fraction()¶: Method to calculate and return the mole fraction that is Strontium element, [-]

Strontium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Strontium element, [kg/s]

Strontium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Strontium element, [-]

Sulfur_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Sulfur, [atoms/s]

Sulfur_atom_flow()¶: Method to calculate and return the mole flow that is Sulfur, [mol/s]

Sulfur_atom_fraction()¶: Method to calculate and return the mole fraction that is Sulfur element, [-]

Sulfur_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Sulfur element, [kg/s]

Sulfur_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Sulfur element, [-]

property TWAs¶

Time-weighted average exposure limits to chemicals (and their units; ppm or mg/m^3), [various].

Returns

TWAslist[tuple[(float, str)]]: Time-weighted average exposure limits to chemicals (and their units; ppm or mg/m^3), [various].

T_MAX_FIXED = 10000.0¶

T_MAX_FLASH = 10000.0¶

T_MIN_FIXED = 0.001¶

T_MIN_FLASH = 1e-300¶

T_REF_IG = 298.15¶

T_REF_IG_INV = 0.0033540164346805303¶: The numerical inverse of T_REF_IG, stored to save a division.

property T_calc¶

T_max_at_V(V)[source]¶

Method to calculate the maximum temperature the phase can create at a constant volume, if one exists; returns None otherwise.

Parameters

Vfloat: Constant molar volume, [m^3/mol]
Pmaxfloat: Maximum possible isochoric pressure, if already known [Pa]

Returns

Tfloat: Maximum possible temperature, [K]

Tantalum_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Tantalum, [atoms/s]

Tantalum_atom_flow()¶: Method to calculate and return the mole flow that is Tantalum, [mol/s]

Tantalum_atom_fraction()¶: Method to calculate and return the mole fraction that is Tantalum element, [-]

Tantalum_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Tantalum element, [kg/s]

Tantalum_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Tantalum element, [-]

property Tautoignitions¶

Autoignition temperatures for each component, [K].

Returns

Tautoignitionslist[float]: Autoignition temperatures for each component, [K].

property Tbs¶

Boiling temperatures for each component, [K].

Returns

Tbslist[float]: Boiling temperatures for each component, [K].

property Tcs¶

Critical temperatures for each component, [K].

Returns

Tcslist[float]: Critical temperatures for each component, [K].

Technetium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Technetium, [atoms/s]

Technetium_atom_flow()¶: Method to calculate and return the mole flow that is Technetium, [mol/s]

Technetium_atom_fraction()¶: Method to calculate and return the mole fraction that is Technetium element, [-]

Technetium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Technetium element, [kg/s]

Technetium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Technetium element, [-]

Tellurium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Tellurium, [atoms/s]

Tellurium_atom_flow()¶: Method to calculate and return the mole flow that is Tellurium, [mol/s]

Tellurium_atom_fraction()¶: Method to calculate and return the mole fraction that is Tellurium element, [-]

Tellurium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Tellurium element, [kg/s]

Tellurium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Tellurium element, [-]

Tennessine_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Tennessine, [atoms/s]

Tennessine_atom_flow()¶: Method to calculate and return the mole flow that is Tennessine, [mol/s]

Tennessine_atom_fraction()¶: Method to calculate and return the mole fraction that is Tennessine element, [-]

Tennessine_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Tennessine element, [kg/s]

Tennessine_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Tennessine element, [-]

Terbium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Terbium, [atoms/s]

Terbium_atom_flow()¶: Method to calculate and return the mole flow that is Terbium, [mol/s]

Terbium_atom_fraction()¶: Method to calculate and return the mole fraction that is Terbium element, [-]

Terbium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Terbium element, [kg/s]

Terbium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Terbium element, [-]

property Tflashs¶

Flash point temperatures for each component, [K].

Returns

Tflashslist[float]: Flash point temperatures for each component, [K].

Thallium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Thallium, [atoms/s]

Thallium_atom_flow()¶: Method to calculate and return the mole flow that is Thallium, [mol/s]

Thallium_atom_fraction()¶: Method to calculate and return the mole fraction that is Thallium element, [-]

Thallium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Thallium element, [kg/s]

Thallium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Thallium element, [-]

Thorium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Thorium, [atoms/s]

Thorium_atom_flow()¶: Method to calculate and return the mole flow that is Thorium, [mol/s]

Thorium_atom_fraction()¶: Method to calculate and return the mole fraction that is Thorium element, [-]

Thorium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Thorium element, [kg/s]

Thorium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Thorium element, [-]

Thulium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Thulium, [atoms/s]

Thulium_atom_flow()¶: Method to calculate and return the mole flow that is Thulium, [mol/s]

Thulium_atom_fraction()¶: Method to calculate and return the mole fraction that is Thulium element, [-]

Thulium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Thulium element, [kg/s]

Thulium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Thulium element, [-]

Tin_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Tin, [atoms/s]

Tin_atom_flow()¶: Method to calculate and return the mole flow that is Tin, [mol/s]

Tin_atom_fraction()¶: Method to calculate and return the mole fraction that is Tin element, [-]

Tin_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Tin element, [kg/s]

Tin_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Tin element, [-]

Titanium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Titanium, [atoms/s]

Titanium_atom_flow()¶: Method to calculate and return the mole flow that is Titanium, [mol/s]

Titanium_atom_fraction()¶: Method to calculate and return the mole fraction that is Titanium element, [-]

Titanium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Titanium element, [kg/s]

Titanium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Titanium element, [-]

Tmc()[source]¶

Method to calculate and return the mechanical critical temperature of the phase.

Returns

Tmcfloat: Mechanical critical temperature, [K]

property Tms¶

Melting temperatures for each component, [K].

Returns

Tmslist[float]: Melting temperatures for each component, [K].

property Tts¶

Triple point temperatures for each component, [K].

Returns

Ttslist[float]: Triple point temperatures for each component, [K].

Tungsten_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Tungsten, [atoms/s]

Tungsten_atom_flow()¶: Method to calculate and return the mole flow that is Tungsten, [mol/s]

Tungsten_atom_fraction()¶: Method to calculate and return the mole fraction that is Tungsten element, [-]

Tungsten_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Tungsten element, [kg/s]

Tungsten_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Tungsten element, [-]

U()[source]¶

Method to calculate and return the internal energy of the phase.

U = H - PV

Returns

Ufloat: Internal energy, [J/mol]

property UFLs¶

Upper flammability limits for each component, [-].

Returns

UFLslist[float]: Upper flammability limits for each component, [-].

property UNIFAC_Dortmund_groups¶

UNIFAC_Dortmund_group: count groups for each component, [-].

Returns

UNIFAC_Dortmund_groupslist[dict]: UNIFAC_Dortmund_group: count groups for each component, [-].

property UNIFAC_Qs¶

UNIFAC Q parameters for each component, [-].

Returns

UNIFAC_Qslist[float]: UNIFAC Q parameters for each component, [-].

property UNIFAC_Rs¶

UNIFAC R parameters for each component, [-].

Returns

UNIFAC_Rslist[float]: UNIFAC R parameters for each component, [-].

property UNIFAC_groups¶

UNIFAC_group: count groups for each component, [-].

Returns

UNIFAC_groupslist[dict]: UNIFAC_group: count groups for each component, [-].

U_dep()[source]¶

Method to calculate and return the departure internal energy of the phase.

U_{dep} = H_{dep} - PV_{dep}

Returns

U_depfloat: Departure internal energy, [J/mol]

U_dep_flow()¶

Method to return the flow rate of the difference between the ideal-gas internal energy of this phase and the actual internal energy of the phase This method is only available when the phase is linked to an EquilibriumStream.

Returns

U_dep_flowfloat: Flow rate of departure internal energy, [J/s]

U_dep_mass()[source]¶

Method to calculate and return the departure mass internal energy of the phase.

Returns

U_dep_massfloat: Departure mass internal energy, [J/kg]

U_flow()¶

Method to return the flow rate of internal energy of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

U_flowfloat: Flow rate of internal energy, [J/s]

U_formation_ideal_gas()[source]¶

Method to calculate and return the ideal-gas internal energy of formation of the phase (as if the phase was an ideal gas).

U_{formation}^{ig} = H_{formation}^{ig} - P_{ref}^{ig} V^{ig}

Returns

U_formation_ideal_gasfloat: Internal energy of formation of the phase on a formation basis as an ideal gas, [J/(mol)]

U_formation_ideal_gas_mass()[source]¶

Method to calculate and return the ideal-gas formation mass internal energy of the phase.

Returns

U_formation_ideal_gas_massfloat: Formation mass internal energy, [J/kg]

U_ideal_gas()[source]¶

Method to calculate and return the ideal-gas internal energy of the phase.

U^{ig} = H^{ig} - P V^{ig}

Returns

U_ideal_gasfloat: Ideal gas internal energy, [J/(mol)]

U_ideal_gas_mass()[source]¶

Method to calculate and return the mass ideal-gas internal energy of the phase.

Returns

U_ideal_gas_massfloat: Ideal gas mass internal energy, [J/(kg)]

U_mass()[source]¶

Method to calculate and return mass internal energy of the phase.

U_{mass} = \frac{1000 U_{molar}}{MW}

Returns

U_massfloat: Mass internal energy, [J/(kg)]

U_reactive()[source]¶

Method to calculate and return the internal energy of the phase on a reactive basis.

U_{reactive} = H_{reactive} - PV

Returns

U_reactivefloat: Internal energy of the phase on a reactive basis, [J/(mol)]

U_reactive_mass()[source]¶

Method to calculate and return mass internal energy on a reactive basis of the phase.

U_{reactive,mass} = \frac{1000 U_{reactive, molar}}{MW}

Returns

U_reactive_massfloat: Mass internal energy on a reactive basis, [J/kg]

Uranium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Uranium, [atoms/s]

Uranium_atom_flow()¶: Method to calculate and return the mole flow that is Uranium, [mol/s]

Uranium_atom_fraction()¶: Method to calculate and return the mole fraction that is Uranium element, [-]

Uranium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Uranium element, [kg/s]

Uranium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Uranium element, [-]

V()[source]¶

Method to return the molar volume of the phase.

Returns

Vfloat: Molar volume, [m^3/mol]

property VF¶

Method to return the vapor fraction of the phase. If no vapor/gas is present, 0 is always returned. This method is only available when the phase is linked to an EquilibriumState.

Returns

VFfloat: Vapor fraction, [-]

property VF_calc¶

V_MAX_FIXED = 1000000000.0¶

V_MIN_FIXED = 1e-09¶

V_dep()[source]¶

Method to calculate and return the departure (from ideal gas behavior) molar volume of the phase.

V_{dep} = V - \frac{RT}{P}

Returns

V_depfloat: Departure molar volume, [m^3/mol]

V_from_phi()[source]¶

Method to calculate and return the molar volume of the fluid as calculated from the pressure derivatives of fugacity coefficients.

V^{\text{from phi P der}} = \left(\left(\sum_i z_i \frac{\partial \ln \phi_i}{\partial P}\right)P + 1\right)RT/P

Returns

Vfloat: Molar volume, [m^3/mol]

V_gas()¶

Method to calculate and return the ideal-gas molar volume of the phase at the chosen reference temperature and pressure, according to the temperature variable T_gas_ref and pressure variable P_gas_ref of the thermo.bulk.BulkSettings.

V^{ig} = \frac{RT_{ref}}{P_{ref}}

Returns

V_gasfloat: Ideal gas molar volume at the reference temperature and pressure, [m^3/mol]

V_gas_normal()¶

Method to calculate and return the ideal-gas molar volume of the phase at the normal temperature and pressure, according to the temperature variable T_normal and pressure variable P_normal of the thermo.bulk.BulkSettings.

V^{ig} = \frac{RT_{norm}}{P_{norm}}

Returns

V_gas_normalfloat: Ideal gas molar volume at normal temperature and pressure, [m^3/mol]

V_gas_standard()¶

Method to calculate and return the ideal-gas molar volume of the phase at the standard temperature and pressure, according to the temperature variable T_standard and pressure variable P_standard of the thermo.bulk.BulkSettings.

V^{ig} = \frac{RT_{std}}{P_{std}}

Returns

V_gas_standardfloat: Ideal gas molar volume at standard temperature and pressure, [m^3/mol]

V_ideal_gas()[source]¶

Method to calculate and return the ideal-gas molar volume of the phase.

V^{ig} = \frac{RT}{P}

Returns

Vfloat: Ideal gas molar volume, [m^3/mol]

V_iter(force=False)[source]¶

Method to calculate and return the volume of the phase in a way suitable for a TV resolution to converge on the same pressure. This often means the return value of this method is an mpmath mpf. This dummy method simply returns the implemented V method.

Returns

Vfloat or mpf: Molar volume, [m^3/mol]

V_liquid_ref()¶

Method to calculate and return the liquid reference molar volume according to the temperature variable T_liquid_volume_ref of thermo.bulk.BulkSettings and the composition of the phase.

V = \sum_i z_i V_i

Returns

V_liquid_reffloat: Liquid molar volume at the reference condition, [m^3/mol]

V_mass()¶

Method to calculate and return the specific volume of the phase.

V_{mass} = \frac{1000\cdot VM}{MW}

Returns

V_massfloat: Specific volume of the phase, [m^3/kg]

V_phi_consistency()[source]¶

Method to calculate and return a consistency check between molar volume, and the fugacity coefficients’ pressures derivatives.

V^{\text{from phi P der}} = \left(\left(\sum_i z_i \frac{\partial \ln \phi_i}{\partial P}\right)P + 1\right)RT/P

Returns

errorfloat: Relative consistency error $|1 - V^{\text{from phi P der}}/V^\text{implemented}|$ , [-]

property Van_der_Waals_areas¶

Unnormalized Van der Waals areas for each component, [m^2/mol].

Returns

Van_der_Waals_areaslist[float]: Unnormalized Van der Waals areas for each component, [m^2/mol].

property Van_der_Waals_volumes¶

Unnormalized Van der Waals volumes for each component, [m^3/mol].

Returns

Van_der_Waals_volumeslist[float]: Unnormalized Van der Waals volumes for each component, [m^3/mol].

Vanadium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Vanadium, [atoms/s]

Vanadium_atom_flow()¶: Method to calculate and return the mole flow that is Vanadium, [mol/s]

Vanadium_atom_fraction()¶: Method to calculate and return the mole fraction that is Vanadium element, [-]

Vanadium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Vanadium element, [kg/s]

Vanadium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Vanadium element, [-]

property Vcs¶

Critical molar volumes for each component, [m^3/mol].

Returns

Vcslist[float]: Critical molar volumes for each component, [m^3/mol].

Vfgs()¶

Method to calculate and return the ideal-gas volume fractions of the components of the phase. This is the same as the mole fractions.

Returns

Vfgslist[float]: Ideal-gas volume fractions of the components of the phase, [-]

property Vfgs_calc¶

Vfls()¶

Method to calculate and return the ideal-liquid volume fractions of the components of the phase, using the standard liquid densities at the temperature variable T_liquid_volume_ref of thermo.bulk.BulkSettings and the composition of the phase.

Returns

Vflslist[float]: Ideal-liquid volume fractions of the components of the phase, [-]

property Vfls_calc¶

Vls()¶

Method to calculate and return the pure-component liquid temperature-dependent molar volume of each species from the thermo.volume.VolumeLiquid objects.

These values are normally along the saturation line.

Returns

Vlslist[float]: Pure component temperature dependent liquid molar volume, [m^3/mol]

Vmc()[source]¶

Method to calculate and return the mechanical critical volume of the phase.

Returns

Vmcfloat: Mechanical critical volume, [m^3/mol]

property Vmg_STPs¶

Gas molar volumes for each component at STP; metastable if normally another state, [m^3/mol].

Returns

Vmg_STPslist[float]: Gas molar volumes for each component at STP; metastable if normally another state, [m^3/mol].

property Vml_60Fs¶

Liquid molar volumes for each component at 60 °F, [m^3/mol].

Returns

Vml_60Fslist[float]: Liquid molar volumes for each component at 60 °F, [m^3/mol].

property Vml_STPs¶

Liquid molar volumes for each component at STP, [m^3/mol].

Returns

Vml_STPslist[float]: Liquid molar volumes for each component at STP, [m^3/mol].

property Vml_Tms¶

Liquid molar volumes for each component at their respective melting points, [m^3/mol].

Returns

Vml_Tmslist[float]: Liquid molar volumes for each component at their respective melting points, [m^3/mol].

property Vms_Tms¶

Solid molar volumes for each component at their respective melting points, [m^3/mol].

Returns

Vms_Tmslist[float]: Solid molar volumes for each component at their respective melting points, [m^3/mol].

Vss()¶

Method to calculate and return the pure-component solid temperature-dependent molar volume of each species from the thermo.volume.VolumeSolid objects.

Returns

Vsslist[float]: Pure component temperature dependent solid molar volume, [m^3/mol]

Wobbe_index()¶

Method to calculate and return the molar Wobbe index of the object, [J/mol].

I_W = \frac{H_{comb}^{higher}}{\sqrt{\text{SG}}}

Returns

Wobbe_indexfloat: Molar Wobbe index, [J/(mol)]

Wobbe_index_lower()¶

Method to calculate and return the molar lower Wobbe index of the: object, [J/mol].

I_W = \frac{H_{comb}^{lower}}{\sqrt{\text{SG}}}

Returns

Wobbe_index_lowerfloat: Molar lower Wobbe index, [J/(mol)]

Wobbe_index_lower_mass()¶

Method to calculate and return the lower mass Wobbe index of the object, [J/kg].

I_W = \frac{H_{comb}^{lower}}{\sqrt{\text{SG}}}

Returns

Wobbe_index_lower_massfloat: Mass lower Wobbe index, [J/(kg)]

Wobbe_index_lower_normal()¶

Method to calculate and return the volumetric normal lower Wobbe index of the object, [J/m^3]. The normal gas volume is used in this calculation.

I_W = \frac{H_{comb}^{lower}}{\sqrt{\text{SG}}}

Returns

Wobbe_index_lower_normalfloat: Volumetric normal lower Wobbe index, [J/(m^3)]

Wobbe_index_lower_standard()¶

Method to calculate and return the volumetric standard lower Wobbe index of the object, [J/m^3]. The standard gas volume is used in this calculation.

I_W = \frac{H_{comb}^{lower}}{\sqrt{\text{SG}}}

Returns

Wobbe_index_lower_standardfloat: Volumetric standard lower Wobbe index, [J/(m^3)]

Wobbe_index_mass()¶

Method to calculate and return the mass Wobbe index of the object, [J/kg].

I_W = \frac{H_{comb}^{higher}}{\sqrt{\text{SG}}}

Returns

Wobbe_index_massfloat: Mass Wobbe index, [J/(kg)]

Wobbe_index_normal()¶

Method to calculate and return the volumetric normal Wobbe index of the object, [J/m^3]. The normal gas volume is used in this calculation.

I_W = \frac{H_{comb}^{higher}}{\sqrt{\text{SG}}}

Returns

Wobbe_indexfloat: Volumetric normal Wobbe index, [J/(m^3)]

Wobbe_index_standard()¶

Method to calculate and return the volumetric standard Wobbe index of the object, [J/m^3]. The standard gas volume is used in this calculation.

I_W = \frac{H_{comb}^{higher}}{\sqrt{\text{SG}}}

Returns

Wobbe_index_standardfloat: Volumetric standard Wobbe index, [J/(m^3)]

Xenon_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Xenon, [atoms/s]

Xenon_atom_flow()¶: Method to calculate and return the mole flow that is Xenon, [mol/s]

Xenon_atom_fraction()¶: Method to calculate and return the mole fraction that is Xenon element, [-]

Xenon_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Xenon element, [kg/s]

Xenon_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Xenon element, [-]

Ytterbium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Ytterbium, [atoms/s]

Ytterbium_atom_flow()¶: Method to calculate and return the mole flow that is Ytterbium, [mol/s]

Ytterbium_atom_fraction()¶: Method to calculate and return the mole fraction that is Ytterbium element, [-]

Ytterbium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Ytterbium element, [kg/s]

Ytterbium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Ytterbium element, [-]

Yttrium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Yttrium, [atoms/s]

Yttrium_atom_flow()¶: Method to calculate and return the mole flow that is Yttrium, [mol/s]

Yttrium_atom_fraction()¶: Method to calculate and return the mole fraction that is Yttrium element, [-]

Yttrium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Yttrium element, [kg/s]

Yttrium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Yttrium element, [-]

Z()[source]¶

Method to calculate and return the compressibility factor of the phase.

Z = \frac{PV}{RT}

Returns

Zfloat: Compressibility factor, [-]

property Zcs¶

Critical compressibilities for each component, [-].

Returns

Zcslist[float]: Critical compressibilities for each component, [-].

Zinc_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Zinc, [atoms/s]

Zinc_atom_flow()¶: Method to calculate and return the mole flow that is Zinc, [mol/s]

Zinc_atom_fraction()¶: Method to calculate and return the mole fraction that is Zinc element, [-]

Zinc_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Zinc element, [kg/s]

Zinc_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Zinc element, [-]

Zirconium_atom_count_flow()¶: Method to calculate and return the number of atoms in the flow which are Zirconium, [atoms/s]

Zirconium_atom_flow()¶: Method to calculate and return the mole flow that is Zirconium, [mol/s]

Zirconium_atom_fraction()¶: Method to calculate and return the mole fraction that is Zirconium element, [-]

Zirconium_atom_mass_flow()¶: Method to calculate and return the mass flow of atoms that are Zirconium element, [kg/s]

Zirconium_atom_mass_fraction()¶: Method to calculate and return the mass fraction of the phase that is Zirconium element, [-]

Zmc()[source]¶

Method to calculate and return the mechanical critical compressibility of the phase.

Returns

Zmcfloat: Mechanical critical compressibility, [-]

__eq__(other)[source]¶: Return self==value.

__hash__()[source]¶

Method to calculate and return a hash representing the exact state of the object.

Returns

hashint: Hash of the object, [-]

activities()[source]¶

Method to calculate and return the activities of each component in the phase [-].

a_i(T, P, x; f_i^0) = \frac{f_i(T, P, x)}{f_i^0(T, P_i^0)}

Returns

activitieslist[float]: Activities, [-]

property aliases¶

Aliases for each component, [-].

Returns

aliaseslist[str]: Aliases for each component, [-].

alpha()[source]¶

Method to calculate and return the thermal diffusivity of the phase.

\alpha = \frac{k}{\rho Cp}

Returns

alphafloat: Thermal diffusivity, [m^2/s]

ammonia_molar_weight()¶

Method to calculate and return the effective quantiy of ammonia in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the ammonia component.

ammonia_partial_pressure()¶: Method to calculate and return the ideal partial pressure of ammonia, [Pa]

argon_molar_weight()¶

Method to calculate and return the effective quantiy of argon in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the argon component.

argon_partial_pressure()¶: Method to calculate and return the ideal partial pressure of argon, [Pa]

as_EquilibriumState(flasher=None)[source]¶

as_EquilibriumStream(flasher=None, n=None)[source]¶

as_json()[source]¶

Method to create a JSON-friendly serialization of the phase which can be stored, and reloaded later.

Returns

json_reprdict: JSON-friendly representation, [-]

Examples

>>> import json
>>> from thermo import IAPWS95Liquid
>>> phase = IAPWS95Liquid(T=300, P=1e5, zs=[1])
>>> new_phase = Phase.from_json(json.loads(json.dumps(phase.as_json())))
>>> assert phase == new_phase

atom_content()¶

Method to calculate and return the number of moles of each atom in the phase per mole of the phase; returns a dictionary of atom counts, containing only those elements who are present.

Returns

atom_contentdict[str: float]: Atom counts, [-]

atom_count_flows()¶

Method to calculate and return the atom count flow rates of the phase; returns a dictionary of atom count flows, containing only those elements who are present.

Returns

atom_count_flowsdict[str: float]: Atom flows, [atoms/s]

atom_flows()¶

Method to calculate and return the atomic flow rates of the phase; returns a dictionary of atom flows, containing only those elements who are present.

Returns

atom_flowsdict[str: float]: Atom flows, [mol/s]

atom_fractions()¶

Method to calculate and return the atomic composition of the phase; returns a dictionary of atom fraction (by count), containing only those elements who are present.

Returns

atom_fractionsdict[str: float]: Atom fractions, [-]

atom_mass_flows()¶

Method to calculate and return the atomic mass flow rates of the phase; returns a dictionary of atom mass flows, containing only those elements who are present.

Returns

atom_mass_flowsdict[str: float]: Atom mass flows, [kg/s]

atom_mass_fractions()¶

Method to calculate and return the atomic mass fractions of the phase; returns a dictionary of atom fraction (by mass), containing only those elements who arxe present.

Returns

atom_mass_fractionsdict[str: float]: Atom mass fractions, [-]

property atomss¶

Breakdown of each component into its elements and their counts, as a dict, [-].

Returns

atomsslist[dict]: Breakdown of each component into its elements and their counts, as a dict, [-].

property beta¶

Method to return the phase fraction of this phase. This method is only available when the phase is linked to an EquilibriumState.

Returns

betafloat: Phase fraction on a molar basis, [-]

property beta_mass¶

Method to return the mass phase fraction of this phase. This method is only available when the phase is linked to an EquilibriumState.

Returns

beta_massfloat: Phase fraction on a mass basis, [-]

property beta_volume¶

Method to return the volumetric phase fraction of this phase. This method is only available when the phase is linked to an EquilibriumState.

Returns

beta_volumefloat: Phase fraction on a volumetric basis, [-]

property beta_volume_liquid_ref¶

Method to return the standard liquid volume fraction of this phase. This method is only available when the phase is linked to an EquilibriumState.

Returns

beta_volumefloat: Phase fraction on a volumetric basis, [-]

bulk_phase_type = False¶

carbon_dioxide_molar_weight()¶

Method to calculate and return the effective quantiy of carbon_dioxide in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the carbon_dioxide component.

carbon_dioxide_partial_pressure()¶: Method to calculate and return the ideal partial pressure of carbon_dioxide, [Pa]

property charges¶

Charge number (valence) for each component, [-].

Returns

chargeslist[float]: Charge number (valence) for each component, [-].

chemical_potential()[source]¶

Method to calculate and return the chemical potentials of each component in the phase [-]. For a pure substance, this is the molar Gibbs energy on a reactive basis.

\frac{\partial G}{\partial n_i}_{T, P, N_{j \ne i}}

Returns

chemical_potentiallist[float]: Chemical potentials, [J/mol]

composition_independent = False¶

concentrations()[source]¶

Method to return the molar concentrations of each component in the phase in units of mol/m^3. Molarity is a term used in chemistry for a similar concept, usually given in units of mol/L.

Returns

concentrationslist[float]: Molar concentrations of all the components in the phase, [mol/m^3]

concentrations_gas()[source]¶

Method to return the molar concentrations of each component in the phase in units of mol/m^3, using the ideal-gas molar volume of the phase at the chosen reference temperature and pressure.

Returns

concentrations_gaslist[float]: Molar concentrations of all the components in the phase, [mol/m^3]

concentrations_gas_normal()[source]¶

Method to return the molar concentrations of each component in the phase in units of mol/m^3, using the ideal-gas molar volume of the phase at the normal temperature and pressure.

Returns

concentrations_gas_normallist[float]: Molar concentrations of all the components in the phase, [mol/m^3]

concentrations_gas_standard()[source]¶

Method to return the molar concentrations of each component in the phase in units of mol/m^3, using the ideal-gas molar volume of the phase at the standard temperature and pressure.

Returns

concentrations_gas_standardlist[float]: Molar concentrations of all the components in the phase, [mol/m^3]

concentrations_mass()[source]¶

Method to return the mass concentrations of each component in the phase in units of kg/m^3.

Returns

concentrations_masslist[float]: Mass concentrations of all the components in the phase, [kg/m^3]

concentrations_mass_gas()[source]¶

Method to return the mass concentrations of each component in the phase in units of kg/m^3, using the ideal-gas molar volume of the phase at the chosen reference temperature and pressure.

Returns

concentrations_mass_gaslist[float]: Mass concentrations of all the components in the phase, [kg/m^3]

concentrations_mass_gas_normal()[source]¶

Method to return the mass concentrations of each component in the phase in units of kg/m^3, using the ideal-gas molar volume of the phase at the normal temperature and pressure.

Returns

concentrations_mass_gas_normallist[float]: Mass concentrations of all the components in the phase, [kg/m^3]

concentrations_mass_gas_standard()[source]¶

Method to return the mass concentrations of each component in the phase in units of kg/m^3, using the ideal-gas molar volume of the phase at the standard temperature and pressure.

Returns

concentrations_mass_gas_standardlist[float]: Mass concentrations of all the components in the phase, [kg/m^3]

property conductivities¶

Electrical conductivities for each component, [S/m].

Returns

conductivitieslist[float]: Electrical conductivities for each component, [S/m].

property conductivity_Ts¶

Temperatures at which the electrical conductivities for each component were measured, [K].

Returns

conductivity_Tslist[float]: Temperatures at which the electrical conductivities for each component were measured, [K].

constants¶

correlations¶

d2G_mass_dP2(prop='d2G_dP2')¶

d2G_mass_dPdT(prop='d2G_dPdT')¶

d2G_mass_dT2(prop='d2G_dT2')¶

d2G_mass_dTdP(prop='d2G_dTdP')¶

d2P_dT2()[source]¶

Method to calculate and return the second temperature derivative of pressure of the phase.

Returns

d2P_dT2float: Second temperature derivative of pressure, [Pa/K^2]

d2P_dTdV()[source]¶

Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.

Returns

d2P_dTdVfloat: Second volume derivative of pressure, [mol*Pa^2/(J*K)]

d2P_dTdrho()[source]¶

Method to calculate and return the temperature derivative and then molar density derivative of the pressure of the phase.

\frac{\partial^2 P}{\partial T \partial \rho} = -V^2 \left(\frac{\partial^2 P}{\partial T \partial V}\right)

Returns

d2P_dTdrhofloat: Temperature derivative and then molar density derivative of the pressure, [Pa*m^3/(K*mol)]

d2P_dV2()[source]¶

Method to calculate and return the second volume derivative of pressure of the phase.

Returns

d2P_dV2float: Second volume derivative of pressure, [Pa*mol^2/m^6]

d2P_dVdT()[source]¶

Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase. This is an alias of d2P_dTdV.

\frac{\partial^2 P}{\partial V \partial T}

Returns

d2P_dVdTfloat: Second volume derivative of pressure, [mol*Pa^2/(J*K)]

d2P_drho2()[source]¶

Method to calculate and return the second molar density derivative of pressure of the phase.

\frac{\partial^2 P}{\partial \rho^2} = -V^2\left( -V^2 \left(\frac{\partial^2 P}{\partial V^2}\right)_T -2 V \left(\frac{\partial P}{\partial V}\right)_T \right)

Returns

d2P_drho2float: Second molar density derivative of pressure, [Pa*m^6/mol^2]

d2T_dP2()[source]¶

Method to calculate and return the constant-volume second pressure derivative of temperature of the phase.

\left(\frac{\partial^2 T}{\partial P^2}\right)_V = -\left(\frac{\partial^2 P}{\partial T^2}\right)_V \left(\frac{\partial T}{\partial P}\right)_V^3

Returns

d2T_dP2float: Constant-volume second pressure derivative of temperature, [K/Pa^2]

d2T_dP2_V()¶

Method to calculate and return the constant-volume second pressure derivative of temperature of the phase.

\left(\frac{\partial^2 T}{\partial P^2}\right)_V = -\left(\frac{\partial^2 P}{\partial T^2}\right)_V \left(\frac{\partial T}{\partial P}\right)_V^3

Returns

d2T_dP2float: Constant-volume second pressure derivative of temperature, [K/Pa^2]

d2T_dPdV()[source]¶

Method to calculate and return the derivative of pressure and then the derivative of volume of temperature of the phase.

\left(\frac{\partial^2 T}{\partial P\partial V}\right) = - \left[\left(\frac{\partial^2 P}{\partial T \partial V}\right) \left(\frac{\partial P}{\partial T}\right)_V - \left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial^2 P}{\partial T^2}\right)_V \right]\left(\frac{\partial P}{\partial T}\right)_V^{-3}

Returns

d2T_dPdVfloat: Derivative of pressure and then the derivative of volume of temperature, [K*mol/(Pa*m^3)]

d2T_dPdrho()[source]¶

Method to calculate and return the pressure derivative and then molar density derivative of the temperature of the phase.

\frac{\partial^2 T}{\partial P \partial \rho} = -V^2 \left(\frac{\partial^2 T}{\partial P \partial V}\right)

Returns

d2T_dPdrhofloat: Pressure derivative and then molar density derivative of the temperature, [K*m^3/(Pa*mol)]

d2T_dV2()[source]¶

Method to calculate and return the constant-pressure second volume derivative of temperature of the phase.

\left(\frac{\partial^2 T}{\partial V^2}\right)_P = -\left[ \left(\frac{\partial^2 P}{\partial V^2}\right)_T \left(\frac{\partial P}{\partial T}\right)_V - \left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial^2 P}{\partial T \partial V}\right) \right] \left(\frac{\partial P}{\partial T}\right)^{-2}_V + \left[\left(\frac{\partial^2 P}{\partial T\partial V}\right) \left(\frac{\partial P}{\partial T}\right)_V - \left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial^2 P}{\partial T^2}\right)_V\right] \left(\frac{\partial P}{\partial T}\right)_V^{-3} \left(\frac{\partial P}{\partial V}\right)_T

Returns

d2T_dV2float: Constant-pressure second volume derivative of temperature, [K*mol^2/m^6]

d2T_dV2_P()¶

Method to calculate and return the constant-pressure second volume derivative of temperature of the phase.

\left(\frac{\partial^2 T}{\partial V^2}\right)_P = -\left[ \left(\frac{\partial^2 P}{\partial V^2}\right)_T \left(\frac{\partial P}{\partial T}\right)_V - \left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial^2 P}{\partial T \partial V}\right) \right] \left(\frac{\partial P}{\partial T}\right)^{-2}_V + \left[\left(\frac{\partial^2 P}{\partial T\partial V}\right) \left(\frac{\partial P}{\partial T}\right)_V - \left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial^2 P}{\partial T^2}\right)_V\right] \left(\frac{\partial P}{\partial T}\right)_V^{-3} \left(\frac{\partial P}{\partial V}\right)_T

Returns

d2T_dV2float: Constant-pressure second volume derivative of temperature, [K*mol^2/m^6]

d2T_dVdP()¶

Method to calculate and return the derivative of pressure and then the derivative of volume of temperature of the phase.

\left(\frac{\partial^2 T}{\partial P\partial V}\right) = - \left[\left(\frac{\partial^2 P}{\partial T \partial V}\right) \left(\frac{\partial P}{\partial T}\right)_V - \left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial^2 P}{\partial T^2}\right)_V \right]\left(\frac{\partial P}{\partial T}\right)_V^{-3}

Returns

d2T_dPdVfloat: Derivative of pressure and then the derivative of volume of temperature, [K*mol/(Pa*m^3)]

d2T_drho2()[source]¶

Method to calculate and return the second molar density derivative of temperature of the phase.

\frac{\partial^2 T}{\partial \rho^2} = -V^2\left( -V^2 \left(\frac{\partial^2 T}{\partial V^2}\right)_P -2 V \left(\frac{\partial T}{\partial V}\right)_P \right)

Returns

d2T_drho2float: Second molar density derivative of temperature, [K*m^6/mol^2]

d2V_dP2()[source]¶

Method to calculate and return the constant-temperature pressure derivative of volume of the phase.

\left(\frac{\partial^2 V}{\partial P^2}\right)_T = -\frac{\left(\frac{\partial^2 P}{\partial V^2}\right)_T} {\left(\frac{\partial P}{\partial V}\right)_T^3}

Returns

d2V_dP2float: Constant-temperature pressure derivative of volume, [m^3/(mol*Pa^2)]

d2V_dP2_T()¶

Method to calculate and return the constant-temperature pressure derivative of volume of the phase.

\left(\frac{\partial^2 V}{\partial P^2}\right)_T = -\frac{\left(\frac{\partial^2 P}{\partial V^2}\right)_T} {\left(\frac{\partial P}{\partial V}\right)_T^3}

Returns

d2V_dP2float: Constant-temperature pressure derivative of volume, [m^3/(mol*Pa^2)]

d2V_dPdT()[source]¶

Method to calculate and return the derivative of pressure and then the derivative of temperature of volume of the phase.

\left(\frac{\partial^2 V}{\partial T\partial P}\right) = - \left[\left(\frac{\partial^2 P}{\partial T \partial V}\right) \left(\frac{\partial P}{\partial V}\right)_T - \left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial^2 P}{\partial V^2}\right)_T \right]\left(\frac{\partial P}{\partial V}\right)_T^{-3}

Returns

d2V_dPdTfloat: Derivative of pressure and then the derivative of temperature of volume, [m^3/(mol*K*Pa)]

d2V_dT2()[source]¶

Method to calculate and return the constant-pressure second temperature derivative of volume of the phase.

\left(\frac{\partial^2 V}{\partial T^2}\right)_P = -\left[ \left(\frac{\partial^2 P}{\partial T^2}\right)_V \left(\frac{\partial P}{\partial V}\right)_T - \left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial^2 P}{\partial T \partial V}\right) \right] \left(\frac{\partial P}{\partial V}\right)^{-2}_T + \left[\left(\frac{\partial^2 P}{\partial T\partial V}\right) \left(\frac{\partial P}{\partial V}\right)_T - \left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial^2 P}{\partial V^2}\right)_T\right] \left(\frac{\partial P}{\partial V}\right)_T^{-3} \left(\frac{\partial P}{\partial T}\right)_V

Returns

d2V_dT2float: Constant-pressure second temperature derivative of volume, [m^3/(mol*K^2)]

d2V_dT2_P()¶

Method to calculate and return the constant-pressure second temperature derivative of volume of the phase.

\left(\frac{\partial^2 V}{\partial T^2}\right)_P = -\left[ \left(\frac{\partial^2 P}{\partial T^2}\right)_V \left(\frac{\partial P}{\partial V}\right)_T - \left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial^2 P}{\partial T \partial V}\right) \right] \left(\frac{\partial P}{\partial V}\right)^{-2}_T + \left[\left(\frac{\partial^2 P}{\partial T\partial V}\right) \left(\frac{\partial P}{\partial V}\right)_T - \left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial^2 P}{\partial V^2}\right)_T\right] \left(\frac{\partial P}{\partial V}\right)_T^{-3} \left(\frac{\partial P}{\partial T}\right)_V

Returns

d2V_dT2float: Constant-pressure second temperature derivative of volume, [m^3/(mol*K^2)]

d2V_dTdP()¶

Method to calculate and return the derivative of pressure and then the derivative of temperature of volume of the phase.

\left(\frac{\partial^2 V}{\partial T\partial P}\right) = - \left[\left(\frac{\partial^2 P}{\partial T \partial V}\right) \left(\frac{\partial P}{\partial V}\right)_T - \left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial^2 P}{\partial V^2}\right)_T \right]\left(\frac{\partial P}{\partial V}\right)_T^{-3}

Returns

d2V_dPdTfloat: Derivative of pressure and then the derivative of temperature of volume, [m^3/(mol*K*Pa)]

d2rho_dP2()[source]¶

Method to calculate and return the second pressure derivative of molar density of the phase.

\frac{\partial^2 \rho}{\partial P^2} = -\frac{1}{V^2} \left(\frac{\partial^2 V}{\partial P^2}\right)_T + \frac{2}{V^3} \left(\frac{\partial V}{\partial P}\right)_T^2

Returns

d2rho_dP2float: Second pressure derivative of molar density, [mol^2/(Pa*m^6)]

d2rho_dPdT()[source]¶

Method to calculate and return the pressure derivative and then temperature derivative of the molar density of the phase.

\frac{\partial^2 \rho}{\partial P \partial T} = -\frac{1}{V^2} \left(\frac{\partial^2 V}{\partial P \partial T}\right) + \frac{2}{V^3} \left(\frac{\partial V}{\partial T}\right)_P \left(\frac{\partial V}{\partial P}\right)_T

Returns

d2rho_dPdTfloat: Pressure derivative and then temperature derivative of the molar density, [mol/(m^3*K*Pa)]

d2rho_dT2()[source]¶

Method to calculate and return the second temperature derivative of molar density of the phase.

\frac{\partial^2 \rho}{\partial T^2} = -\frac{1}{V^2} \left(\frac{\partial^2 V}{\partial T^2}\right)_P + \frac{2}{V^3} \left(\frac{\partial V}{\partial T}\right)_T^2

Returns

d2rho_dT2float: Second temperature derivative of molar density, [mol^2/(K*m^6)]

dA_dP()[source]¶

Method to calculate and return the constant-temperature pressure derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial P}\right)_{T} = -T \left(\frac{\partial S}{\partial P}\right)_{T} + \left(\frac{\partial U}{\partial P}\right)_{T}

Returns

dA_dPfloat: Constant-temperature pressure derivative of Helmholtz energy, [J/(mol*Pa)]

dA_dP_T()¶

Method to calculate and return the constant-temperature pressure derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial P}\right)_{T} = -T \left(\frac{\partial S}{\partial P}\right)_{T} + \left(\frac{\partial U}{\partial P}\right)_{T}

Returns

dA_dPfloat: Constant-temperature pressure derivative of Helmholtz energy, [J/(mol*Pa)]

dA_dP_V()[source]¶

Method to calculate and return the constant-volume pressure derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial P}\right)_{V} = \left(\frac{\partial H}{\partial P}\right)_{V} - V - S\left(\frac{\partial T}{\partial P}\right)_{V} -T \left(\frac{\partial S}{\partial P}\right)_{V}

Returns

dA_dP_Vfloat: Constant-volume pressure derivative of Helmholtz energy, [J/(mol*Pa)]

dA_dT()[source]¶

Method to calculate and return the constant-pressure temperature derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial T}\right)_{P} = -T \left(\frac{\partial S}{\partial T}\right)_{P} - S + \left(\frac{\partial U}{\partial T}\right)_{P}

Returns

dA_dTfloat: Constant-pressure temperature derivative of Helmholtz energy, [J/(mol*K)]

dA_dT_P()¶

Method to calculate and return the constant-pressure temperature derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial T}\right)_{P} = -T \left(\frac{\partial S}{\partial T}\right)_{P} - S + \left(\frac{\partial U}{\partial T}\right)_{P}

Returns

dA_dTfloat: Constant-pressure temperature derivative of Helmholtz energy, [J/(mol*K)]

dA_dT_V()[source]¶

Method to calculate and return the constant-volume temperature derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial T}\right)_{V} = \left(\frac{\partial H}{\partial T}\right)_{V} - V \left(\frac{\partial P}{\partial T}\right)_{V} - T \left(\frac{\partial S}{\partial T}\right)_{V} - S

Returns

dA_dT_Vfloat: Constant-volume temperature derivative of Helmholtz energy, [J/(mol*K)]

dA_dV_P()[source]¶

Method to calculate and return the constant-pressure volume derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial V}\right)_{P} = \left(\frac{\partial A}{\partial T}\right)_{P} \left(\frac{\partial T}{\partial V}\right)_{P}

Returns

dA_dV_Pfloat: Constant-pressure volume derivative of Helmholtz energy, [J/(m^3)]

dA_dV_T()[source]¶

Method to calculate and return the constant-temperature volume derivative of Helmholtz energy.

\left(\frac{\partial A}{\partial V}\right)_{T} = \left(\frac{\partial A}{\partial P}\right)_{T} \left(\frac{\partial P}{\partial V}\right)_{T}

Returns

dA_dV_Tfloat: Constant-temperature volume derivative of Helmholtz energy, [J/(m^3)]

dA_mass_dP(prop='dA_dP')¶

Method to calculate and return the pressure derivative of mass Helmholtz energy of the phase at constant temperature.

$\left(\frac{\partial A_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dA_mass_dPfloat: The pressure derivative of mass Helmholtz energy of the phase at constant temperature, [J/mol/Pa]

dA_mass_dP_T(prop='dA_dP_T')¶

Method to calculate and return the pressure derivative of mass Helmholtz energy of the phase at constant temperature.

$\left(\frac{\partial A_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dA_mass_dP_Tfloat: The pressure derivative of mass Helmholtz energy of the phase at constant temperature, [J/mol/Pa]

dA_mass_dP_V(prop='dA_dP_V')¶

Method to calculate and return the pressure derivative of mass Helmholtz energy of the phase at constant volume.

$\left(\frac{\partial A_{\text{mass}}}{\partial P}\right)_{V}$

Returns

dA_mass_dP_Vfloat: The pressure derivative of mass Helmholtz energy of the phase at constant volume, [J/mol/Pa]

dA_mass_dT(prop='dA_dT')¶

Method to calculate and return the temperature derivative of mass Helmholtz energy of the phase at constant pressure.

$\left(\frac{\partial A_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dA_mass_dTfloat: The temperature derivative of mass Helmholtz energy of the phase at constant pressure, [J/mol/K]

dA_mass_dT_P(prop='dA_dT_P')¶

Method to calculate and return the temperature derivative of mass Helmholtz energy of the phase at constant pressure.

$\left(\frac{\partial A_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dA_mass_dT_Pfloat: The temperature derivative of mass Helmholtz energy of the phase at constant pressure, [J/mol/K]

dA_mass_dT_V(prop='dA_dT_V')¶

Method to calculate and return the temperature derivative of mass Helmholtz energy of the phase at constant volume.

$\left(\frac{\partial A_{\text{mass}}}{\partial T}\right)_{V}$

Returns

dA_mass_dT_Vfloat: The temperature derivative of mass Helmholtz energy of the phase at constant volume, [J/mol/K]

dA_mass_dV_P(prop='dA_dV_P')¶

Method to calculate and return the volume derivative of mass Helmholtz energy of the phase at constant pressure.

$\left(\frac{\partial A_{\text{mass}}}{\partial V}\right)_{P}$

Returns

dA_mass_dV_Pfloat: The volume derivative of mass Helmholtz energy of the phase at constant pressure, [J/mol/m^3/mol]

dA_mass_dV_T(prop='dA_dV_T')¶

Method to calculate and return the volume derivative of mass Helmholtz energy of the phase at constant temperature.

$\left(\frac{\partial A_{\text{mass}}}{\partial V}\right)_{T}$

Returns

dA_mass_dV_Tfloat: The volume derivative of mass Helmholtz energy of the phase at constant temperature, [J/mol/m^3/mol]

dCpigs_dT_pure()[source]¶

Method to calculate and return the first temperature derivative of ideal-gas heat capacities of every component in the phase. This method is powered by the HeatCapacityGases objects, except when all components have the same heat capacity form and a fast implementation has been written for it (currently only polynomials).

\frac{\partial C_p^{ig}}{\partial T}

Returns

dCp_ig_dTlist[float]: First temperature derivatives of molar ideal gas heat capacities, [J/(mol*K^2)]

dCv_dP_T()[source]¶

Method to calculate the pressure derivative of Cv, constant volume heat capacity, at constant temperature.

\left(\frac{\partial C_v}{\partial P}\right)_T = - T \operatorname{dPdT_{V}}{\left(P \right)} \frac{d}{d P} \operatorname{dVdT_{P}}{\left(P \right)} - T \operatorname{ dVdT_{P}}{\left(P \right)} \frac{d}{d P} \operatorname{dPdT_{V}} {\left(P \right)} + \frac{d}{d P} \operatorname{Cp}{\left(P\right)}

Returns

dCv_dP_Tfloat: Pressure derivative of constant volume heat capacity at constant temperature, [J/mol/K/Pa]

Notes

Requires d2V_dTdP, d2P_dTdP, and d2H_dTdP.

dCv_dT_P()[source]¶

Method to calculate the temperature derivative of Cv, constant volume heat capacity, at constant pressure.

\left(\frac{\partial C_v}{\partial T}\right)_P = - \frac{T \operatorname{dPdT_{V}}^{2}{\left(T \right)} \frac{d}{dT} \operatorname{dPdV_{T}}{\left(T \right)}}{\operatorname{dPdV_{T}}^{2} {\left(T \right)}} + \frac{2 T \operatorname{dPdT_{V}}{\left(T \right)} \frac{d}{d T} \operatorname{dPdT_{V}}{\left(T \right)}} {\operatorname{dPdV_{T}}{\left(T \right)}} + \frac{\operatorname{ dPdT_{V}}^{2}{\left(T \right)}}{\operatorname{dPdV_{T}}{\left(T \right)}} + \frac{d}{d T} \operatorname{Cp}{\left(T \right)}

Returns

dCv_dT_Pfloat: Temperature derivative of constant volume heat capacity at constant pressure, [J/mol/K^2]

Notes

Requires d2P_dT2_PV, d2P_dVdT_TP, and d2H_dT2.

dCv_mass_dP_T(prop='dCv_dP_T')¶

Method to calculate and return the pressure derivative of mass Constant-volume heat capacity of the phase at constant temperature.

$\left(\frac{\partial Cv_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dCv_mass_dP_Tfloat: The pressure derivative of mass Constant-volume heat capacity of the phase at constant temperature, [J/(mol*K)/Pa]

dCv_mass_dT_P(prop='dCv_dT_P')¶

Method to calculate and return the temperature derivative of mass Constant-volume heat capacity of the phase at constant pressure.

$\left(\frac{\partial Cv_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dCv_mass_dT_Pfloat: The temperature derivative of mass Constant-volume heat capacity of the phase at constant pressure, [J/(mol*K)/K]

dG_dP()[source]¶

Method to calculate and return the constant-temperature pressure derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial P}\right)_{T} = -T\left(\frac{\partial S}{\partial P}\right)_{T} + \left(\frac{\partial H}{\partial P}\right)_{T}

Returns

dG_dPfloat: Constant-temperature pressure derivative of Gibbs free energy, [J/(mol*Pa)]

dG_dP_T()¶

Method to calculate and return the constant-temperature pressure derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial P}\right)_{T} = -T\left(\frac{\partial S}{\partial P}\right)_{T} + \left(\frac{\partial H}{\partial P}\right)_{T}

Returns

dG_dPfloat: Constant-temperature pressure derivative of Gibbs free energy, [J/(mol*Pa)]

dG_dP_V()[source]¶

Method to calculate and return the constant-volume pressure derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial P}\right)_{V} = -T\left(\frac{\partial S}{\partial P}\right)_{V} - S \left(\frac{\partial T}{\partial P}\right)_{V} + \left(\frac{\partial H}{\partial P}\right)_{V}

Returns

dG_dP_Vfloat: Constant-volume pressure derivative of Gibbs free energy, [J/(mol*Pa)]

dG_dT()[source]¶

Method to calculate and return the constant-pressure temperature derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial T}\right)_{P} = -T\left(\frac{\partial S}{\partial T}\right)_{P} - S + \left(\frac{\partial H}{\partial T}\right)_{P}

Returns

dG_dTfloat: Constant-pressure temperature derivative of Gibbs free energy, [J/(mol*K)]

dG_dT_P()¶

Method to calculate and return the constant-pressure temperature derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial T}\right)_{P} = -T\left(\frac{\partial S}{\partial T}\right)_{P} - S + \left(\frac{\partial H}{\partial T}\right)_{P}

Returns

dG_dTfloat: Constant-pressure temperature derivative of Gibbs free energy, [J/(mol*K)]

dG_dT_V()[source]¶

Method to calculate and return the constant-volume temperature derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial T}\right)_{V} = -T\left(\frac{\partial S}{\partial T}\right)_{V} - S + \left(\frac{\partial H}{\partial T}\right)_{V}

Returns

dG_dT_Vfloat: Constant-volume temperature derivative of Gibbs free energy, [J/(mol*K)]

dG_dV_P()[source]¶

Method to calculate and return the constant-pressure volume derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial V}\right)_{P} = \left(\frac{\partial G}{\partial T}\right)_{P} \left(\frac{\partial T}{\partial V}\right)_{P}

Returns

dG_dV_Pfloat: Constant-pressure volume derivative of Gibbs free energy, [J/(m^3)]

dG_dV_T()[source]¶

Method to calculate and return the constant-temperature volume derivative of Gibbs free energy.

\left(\frac{\partial G}{\partial V}\right)_{T} = \left(\frac{\partial G}{\partial P}\right)_{T} \left(\frac{\partial P}{\partial V}\right)_{T}

Returns

dG_dV_Tfloat: Constant-temperature volume derivative of Gibbs free energy, [J/(m^3)]

dG_mass_dP(prop='dG_dP')¶

Method to calculate and return the pressure derivative of mass Gibbs free energy of the phase at constant temperature.

$\left(\frac{\partial G_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dG_mass_dPfloat: The pressure derivative of mass Gibbs free energy of the phase at constant temperature, [J/mol/Pa]

dG_mass_dP_T(prop='dG_dP_T')¶

Method to calculate and return the pressure derivative of mass Gibbs free energy of the phase at constant temperature.

$\left(\frac{\partial G_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dG_mass_dP_Tfloat: The pressure derivative of mass Gibbs free energy of the phase at constant temperature, [J/mol/Pa]

dG_mass_dP_V(prop='dG_dP_V')¶

Method to calculate and return the pressure derivative of mass Gibbs free energy of the phase at constant volume.

$\left(\frac{\partial G_{\text{mass}}}{\partial P}\right)_{V}$

Returns

dG_mass_dP_Vfloat: The pressure derivative of mass Gibbs free energy of the phase at constant volume, [J/mol/Pa]

dG_mass_dT(prop='dG_dT')¶

Method to calculate and return the temperature derivative of mass Gibbs free energy of the phase at constant pressure.

$\left(\frac{\partial G_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dG_mass_dTfloat: The temperature derivative of mass Gibbs free energy of the phase at constant pressure, [J/mol/K]

dG_mass_dT_P(prop='dG_dT_P')¶

Method to calculate and return the temperature derivative of mass Gibbs free energy of the phase at constant pressure.

$\left(\frac{\partial G_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dG_mass_dT_Pfloat: The temperature derivative of mass Gibbs free energy of the phase at constant pressure, [J/mol/K]

dG_mass_dT_V(prop='dG_dT_V')¶

Method to calculate and return the temperature derivative of mass Gibbs free energy of the phase at constant volume.

$\left(\frac{\partial G_{\text{mass}}}{\partial T}\right)_{V}$

Returns

dG_mass_dT_Vfloat: The temperature derivative of mass Gibbs free energy of the phase at constant volume, [J/mol/K]

dG_mass_dV_P(prop='dG_dV_P')¶

Method to calculate and return the volume derivative of mass Gibbs free energy of the phase at constant pressure.

$\left(\frac{\partial G_{\text{mass}}}{\partial V}\right)_{P}$

Returns

dG_mass_dV_Pfloat: The volume derivative of mass Gibbs free energy of the phase at constant pressure, [J/mol/m^3/mol]

dG_mass_dV_T(prop='dG_dV_T')¶

Method to calculate and return the volume derivative of mass Gibbs free energy of the phase at constant temperature.

$\left(\frac{\partial G_{\text{mass}}}{\partial V}\right)_{T}$

Returns

dG_mass_dV_Tfloat: The volume derivative of mass Gibbs free energy of the phase at constant temperature, [J/mol/m^3/mol]

dH_dP_T()[source]¶

Method to calculate and return the pressure derivative of enthalpy of the phase at constant pressure.

Returns

dH_dP_Tfloat: Pressure derivative of enthalpy, [J/(mol*Pa)]

dH_dT_P()[source]¶

Method to calculate and return the temperature derivative of enthalpy of the phase at constant pressure.

Returns

dH_dT_Pfloat: Temperature derivative of enthalpy, [J/(mol*K)]

dH_dns()[source]¶

Method to calculate and return the mole number derivative of the enthalpy of the phase.

\frac{\partial H}{\partial n_i}

Returns

dH_dnslist[float]: Mole number derivatives of the enthalpy of the phase, [J/mol^2]

dH_mass_dP(prop='dH_dP')¶

Method to calculate and return the pressure derivative of mass enthalpy of the phase at constant temperature.

$\left(\frac{\partial H_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dH_mass_dPfloat: The pressure derivative of mass enthalpy of the phase at constant temperature, [J/mol/Pa]

dH_mass_dP_T(prop='dH_dP_T')¶

Method to calculate and return the pressure derivative of mass enthalpy of the phase at constant temperature.

$\left(\frac{\partial H_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dH_mass_dP_Tfloat: The pressure derivative of mass enthalpy of the phase at constant temperature, [J/mol/Pa]

dH_mass_dP_V(prop='dH_dP_V')¶

Method to calculate and return the pressure derivative of mass enthalpy of the phase at constant volume.

$\left(\frac{\partial H_{\text{mass}}}{\partial P}\right)_{V}$

Returns

dH_mass_dP_Vfloat: The pressure derivative of mass enthalpy of the phase at constant volume, [J/mol/Pa]

dH_mass_dT(prop='dH_dT')¶

Method to calculate and return the temperature derivative of mass enthalpy of the phase at constant pressure.

$\left(\frac{\partial H_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dH_mass_dTfloat: The temperature derivative of mass enthalpy of the phase at constant pressure, [J/mol/K]

dH_mass_dT_P(prop='dH_dT_P')¶

Method to calculate and return the temperature derivative of mass enthalpy of the phase at constant pressure.

$\left(\frac{\partial H_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dH_mass_dT_Pfloat: The temperature derivative of mass enthalpy of the phase at constant pressure, [J/mol/K]

dH_mass_dT_V(prop='dH_dT_V')¶

Method to calculate and return the temperature derivative of mass enthalpy of the phase at constant volume.

$\left(\frac{\partial H_{\text{mass}}}{\partial T}\right)_{V}$

Returns

dH_mass_dT_Vfloat: The temperature derivative of mass enthalpy of the phase at constant volume, [J/mol/K]

dH_mass_dV_P(prop='dH_dV_P')¶

Method to calculate and return the volume derivative of mass enthalpy of the phase at constant pressure.

$\left(\frac{\partial H_{\text{mass}}}{\partial V}\right)_{P}$

Returns

dH_mass_dV_Pfloat: The volume derivative of mass enthalpy of the phase at constant pressure, [J/mol/m^3/mol]

dH_mass_dV_T(prop='dH_dV_T')¶

Method to calculate and return the volume derivative of mass enthalpy of the phase at constant temperature.

$\left(\frac{\partial H_{\text{mass}}}{\partial V}\right)_{T}$

Returns

dH_mass_dV_Tfloat: The volume derivative of mass enthalpy of the phase at constant temperature, [J/mol/m^3/mol]

dP_dP_A(property='P', differentiate_by='P', at_constant='A')¶

Method to calculate and return the pressure derivative of pressure of the phase at constant Helmholtz energy.

$\left(\frac{\partial P}{\partial P}\right)_{A}$

Returns

dP_dP_Afloat: The pressure derivative of pressure of the phase at constant Helmholtz energy, [Pa/Pa]

dP_dP_G(property='P', differentiate_by='P', at_constant='G')¶

Method to calculate and return the pressure derivative of pressure of the phase at constant Gibbs energy.

$\left(\frac{\partial P}{\partial P}\right)_{G}$

Returns

dP_dP_Gfloat: The pressure derivative of pressure of the phase at constant Gibbs energy, [Pa/Pa]

dP_dP_H(property='P', differentiate_by='P', at_constant='H')¶

Method to calculate and return the pressure derivative of pressure of the phase at constant enthalpy.

$\left(\frac{\partial P}{\partial P}\right)_{H}$

Returns

dP_dP_Hfloat: The pressure derivative of pressure of the phase at constant enthalpy, [Pa/Pa]

dP_dP_S(property='P', differentiate_by='P', at_constant='S')¶

Method to calculate and return the pressure derivative of pressure of the phase at constant entropy.

$\left(\frac{\partial P}{\partial P}\right)_{S}$

Returns

dP_dP_Sfloat: The pressure derivative of pressure of the phase at constant entropy, [Pa/Pa]

dP_dP_T()[source]¶

Method to calculate and return the pressure derivative of pressure of the phase at constant temperature.

Returns

dP_dP_Tfloat: Pressure derivative of pressure of the phase at constant temperature, [-]

dP_dP_U(property='P', differentiate_by='P', at_constant='U')¶

Method to calculate and return the pressure derivative of pressure of the phase at constant internal energy.

$\left(\frac{\partial P}{\partial P}\right)_{U}$

Returns

dP_dP_Ufloat: The pressure derivative of pressure of the phase at constant internal energy, [Pa/Pa]

dP_dP_V()[source]¶

Method to calculate and return the pressure derivative of pressure of the phase at constant volume.

Returns

dP_dP_Vfloat: Pressure derivative of pressure of the phase at constant volume, [-]

dP_dT()[source]¶

Method to calculate and return the first temperature derivative of pressure of the phase.

Returns

dP_dTfloat: First temperature derivative of pressure, [Pa/K]

dP_dT_A(property='P', differentiate_by='T', at_constant='A')¶

Method to calculate and return the temperature derivative of pressure of the phase at constant Helmholtz energy.

$\left(\frac{\partial P}{\partial T}\right)_{A}$

Returns

dP_dT_Afloat: The temperature derivative of pressure of the phase at constant Helmholtz energy, [Pa/K]

dP_dT_G(property='P', differentiate_by='T', at_constant='G')¶

Method to calculate and return the temperature derivative of pressure of the phase at constant Gibbs energy.

$\left(\frac{\partial P}{\partial T}\right)_{G}$

Returns

dP_dT_Gfloat: The temperature derivative of pressure of the phase at constant Gibbs energy, [Pa/K]

dP_dT_H(property='P', differentiate_by='T', at_constant='H')¶

Method to calculate and return the temperature derivative of pressure of the phase at constant enthalpy.

$\left(\frac{\partial P}{\partial T}\right)_{H}$

Returns

dP_dT_Hfloat: The temperature derivative of pressure of the phase at constant enthalpy, [Pa/K]

dP_dT_P()[source]¶

Method to calculate and return the temperature derivative of temperature of the phase at constant pressure.

Returns

dP_dT_Pfloat: Temperature derivative of temperature, [-]

dP_dT_S(property='P', differentiate_by='T', at_constant='S')¶

Method to calculate and return the temperature derivative of pressure of the phase at constant entropy.

$\left(\frac{\partial P}{\partial T}\right)_{S}$

Returns

dP_dT_Sfloat: The temperature derivative of pressure of the phase at constant entropy, [Pa/K]

dP_dT_U(property='P', differentiate_by='T', at_constant='U')¶

Method to calculate and return the temperature derivative of pressure of the phase at constant internal energy.

$\left(\frac{\partial P}{\partial T}\right)_{U}$

Returns

dP_dT_Ufloat: The temperature derivative of pressure of the phase at constant internal energy, [Pa/K]

dP_dV()[source]¶

Method to calculate and return the first volume derivative of pressure of the phase.

Returns

dP_dVfloat: First volume derivative of pressure, [Pa*mol/m^3]

dP_dV_A(property='P', differentiate_by='V', at_constant='A')¶

Method to calculate and return the volume derivative of pressure of the phase at constant Helmholtz energy.

$\left(\frac{\partial P}{\partial V}\right)_{A}$

Returns

dP_dV_Afloat: The volume derivative of pressure of the phase at constant Helmholtz energy, [Pa/m^3/mol]

dP_dV_G(property='P', differentiate_by='V', at_constant='G')¶

Method to calculate and return the volume derivative of pressure of the phase at constant Gibbs energy.

$\left(\frac{\partial P}{\partial V}\right)_{G}$

Returns

dP_dV_Gfloat: The volume derivative of pressure of the phase at constant Gibbs energy, [Pa/m^3/mol]

dP_dV_H(property='P', differentiate_by='V', at_constant='H')¶

Method to calculate and return the volume derivative of pressure of the phase at constant enthalpy.

$\left(\frac{\partial P}{\partial V}\right)_{H}$

Returns

dP_dV_Hfloat: The volume derivative of pressure of the phase at constant enthalpy, [Pa/m^3/mol]

dP_dV_P()[source]¶

Method to calculate and return the volume derivative of pressure of the phase at constant pressure.

Returns

dP_dV_Pfloat: Volume derivative of pressure of the phase at constant pressure, [Pa*mol/m^3]

dP_dV_S(property='P', differentiate_by='V', at_constant='S')¶

Method to calculate and return the volume derivative of pressure of the phase at constant entropy.

$\left(\frac{\partial P}{\partial V}\right)_{S}$

Returns

dP_dV_Sfloat: The volume derivative of pressure of the phase at constant entropy, [Pa/m^3/mol]

dP_dV_U(property='P', differentiate_by='V', at_constant='U')¶

Method to calculate and return the volume derivative of pressure of the phase at constant internal energy.

$\left(\frac{\partial P}{\partial V}\right)_{U}$

Returns

dP_dV_Ufloat: The volume derivative of pressure of the phase at constant internal energy, [Pa/m^3/mol]

dP_drho()[source]¶

Method to calculate and return the molar density derivative of pressure of the phase.

\frac{\partial P}{\partial \rho} = -V^2\left(\frac{\partial P}{\partial V}\right)_T

Returns

dP_drhofloat: Molar density derivative of pressure, [Pa*m^3/mol]

dP_drho_A(property='P', differentiate_by='rho', at_constant='A')¶

Method to calculate and return the density derivative of pressure of the phase at constant Helmholtz energy.

$\left(\frac{\partial P}{\partial \rho}\right)_{A}$

Returns

dP_drho_Afloat: The density derivative of pressure of the phase at constant Helmholtz energy, [Pa/mol/m^3]

dP_drho_G(property='P', differentiate_by='rho', at_constant='G')¶

Method to calculate and return the density derivative of pressure of the phase at constant Gibbs energy.

$\left(\frac{\partial P}{\partial \rho}\right)_{G}$

Returns

dP_drho_Gfloat: The density derivative of pressure of the phase at constant Gibbs energy, [Pa/mol/m^3]

dP_drho_H(property='P', differentiate_by='rho', at_constant='H')¶

Method to calculate and return the density derivative of pressure of the phase at constant enthalpy.

$\left(\frac{\partial P}{\partial \rho}\right)_{H}$

Returns

dP_drho_Hfloat: The density derivative of pressure of the phase at constant enthalpy, [Pa/mol/m^3]

dP_drho_S(property='P', differentiate_by='rho', at_constant='S')¶

Method to calculate and return the density derivative of pressure of the phase at constant entropy.

$\left(\frac{\partial P}{\partial \rho}\right)_{S}$

Returns

dP_drho_Sfloat: The density derivative of pressure of the phase at constant entropy, [Pa/mol/m^3]

dP_drho_U(property='P', differentiate_by='rho', at_constant='U')¶

Method to calculate and return the density derivative of pressure of the phase at constant internal energy.

$\left(\frac{\partial P}{\partial \rho}\right)_{U}$

Returns

dP_drho_Ufloat: The density derivative of pressure of the phase at constant internal energy, [Pa/mol/m^3]

dS_dP_T()[source]¶

Method to calculate and return the pressure derivative of entropy of the phase at constant pressure.

Returns

dS_dP_Tfloat: Pressure derivative of entropy, [J/(mol*K*Pa)]

dS_dV_P()[source]¶

Method to calculate and return the volume derivative of entropy of the phase at constant pressure.

Returns

dS_dV_Pfloat: Volume derivative of entropy, [J/(K*m^3)]

dS_dV_T()[source]¶

Method to calculate and return the volume derivative of entropy of the phase at constant temperature.

Returns

dS_dV_Tfloat: Volume derivative of entropy, [J/(K*m^3)]

dS_dns()[source]¶

Method to calculate and return the mole number derivative of the entropy of the phase.

\frac{\partial S}{\partial n_i}

Returns

dS_dnslist[float]: Mole number derivatives of the entropy of the phase, [J/(mol^2*K)]

dS_mass_dP(prop='dS_dP')¶

Method to calculate and return the pressure derivative of mass entropy of the phase at constant temperature.

$\left(\frac{\partial S_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dS_mass_dPfloat: The pressure derivative of mass entropy of the phase at constant temperature, [J/(mol*K)/Pa]

dS_mass_dP_T(prop='dS_dP_T')¶

Method to calculate and return the pressure derivative of mass entropy of the phase at constant temperature.

$\left(\frac{\partial S_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dS_mass_dP_Tfloat: The pressure derivative of mass entropy of the phase at constant temperature, [J/(mol*K)/Pa]

dS_mass_dP_V(prop='dS_dP_V')¶

Method to calculate and return the pressure derivative of mass entropy of the phase at constant volume.

$\left(\frac{\partial S_{\text{mass}}}{\partial P}\right)_{V}$

Returns

dS_mass_dP_Vfloat: The pressure derivative of mass entropy of the phase at constant volume, [J/(mol*K)/Pa]

dS_mass_dT(prop='dS_dT')¶

Method to calculate and return the temperature derivative of mass entropy of the phase at constant pressure.

$\left(\frac{\partial S_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dS_mass_dTfloat: The temperature derivative of mass entropy of the phase at constant pressure, [J/(mol*K)/K]

dS_mass_dT_P(prop='dS_dT_P')¶

Method to calculate and return the temperature derivative of mass entropy of the phase at constant pressure.

$\left(\frac{\partial S_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dS_mass_dT_Pfloat: The temperature derivative of mass entropy of the phase at constant pressure, [J/(mol*K)/K]

dS_mass_dT_V(prop='dS_dT_V')¶

Method to calculate and return the temperature derivative of mass entropy of the phase at constant volume.

$\left(\frac{\partial S_{\text{mass}}}{\partial T}\right)_{V}$

Returns

dS_mass_dT_Vfloat: The temperature derivative of mass entropy of the phase at constant volume, [J/(mol*K)/K]

dS_mass_dV_P(prop='dS_dV_P')¶

Method to calculate and return the volume derivative of mass entropy of the phase at constant pressure.

$\left(\frac{\partial S_{\text{mass}}}{\partial V}\right)_{P}$

Returns

dS_mass_dV_Pfloat: The volume derivative of mass entropy of the phase at constant pressure, [J/(mol*K)/m^3/mol]

dS_mass_dV_T(prop='dS_dV_T')¶

Method to calculate and return the volume derivative of mass entropy of the phase at constant temperature.

$\left(\frac{\partial S_{\text{mass}}}{\partial V}\right)_{T}$

Returns

dS_mass_dV_Tfloat: The volume derivative of mass entropy of the phase at constant temperature, [J/(mol*K)/m^3/mol]

dT_dP()[source]¶

Method to calculate and return the constant-volume pressure derivative of temperature of the phase.

\left(\frac{\partial T}{\partial P}\right)_V = \frac{1}{\left(\frac{ \partial P}{\partial T}\right)_V}

Returns

dT_dPfloat: Constant-volume pressure derivative of temperature, [K/Pa]

dT_dP_A(property='T', differentiate_by='P', at_constant='A')¶

Method to calculate and return the pressure derivative of temperature of the phase at constant Helmholtz energy.

$\left(\frac{\partial T}{\partial P}\right)_{A}$

Returns

dT_dP_Afloat: The pressure derivative of temperature of the phase at constant Helmholtz energy, [K/Pa]

dT_dP_G(property='T', differentiate_by='P', at_constant='G')¶

Method to calculate and return the pressure derivative of temperature of the phase at constant Gibbs energy.

$\left(\frac{\partial T}{\partial P}\right)_{G}$

Returns

dT_dP_Gfloat: The pressure derivative of temperature of the phase at constant Gibbs energy, [K/Pa]

dT_dP_H(property='T', differentiate_by='P', at_constant='H')¶

Method to calculate and return the pressure derivative of temperature of the phase at constant enthalpy.

$\left(\frac{\partial T}{\partial P}\right)_{H}$

Returns

dT_dP_Hfloat: The pressure derivative of temperature of the phase at constant enthalpy, [K/Pa]

dT_dP_S(property='T', differentiate_by='P', at_constant='S')¶

Method to calculate and return the pressure derivative of temperature of the phase at constant entropy.

$\left(\frac{\partial T}{\partial P}\right)_{S}$

Returns

dT_dP_Sfloat: The pressure derivative of temperature of the phase at constant entropy, [K/Pa]

dT_dP_T()[source]¶

Method to calculate and return the pressure derivative of temperature of the phase at constant temperature.

Returns

dT_dP_Tfloat: Pressure derivative of temperature of the phase at constant temperature, [K/Pa]

dT_dP_U(property='T', differentiate_by='P', at_constant='U')¶

Method to calculate and return the pressure derivative of temperature of the phase at constant internal energy.

$\left(\frac{\partial T}{\partial P}\right)_{U}$

Returns

dT_dP_Ufloat: The pressure derivative of temperature of the phase at constant internal energy, [K/Pa]

dT_dP_V()¶

Method to calculate and return the constant-volume pressure derivative of temperature of the phase.

\left(\frac{\partial T}{\partial P}\right)_V = \frac{1}{\left(\frac{ \partial P}{\partial T}\right)_V}

Returns

dT_dPfloat: Constant-volume pressure derivative of temperature, [K/Pa]

dT_dT_A(property='T', differentiate_by='T', at_constant='A')¶

Method to calculate and return the temperature derivative of temperature of the phase at constant Helmholtz energy.

$\left(\frac{\partial T}{\partial T}\right)_{A}$

Returns

dT_dT_Afloat: The temperature derivative of temperature of the phase at constant Helmholtz energy, [K/K]

dT_dT_G(property='T', differentiate_by='T', at_constant='G')¶

Method to calculate and return the temperature derivative of temperature of the phase at constant Gibbs energy.

$\left(\frac{\partial T}{\partial T}\right)_{G}$

Returns

dT_dT_Gfloat: The temperature derivative of temperature of the phase at constant Gibbs energy, [K/K]

dT_dT_H(property='T', differentiate_by='T', at_constant='H')¶

Method to calculate and return the temperature derivative of temperature of the phase at constant enthalpy.

$\left(\frac{\partial T}{\partial T}\right)_{H}$

Returns

dT_dT_Hfloat: The temperature derivative of temperature of the phase at constant enthalpy, [K/K]

dT_dT_P()[source]¶

Method to calculate and return the temperature derivative of temperature of the phase at constant pressure.

Returns

dT_dT_Pfloat: Temperature derivative of temperature of the phase at constant pressure, [-]

dT_dT_S(property='T', differentiate_by='T', at_constant='S')¶

Method to calculate and return the temperature derivative of temperature of the phase at constant entropy.

$\left(\frac{\partial T}{\partial T}\right)_{S}$

Returns

dT_dT_Sfloat: The temperature derivative of temperature of the phase at constant entropy, [K/K]

dT_dT_U(property='T', differentiate_by='T', at_constant='U')¶

Method to calculate and return the temperature derivative of temperature of the phase at constant internal energy.

$\left(\frac{\partial T}{\partial T}\right)_{U}$

Returns

dT_dT_Ufloat: The temperature derivative of temperature of the phase at constant internal energy, [K/K]

dT_dT_V()[source]¶

Method to calculate and return the temperature derivative of temperature of the phase at constant volume.

Returns

dT_dT_Vfloat: Temperature derivative of temperature of the phase at constant volume, [-]

dT_dV()[source]¶

Method to calculate and return the constant-pressure volume derivative of temperature of the phase.

\left(\frac{\partial T}{\partial V}\right)_P = \frac{1} {\left(\frac{\partial V}{\partial T}\right)_P}

Returns

dT_dVfloat: Constant-pressure volume derivative of temperature, [K*m^3/(m^3)]

dT_dV_A(property='T', differentiate_by='V', at_constant='A')¶

Method to calculate and return the volume derivative of temperature of the phase at constant Helmholtz energy.

$\left(\frac{\partial T}{\partial V}\right)_{A}$

Returns

dT_dV_Afloat: The volume derivative of temperature of the phase at constant Helmholtz energy, [K/m^3/mol]

dT_dV_G(property='T', differentiate_by='V', at_constant='G')¶

Method to calculate and return the volume derivative of temperature of the phase at constant Gibbs energy.

$\left(\frac{\partial T}{\partial V}\right)_{G}$

Returns

dT_dV_Gfloat: The volume derivative of temperature of the phase at constant Gibbs energy, [K/m^3/mol]

dT_dV_H(property='T', differentiate_by='V', at_constant='H')¶

Method to calculate and return the volume derivative of temperature of the phase at constant enthalpy.

$\left(\frac{\partial T}{\partial V}\right)_{H}$

Returns

dT_dV_Hfloat: The volume derivative of temperature of the phase at constant enthalpy, [K/m^3/mol]

dT_dV_P()¶

Method to calculate and return the constant-pressure volume derivative of temperature of the phase.

\left(\frac{\partial T}{\partial V}\right)_P = \frac{1} {\left(\frac{\partial V}{\partial T}\right)_P}

Returns

dT_dVfloat: Constant-pressure volume derivative of temperature, [K*m^3/(m^3)]

dT_dV_S(property='T', differentiate_by='V', at_constant='S')¶

Method to calculate and return the volume derivative of temperature of the phase at constant entropy.

$\left(\frac{\partial T}{\partial V}\right)_{S}$

Returns

dT_dV_Sfloat: The volume derivative of temperature of the phase at constant entropy, [K/m^3/mol]

dT_dV_T()[source]¶

Method to calculate and return the volume derivative of temperature of the phase at constant temperature.

Returns

dT_dV_Tfloat: Pressure derivative of temperature of the phase at constant temperature, [K*mol/m^3]

dT_dV_U(property='T', differentiate_by='V', at_constant='U')¶

Method to calculate and return the volume derivative of temperature of the phase at constant internal energy.

$\left(\frac{\partial T}{\partial V}\right)_{U}$

Returns

dT_dV_Ufloat: The volume derivative of temperature of the phase at constant internal energy, [K/m^3/mol]

dT_drho()[source]¶

Method to calculate and return the molar density derivative of temperature of the phase.

\frac{\partial T}{\partial \rho} = -V^2\left(\frac{\partial T}{\partial V}\right)_P

Returns

dT_drhofloat: Molar density derivative of temperature, [K*m^3/mol]

dT_drho_A(property='T', differentiate_by='rho', at_constant='A')¶

Method to calculate and return the density derivative of temperature of the phase at constant Helmholtz energy.

$\left(\frac{\partial T}{\partial \rho}\right)_{A}$

Returns

dT_drho_Afloat: The density derivative of temperature of the phase at constant Helmholtz energy, [K/mol/m^3]

dT_drho_G(property='T', differentiate_by='rho', at_constant='G')¶

Method to calculate and return the density derivative of temperature of the phase at constant Gibbs energy.

$\left(\frac{\partial T}{\partial \rho}\right)_{G}$

Returns

dT_drho_Gfloat: The density derivative of temperature of the phase at constant Gibbs energy, [K/mol/m^3]

dT_drho_H(property='T', differentiate_by='rho', at_constant='H')¶

Method to calculate and return the density derivative of temperature of the phase at constant enthalpy.

$\left(\frac{\partial T}{\partial \rho}\right)_{H}$

Returns

dT_drho_Hfloat: The density derivative of temperature of the phase at constant enthalpy, [K/mol/m^3]

dT_drho_S(property='T', differentiate_by='rho', at_constant='S')¶

Method to calculate and return the density derivative of temperature of the phase at constant entropy.

$\left(\frac{\partial T}{\partial \rho}\right)_{S}$

Returns

dT_drho_Sfloat: The density derivative of temperature of the phase at constant entropy, [K/mol/m^3]

dT_drho_U(property='T', differentiate_by='rho', at_constant='U')¶

Method to calculate and return the density derivative of temperature of the phase at constant internal energy.

$\left(\frac{\partial T}{\partial \rho}\right)_{U}$

Returns

dT_drho_Ufloat: The density derivative of temperature of the phase at constant internal energy, [K/mol/m^3]

dU_dP()[source]¶

Method to calculate and return the constant-temperature pressure derivative of internal energy.

\left(\frac{\partial U}{\partial P}\right)_{T} = -P \left(\frac{\partial V}{\partial P}\right)_{T} - V + \left(\frac{\partial H}{\partial P}\right)_{T}

Returns

dU_dPfloat: Constant-temperature pressure derivative of internal energy, [J/(mol*Pa)]

dU_dP_T()¶

Method to calculate and return the constant-temperature pressure derivative of internal energy.

\left(\frac{\partial U}{\partial P}\right)_{T} = -P \left(\frac{\partial V}{\partial P}\right)_{T} - V + \left(\frac{\partial H}{\partial P}\right)_{T}

Returns

dU_dPfloat: Constant-temperature pressure derivative of internal energy, [J/(mol*Pa)]

dU_dP_V()[source]¶

Method to calculate and return the constant-volume pressure derivative of internal energy.

\left(\frac{\partial U}{\partial P}\right)_{V} = \left(\frac{\partial H}{\partial P}\right)_{V} - V

Returns

dU_dP_Vfloat: Constant-volume pressure derivative of internal energy, [J/(mol*Pa)]

dU_dT()[source]¶

Method to calculate and return the constant-pressure temperature derivative of internal energy.

\left(\frac{\partial U}{\partial T}\right)_{P} = -P \left(\frac{\partial V}{\partial T}\right)_{P} + \left(\frac{\partial H}{\partial T}\right)_{P}

Returns

dU_dTfloat: Constant-pressure temperature derivative of internal energy, [J/(mol*K)]

dU_dT_P()¶

Method to calculate and return the constant-pressure temperature derivative of internal energy.

\left(\frac{\partial U}{\partial T}\right)_{P} = -P \left(\frac{\partial V}{\partial T}\right)_{P} + \left(\frac{\partial H}{\partial T}\right)_{P}

Returns

dU_dTfloat: Constant-pressure temperature derivative of internal energy, [J/(mol*K)]

dU_dT_V()[source]¶

Method to calculate and return the constant-volume temperature derivative of internal energy.

\left(\frac{\partial U}{\partial T}\right)_{V} = \left(\frac{\partial H}{\partial T}\right)_{V} - V \left(\frac{\partial P}{\partial T}\right)_{V}

Returns

dU_dT_Vfloat: Constant-volume temperature derivative of internal energy, [J/(mol*K)]

dU_dV_P()[source]¶

Method to calculate and return the constant-pressure volume derivative of internal energy.

\left(\frac{\partial U}{\partial V}\right)_{P} = \left(\frac{\partial U}{\partial T}\right)_{P} \left(\frac{\partial T}{\partial V}\right)_{P}

Returns

dU_dV_Pfloat: Constant-pressure volume derivative of internal energy, [J/(m^3)]

dU_dV_T()[source]¶

Method to calculate and return the constant-temperature volume derivative of internal energy.

\left(\frac{\partial U}{\partial V}\right)_{T} = \left(\frac{\partial U}{\partial P}\right)_{T} \left(\frac{\partial P}{\partial V}\right)_{T}

Returns

dU_dV_Tfloat: Constant-temperature volume derivative of internal energy, [J/(m^3)]

dU_mass_dP(prop='dU_dP')¶

Method to calculate and return the pressure derivative of mass internal energy of the phase at constant temperature.

$\left(\frac{\partial U_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dU_mass_dPfloat: The pressure derivative of mass internal energy of the phase at constant temperature, [J/mol/Pa]

dU_mass_dP_T(prop='dU_dP_T')¶

Method to calculate and return the pressure derivative of mass internal energy of the phase at constant temperature.

$\left(\frac{\partial U_{\text{mass}}}{\partial P}\right)_{T}$

Returns

dU_mass_dP_Tfloat: The pressure derivative of mass internal energy of the phase at constant temperature, [J/mol/Pa]

dU_mass_dP_V(prop='dU_dP_V')¶

Method to calculate and return the pressure derivative of mass internal energy of the phase at constant volume.

$\left(\frac{\partial U_{\text{mass}}}{\partial P}\right)_{V}$

Returns

dU_mass_dP_Vfloat: The pressure derivative of mass internal energy of the phase at constant volume, [J/mol/Pa]

dU_mass_dT(prop='dU_dT')¶

Method to calculate and return the temperature derivative of mass internal energy of the phase at constant pressure.

$\left(\frac{\partial U_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dU_mass_dTfloat: The temperature derivative of mass internal energy of the phase at constant pressure, [J/mol/K]

dU_mass_dT_P(prop='dU_dT_P')¶

Method to calculate and return the temperature derivative of mass internal energy of the phase at constant pressure.

$\left(\frac{\partial U_{\text{mass}}}{\partial T}\right)_{P}$

Returns

dU_mass_dT_Pfloat: The temperature derivative of mass internal energy of the phase at constant pressure, [J/mol/K]

dU_mass_dT_V(prop='dU_dT_V')¶

Method to calculate and return the temperature derivative of mass internal energy of the phase at constant volume.

$\left(\frac{\partial U_{\text{mass}}}{\partial T}\right)_{V}$

Returns

dU_mass_dT_Vfloat: The temperature derivative of mass internal energy of the phase at constant volume, [J/mol/K]

dU_mass_dV_P(prop='dU_dV_P')¶

Method to calculate and return the volume derivative of mass internal energy of the phase at constant pressure.

$\left(\frac{\partial U_{\text{mass}}}{\partial V}\right)_{P}$

Returns

dU_mass_dV_Pfloat: The volume derivative of mass internal energy of the phase at constant pressure, [J/mol/m^3/mol]

dU_mass_dV_T(prop='dU_dV_T')¶

Method to calculate and return the volume derivative of mass internal energy of the phase at constant temperature.

$\left(\frac{\partial U_{\text{mass}}}{\partial V}\right)_{T}$

Returns

dU_mass_dV_Tfloat: The volume derivative of mass internal energy of the phase at constant temperature, [J/mol/m^3/mol]

dV_dP()[source]¶

Method to calculate and return the constant-temperature pressure derivative of volume of the phase.

\left(\frac{\partial V}{\partial P}\right)_T = {-\left(\frac{\partial V}{\partial T}\right)_P} {\left(\frac{\partial T}{\partial P}\right)_V}

Returns

dV_dPfloat: Constant-temperature pressure derivative of volume, [m^3/(mol*Pa)]

dV_dP_A(property='V', differentiate_by='P', at_constant='A')¶

Method to calculate and return the pressure derivative of volume of the phase at constant Helmholtz energy.

$\left(\frac{\partial V}{\partial P}\right)_{A}$

Returns

dV_dP_Afloat: The pressure derivative of volume of the phase at constant Helmholtz energy, [m^3/mol/Pa]

dV_dP_G(property='V', differentiate_by='P', at_constant='G')¶

Method to calculate and return the pressure derivative of volume of the phase at constant Gibbs energy.

$\left(\frac{\partial V}{\partial P}\right)_{G}$

Returns

dV_dP_Gfloat: The pressure derivative of volume of the phase at constant Gibbs energy, [m^3/mol/Pa]

dV_dP_H(property='V', differentiate_by='P', at_constant='H')¶

Method to calculate and return the pressure derivative of volume of the phase at constant enthalpy.

$\left(\frac{\partial V}{\partial P}\right)_{H}$

Returns

dV_dP_Hfloat: The pressure derivative of volume of the phase at constant enthalpy, [m^3/mol/Pa]

dV_dP_S(property='V', differentiate_by='P', at_constant='S')¶

Method to calculate and return the pressure derivative of volume of the phase at constant entropy.

$\left(\frac{\partial V}{\partial P}\right)_{S}$

Returns

dV_dP_Sfloat: The pressure derivative of volume of the phase at constant entropy, [m^3/mol/Pa]

dV_dP_T()¶

Method to calculate and return the constant-temperature pressure derivative of volume of the phase.

\left(\frac{\partial V}{\partial P}\right)_T = {-\left(\frac{\partial V}{\partial T}\right)_P} {\left(\frac{\partial T}{\partial P}\right)_V}

Returns

dV_dPfloat: Constant-temperature pressure derivative of volume, [m^3/(mol*Pa)]

dV_dP_U(property='V', differentiate_by='P', at_constant='U')¶

Method to calculate and return the pressure derivative of volume of the phase at constant internal energy.

$\left(\frac{\partial V}{\partial P}\right)_{U}$

Returns

dV_dP_Ufloat: The pressure derivative of volume of the phase at constant internal energy, [m^3/mol/Pa]

dV_dP_V()[source]¶

Method to calculate and return the volume derivative of pressure of the phase at constant volume.

Returns

dV_dP_Vfloat: Pressure derivative of volume of the phase at constant pressure, [m^3/(mol*Pa)]

dV_dT()[source]¶

Method to calculate and return the constant-pressure temperature derivative of volume of the phase.

\left(\frac{\partial V}{\partial T}\right)_P = \frac{-\left(\frac{\partial P}{\partial T}\right)_V} {\left(\frac{\partial P}{\partial V}\right)_T}

Returns

dV_dTfloat: Constant-pressure temperature derivative of volume, [m^3/(mol*K)]

dV_dT_A(property='V', differentiate_by='T', at_constant='A')¶

Method to calculate and return the temperature derivative of volume of the phase at constant Helmholtz energy.

$\left(\frac{\partial V}{\partial T}\right)_{A}$

Returns

dV_dT_Afloat: The temperature derivative of volume of the phase at constant Helmholtz energy, [m^3/mol/K]

dV_dT_G(property='V', differentiate_by='T', at_constant='G')¶

Method to calculate and return the temperature derivative of volume of the phase at constant Gibbs energy.

$\left(\frac{\partial V}{\partial T}\right)_{G}$

Returns

dV_dT_Gfloat: The temperature derivative of volume of the phase at constant Gibbs energy, [m^3/mol/K]

dV_dT_H(property='V', differentiate_by='T', at_constant='H')¶

Method to calculate and return the temperature derivative of volume of the phase at constant enthalpy.

$\left(\frac{\partial V}{\partial T}\right)_{H}$

Returns

dV_dT_Hfloat: The temperature derivative of volume of the phase at constant enthalpy, [m^3/mol/K]

dV_dT_P()¶

Method to calculate and return the constant-pressure temperature derivative of volume of the phase.

\left(\frac{\partial V}{\partial T}\right)_P = \frac{-\left(\frac{\partial P}{\partial T}\right)_V} {\left(\frac{\partial P}{\partial V}\right)_T}

Returns

dV_dTfloat: Constant-pressure temperature derivative of volume, [m^3/(mol*K)]

dV_dT_S(property='V', differentiate_by='T', at_constant='S')¶

Method to calculate and return the temperature derivative of volume of the phase at constant entropy.

$\left(\frac{\partial V}{\partial T}\right)_{S}$

Returns

dV_dT_Sfloat: The temperature derivative of volume of the phase at constant entropy, [m^3/mol/K]

dV_dT_U(property='V', differentiate_by='T', at_constant='U')¶

Method to calculate and return the temperature derivative of volume of the phase at constant internal energy.

$\left(\frac{\partial V}{\partial T}\right)_{U}$

Returns

dV_dT_Ufloat: The temperature derivative of volume of the phase at constant internal energy, [m^3/mol/K]

dV_dT_V()[source]¶

Method to calculate and return the temperature derivative of volume of the phase at constant volume.

Returns

dV_dT_Vfloat: Temperature derivative of volume of the phase at constant volume, [m^3/(mol*K)]

dV_dV_A(property='V', differentiate_by='V', at_constant='A')¶

Method to calculate and return the volume derivative of volume of the phase at constant Helmholtz energy.

$\left(\frac{\partial V}{\partial V}\right)_{A}$

Returns

dV_dV_Afloat: The volume derivative of volume of the phase at constant Helmholtz energy, [m^3/mol/m^3/mol]

dV_dV_G(property='V', differentiate_by='V', at_constant='G')¶

Method to calculate and return the volume derivative of volume of the phase at constant Gibbs energy.

$\left(\frac{\partial V}{\partial V}\right)_{G}$

Returns

dV_dV_Gfloat: The volume derivative of volume of the phase at constant Gibbs energy, [m^3/mol/m^3/mol]

dV_dV_H(property='V', differentiate_by='V', at_constant='H')¶

Method to calculate and return the volume derivative of volume of the phase at constant enthalpy.

$\left(\frac{\partial V}{\partial V}\right)_{H}$

Returns

dV_dV_Hfloat: The volume derivative of volume of the phase at constant enthalpy, [m^3/mol/m^3/mol]

dV_dV_P()[source]¶

Method to calculate and return the volume derivative of volume of the phase at constant pressure.

Returns

dV_dV_Pfloat: Volume derivative of volume of the phase at constant pressure, [-]

dV_dV_S(property='V', differentiate_by='V', at_constant='S')¶

Method to calculate and return the volume derivative of volume of the phase at constant entropy.

$\left(\frac{\partial V}{\partial V}\right)_{S}$

Returns

dV_dV_Sfloat: The volume derivative of volume of the phase at constant entropy, [m^3/mol/m^3/mol]

dV_dV_T()[source]¶

Method to calculate and return the volume derivative of volume of the phase at constant temperature.

Returns

dV_dV_Tfloat: Volume derivative of volume of the phase at constant temperature, [-]

dV_dV_U(property='V', differentiate_by='V', at_constant='U')¶

Method to calculate and return the volume derivative of volume of the phase at constant internal energy.

$\left(\frac{\partial V}{\partial V}\right)_{U}$

Returns

dV_dV_Ufloat: The volume derivative of volume of the phase at constant internal energy, [m^3/mol/m^3/mol]

dV_dns()[source]¶

Method to calculate and return the mole number derivatives of the molar volume V of the phase.

\frac{\partial V}{\partial n_i}

Returns

dV_dnslist[float]: Mole number derivatives of the molar volume of the phase, [m^3/mol^2]

dV_drho_A(property='V', differentiate_by='rho', at_constant='A')¶

Method to calculate and return the density derivative of volume of the phase at constant Helmholtz energy.

$\left(\frac{\partial V}{\partial \rho}\right)_{A}$

Returns

dV_drho_Afloat: The density derivative of volume of the phase at constant Helmholtz energy, [m^3/mol/mol/m^3]

dV_drho_G(property='V', differentiate_by='rho', at_constant='G')¶

Method to calculate and return the density derivative of volume of the phase at constant Gibbs energy.

$\left(\frac{\partial V}{\partial \rho}\right)_{G}$

Returns

dV_drho_Gfloat: The density derivative of volume of the phase at constant Gibbs energy, [m^3/mol/mol/m^3]

dV_drho_H(property='V', differentiate_by='rho', at_constant='H')¶

Method to calculate and return the density derivative of volume of the phase at constant enthalpy.

$\left(\frac{\partial V}{\partial \rho}\right)_{H}$

Returns

dV_drho_Hfloat: The density derivative of volume of the phase at constant enthalpy, [m^3/mol/mol/m^3]

dV_drho_S(property='V', differentiate_by='rho', at_constant='S')¶

Method to calculate and return the density derivative of volume of the phase at constant entropy.

$\left(\frac{\partial V}{\partial \rho}\right)_{S}$

Returns

dV_drho_Sfloat: The density derivative of volume of the phase at constant entropy, [m^3/mol/mol/m^3]

dV_drho_U(property='V', differentiate_by='rho', at_constant='U')¶

Method to calculate and return the density derivative of volume of the phase at constant internal energy.

$\left(\frac{\partial V}{\partial \rho}\right)_{U}$

Returns

dV_drho_Ufloat: The density derivative of volume of the phase at constant internal energy, [m^3/mol/mol/m^3]

dV_dzs()[source]¶

Method to calculate and return the mole fraction derivatives of the molar volume V of the phase.

\frac{\partial V}{\partial z_i}

Returns

dV_dzslist[float]: Mole fraction derivatives of the molar volume of the phase, [m^3/mol]

dZ_dP()[source]¶

Method to calculate and return the pressure derivative of compressibility of the phase.

\frac{\partial Z}{\partial P} = \frac{V + P\left(\frac{\partial V}{\partial P}\right)_T}{RT}

Returns

dZ_dPfloat: Pressure derivative of compressibility, [1/Pa]

dZ_dT()[source]¶

Method to calculate and return the temperature derivative of compressibility of the phase.

\frac{\partial Z}{\partial P} = P\frac{\left(\frac{\partial V}{\partial T}\right)_P - \frac{-V}{T}}{RT}

Returns

dZ_dTfloat: Temperature derivative of compressibility, [1/K]

dZ_dV()[source]¶

Method to calculate and return the volume derivative of compressibility of the phase.

\frac{\partial Z}{\partial V} = \frac{P - \rho \left(\frac{\partial P}{\partial \rho}\right)_T}{RT}

Returns

dZ_dVfloat: Volume derivative of compressibility, [mol/(m^3)]

dZ_dns()[source]¶

Method to calculate and return the mole number derivatives of the compressibility factor Z of the phase.

\frac{\partial Z}{\partial n_i}

Returns

dZ_dnslist[float]: Mole number derivatives of the compressibility factor of the phase, [1/mol]

dZ_dzs()[source]¶

Method to calculate and return the mole fraction derivatives of the compressibility factor Z of the phase.

\frac{\partial Z}{\partial z_i}

Returns

dZ_dzslist[float]: Mole fraction derivatives of the compressibility factor of the phase, [-]

dfugacities_dP()[source]¶

Method to calculate and return the pressure derivative of the fugacities of the components in the phase.

\frac{\partial f_i}{\partial P} = z_i \left(P \frac{\partial \phi_i}{\partial P} + \phi_i \right)

Returns

dfugacities_dPlist[float]: Pressure derivative of fugacities of all components in the phase, [-]

Notes

For models without pressure dependence of fugacity, the returned result may not be exactly zero due to inaccuracy in floating point results; results are likely on the order of 1e-14 or lower in that case.

dfugacities_dT()[source]¶

Method to calculate and return the temperature derivative of fugacities of the phase.

\frac{\partial f_i}{\partial T} = P z_i \frac{\partial \ln \phi_i}{\partial T}

Returns

dfugacities_dTlist[float]: Temperature derivative of fugacities of all components in the phase, [Pa/K]

dfugacities_dns()[source]¶

Method to calculate and return the mole number derivative of the fugacities of the components in the phase.

if i != j:

\frac{\partial f_i}{\partial n_j} = P\phi_i z_i \left( \frac{\partial \ln \phi_i}{\partial n_j} - 1 \right)

if i == j:

\frac{\partial f_i}{\partial n_j} = P\phi_i z_i \left( \frac{\partial \ln \phi_i}{\partial n_j} - 1 \right) + P\phi_i

Returns

dfugacities_dnslist[list[float]]: Mole number derivatives of the fugacities of all components in the phase, [Pa/mol]

dfugacity_dP()[source]¶

Method to calculate and return the pressure derivative of fugacity of the phase; provided the phase is 1 component.

Returns

dfugacity_dPlist[float]: Fugacity first pressure derivative, [-]

dfugacity_dT()[source]¶

Method to calculate and return the temperature derivative of fugacity of the phase; provided the phase is 1 component.

Returns

dfugacity_dTlist[float]: Fugacity first temperature derivative, [Pa/K]

property dipoles¶

Dipole moments for each component, [debye].

Returns

dipoleslist[float]: Dipole moments for each component, [debye].

disobaric_expansion_dP()[source]¶

Method to calculate and return the pressure derivative of isobatic expansion coefficient of the phase.

\frac{\partial \beta}{\partial P} = \frac{1}{V}\left( \left(\frac{\partial^2 V}{\partial T\partial P} \right) -\frac{ \left(\frac{\partial V}{\partial T} \right)_P \left(\frac{\partial V}{\partial P} \right)_T}{V} \right)

Returns

dbeta_dPfloat: Pressure derivative of isobaric coefficient of a thermal expansion, [1/(K*Pa)]

disobaric_expansion_dT()[source]¶

Method to calculate and return the temperature derivative of isobatic expansion coefficient of the phase.

\frac{\partial \beta}{\partial T} = \frac{1}{V}\left( \left(\frac{\partial^2 V}{\partial T^2} \right)_P - \left(\frac{\partial V}{\partial T} \right)_P^2/V \right)

Returns

dbeta_dTfloat: Temperature derivative of isobaric coefficient of a thermal expansion, [1/K^2]

disothermal_compressibility_dT()¶

Method to calculate and return the temperature derivative of isothermal compressibility of the phase.

\frac{\partial \kappa}{\partial T} = -\frac{ \left(\frac{\partial^2 V}{\partial P\partial T} \right)}{V} + \frac{\left(\frac{\partial V}{\partial P} \right)_T\left(\frac{\partial V}{\partial T} \right)_P}{V^2}

Returns

dkappa_dTfloat: First temperature derivative of isothermal coefficient of compressibility, [1/(Pa*K)]

dkappa_dT()[source]¶

Method to calculate and return the temperature derivative of isothermal compressibility of the phase.

\frac{\partial \kappa}{\partial T} = -\frac{ \left(\frac{\partial^2 V}{\partial P\partial T} \right)}{V} + \frac{\left(\frac{\partial V}{\partial P} \right)_T\left(\frac{\partial V}{\partial T} \right)_P}{V^2}

Returns

dkappa_dTfloat: First temperature derivative of isothermal coefficient of compressibility, [1/(Pa*K)]

dlnfugacities_dns()[source]¶

Method to calculate and return the mole number derivative of the log of fugacities of the components in the phase.

\frac{\partial \ln f_i}{\partial n_j} = \frac{1}{f_i} \frac{\partial f_i}{\partial n_j}

Returns

dlnfugacities_dnslist[list[float]]: Mole number derivatives of the log of fugacities of all components in the phase, [log(Pa)/mol]

dlnfugacities_dzs()[source]¶

Method to calculate and return the mole fraction derivative of the log of fugacities of the components in the phase.

\frac{\partial \ln f_i}{\partial z_j} = \frac{1}{f_i} \frac{\partial f_i}{\partial z_j}

Returns

dlnfugacities_dzslist[list[float]]: Mole fraction derivatives of the log of fugacities of all components in the phase, [log(Pa)]

dlnphis_dP()[source]¶

Method to calculate and return the pressure derivative of the log of fugacity coefficients of each component in the phase.

Returns

dlnphis_dPlist[float]: First pressure derivative of log fugacity coefficients, [1/Pa]

dlnphis_dT()[source]¶

Method to calculate and return the temperature derivative of the log of fugacity coefficients of each component in the phase.

Returns

dlnphis_dTlist[float]: First temperature derivative of log fugacity coefficients, [1/K]

dnV_dns()[source]¶

Method to calculate and return the partial mole number derivatives of the molar volume V of the phase.

\frac{\partial n V}{\partial n_i}

Returns

dnV_dnslist[float]: Partial mole number derivatives of the molar volume of the phase, [m^3/mol]

dphis_dP()[source]¶

Method to calculate and return the pressure derivative of fugacity coefficients of the phase.

\frac{\partial \phi_i}{\partial P} = \phi_i \frac{\partial \ln \phi_i}{\partial P}

Returns

dphis_dPlist[float]: Pressure derivative of fugacity coefficients of all components in the phase, [1/Pa]

dphis_dT()[source]¶

Method to calculate and return the temperature derivative of fugacity coefficients of the phase.

\frac{\partial \phi_i}{\partial T} = \phi_i \frac{\partial \ln \phi_i}{\partial T}

Returns

dphis_dTlist[float]: Temperature derivative of fugacity coefficients of all components in the phase, [1/K]

dphis_dzs()[source]¶

Method to calculate and return the molar composition derivative of fugacity coefficients of the phase.

\frac{\partial \phi_i}{\partial z_j} = \phi_i \frac{\partial \ln \phi_i}{\partial z_j}

Returns

dphis_dzslist[list[float]]: Molar derivative of fugacity coefficients of all components in the phase, [-]

drho_dP()[source]¶

Method to calculate and return the pressure derivative of molar density of the phase.

\frac{\partial \rho}{\partial P} = -\frac{1}{V^2}\left(\frac{\partial V}{\partial P}\right)_T

Returns

drho_dPfloat: Pressure derivative of Molar density, [mol/(Pa*m^3)]

drho_dP_A(property='rho', differentiate_by='P', at_constant='A')¶

Method to calculate and return the pressure derivative of density of the phase at constant Helmholtz energy.

$\left(\frac{\partial \rho}{\partial P}\right)_{A}$

Returns

drho_dP_Afloat: The pressure derivative of density of the phase at constant Helmholtz energy, [mol/m^3/Pa]

drho_dP_G(property='rho', differentiate_by='P', at_constant='G')¶

Method to calculate and return the pressure derivative of density of the phase at constant Gibbs energy.

$\left(\frac{\partial \rho}{\partial P}\right)_{G}$

Returns

drho_dP_Gfloat: The pressure derivative of density of the phase at constant Gibbs energy, [mol/m^3/Pa]

drho_dP_H(property='rho', differentiate_by='P', at_constant='H')¶

Method to calculate and return the pressure derivative of density of the phase at constant enthalpy.

$\left(\frac{\partial \rho}{\partial P}\right)_{H}$

Returns

drho_dP_Hfloat: The pressure derivative of density of the phase at constant enthalpy, [mol/m^3/Pa]

drho_dP_S(property='rho', differentiate_by='P', at_constant='S')¶

Method to calculate and return the pressure derivative of density of the phase at constant entropy.

$\left(\frac{\partial \rho}{\partial P}\right)_{S}$

Returns

drho_dP_Sfloat: The pressure derivative of density of the phase at constant entropy, [mol/m^3/Pa]

drho_dP_U(property='rho', differentiate_by='P', at_constant='U')¶

Method to calculate and return the pressure derivative of density of the phase at constant internal energy.

$\left(\frac{\partial \rho}{\partial P}\right)_{U}$

Returns

drho_dP_Ufloat: The pressure derivative of density of the phase at constant internal energy, [mol/m^3/Pa]

drho_dT()[source]¶

Method to calculate and return the temperature derivative of molar density of the phase.

\frac{\partial \rho}{\partial T} = -\frac{1}{V^2}\left(\frac{\partial V}{\partial T}\right)_P

Returns

drho_dTfloat: Temperature derivative of molar density, [mol/(K*m^3)]

drho_dT_A(property='rho', differentiate_by='T', at_constant='A')¶

Method to calculate and return the temperature derivative of density of the phase at constant Helmholtz energy.

$\left(\frac{\partial \rho}{\partial T}\right)_{A}$

Returns

drho_dT_Afloat: The temperature derivative of density of the phase at constant Helmholtz energy, [mol/m^3/K]

drho_dT_G(property='rho', differentiate_by='T', at_constant='G')¶

Method to calculate and return the temperature derivative of density of the phase at constant Gibbs energy.

$\left(\frac{\partial \rho}{\partial T}\right)_{G}$

Returns

drho_dT_Gfloat: The temperature derivative of density of the phase at constant Gibbs energy, [mol/m^3/K]

drho_dT_H(property='rho', differentiate_by='T', at_constant='H')¶

Method to calculate and return the temperature derivative of density of the phase at constant enthalpy.

$\left(\frac{\partial \rho}{\partial T}\right)_{H}$

Returns

drho_dT_Hfloat: The temperature derivative of density of the phase at constant enthalpy, [mol/m^3/K]

drho_dT_S(property='rho', differentiate_by='T', at_constant='S')¶

Method to calculate and return the temperature derivative of density of the phase at constant entropy.

$\left(\frac{\partial \rho}{\partial T}\right)_{S}$

Returns

drho_dT_Sfloat: The temperature derivative of density of the phase at constant entropy, [mol/m^3/K]

drho_dT_U(property='rho', differentiate_by='T', at_constant='U')¶

Method to calculate and return the temperature derivative of density of the phase at constant internal energy.

$\left(\frac{\partial \rho}{\partial T}\right)_{U}$

Returns

drho_dT_Ufloat: The temperature derivative of density of the phase at constant internal energy, [mol/m^3/K]

drho_dT_V()[source]¶

Method to calculate and return the temperature derivative of molar density of the phase at constant volume.

\left(\frac{\partial \rho}{\partial T}\right)_V = 0

Returns

drho_dT_Vfloat: Temperature derivative of molar density of the phase at constant volume, [mol/(m^3*K)]

drho_dV_A(property='rho', differentiate_by='V', at_constant='A')¶

Method to calculate and return the volume derivative of density of the phase at constant Helmholtz energy.

$\left(\frac{\partial \rho}{\partial V}\right)_{A}$

Returns

drho_dV_Afloat: The volume derivative of density of the phase at constant Helmholtz energy, [mol/m^3/m^3/mol]

drho_dV_G(property='rho', differentiate_by='V', at_constant='G')¶

Method to calculate and return the volume derivative of density of the phase at constant Gibbs energy.

$\left(\frac{\partial \rho}{\partial V}\right)_{G}$

Returns

drho_dV_Gfloat: The volume derivative of density of the phase at constant Gibbs energy, [mol/m^3/m^3/mol]

drho_dV_H(property='rho', differentiate_by='V', at_constant='H')¶

Method to calculate and return the volume derivative of density of the phase at constant enthalpy.

$\left(\frac{\partial \rho}{\partial V}\right)_{H}$

Returns

drho_dV_Hfloat: The volume derivative of density of the phase at constant enthalpy, [mol/m^3/m^3/mol]

drho_dV_S(property='rho', differentiate_by='V', at_constant='S')¶

Method to calculate and return the volume derivative of density of the phase at constant entropy.

$\left(\frac{\partial \rho}{\partial V}\right)_{S}$

Returns

drho_dV_Sfloat: The volume derivative of density of the phase at constant entropy, [mol/m^3/m^3/mol]

drho_dV_T()[source]¶

Method to calculate and return the volume derivative of molar density of the phase.

\frac{\partial \rho}{\partial V} = -\frac{1}{V^2}

Returns

drho_dV_Tfloat: Molar density derivative of volume, [mol^2/m^6]

drho_dV_U(property='rho', differentiate_by='V', at_constant='U')¶

Method to calculate and return the volume derivative of density of the phase at constant internal energy.

$\left(\frac{\partial \rho}{\partial V}\right)_{U}$

Returns

drho_dV_Ufloat: The volume derivative of density of the phase at constant internal energy, [mol/m^3/m^3/mol]

drho_drho_A(property='rho', differentiate_by='rho', at_constant='A')¶

Method to calculate and return the density derivative of density of the phase at constant Helmholtz energy.

$\left(\frac{\partial \rho}{\partial \rho}\right)_{A}$

Returns

drho_drho_Afloat: The density derivative of density of the phase at constant Helmholtz energy, [mol/m^3/mol/m^3]

drho_drho_G(property='rho', differentiate_by='rho', at_constant='G')¶

Method to calculate and return the density derivative of density of the phase at constant Gibbs energy.

$\left(\frac{\partial \rho}{\partial \rho}\right)_{G}$

Returns

drho_drho_Gfloat: The density derivative of density of the phase at constant Gibbs energy, [mol/m^3/mol/m^3]

drho_drho_H(property='rho', differentiate_by='rho', at_constant='H')¶

Method to calculate and return the density derivative of density of the phase at constant enthalpy.

$\left(\frac{\partial \rho}{\partial \rho}\right)_{H}$

Returns

drho_drho_Hfloat: The density derivative of density of the phase at constant enthalpy, [mol/m^3/mol/m^3]

drho_drho_S(property='rho', differentiate_by='rho', at_constant='S')¶

Method to calculate and return the density derivative of density of the phase at constant entropy.

$\left(\frac{\partial \rho}{\partial \rho}\right)_{S}$

Returns

drho_drho_Sfloat: The density derivative of density of the phase at constant entropy, [mol/m^3/mol/m^3]

drho_drho_U(property='rho', differentiate_by='rho', at_constant='U')¶

Method to calculate and return the density derivative of density of the phase at constant internal energy.

$\left(\frac{\partial \rho}{\partial \rho}\right)_{U}$

Returns

drho_drho_Ufloat: The density derivative of density of the phase at constant internal energy, [mol/m^3/mol/m^3]

drho_mass_dP()[source]¶

Method to calculate the mass density derivative with respect to pressure, at constant temperature.

\left(\frac{\partial \rho}{\partial P}\right)_{T} = \frac{-\text{MW} \frac{\partial V_m}{\partial P}}{1000 V_m^2}

Returns

drho_mass_dPfloat: Pressure derivative of mass density at constant temperature, [kg/m^3/Pa]

Notes

Requires dV_dP, MW, and V.

drho_mass_dT()[source]¶

Method to calculate the mass density derivative with respect to temperature, at constant pressure.

\left(\frac{\partial \rho}{\partial T}\right)_{P} = \frac{-\text{MW} \frac{\partial V_m}{\partial T}}{1000 V_m^2}

Returns

drho_mass_dTfloat: Temperature derivative of mass density at constant pressure, [kg/m^3/K]

Notes

Requires dV_dT, MW, and V.

dspeed_of_sound_dP_T()[source]¶

Method to calculate the pressure derivative of speed of sound at constant temperature in molar units.

\left(\frac{\partial c}{\partial P}\right)_T = - \frac{\sqrt{- \frac{\operatorname{Cp}{\left(P \right)} V^{2} {\left(P \right)} \operatorname{dPdV_{T}}{\left(P \right)}} {\operatorname{Cv}{\left(P \right)}}} \left(- \frac{ \operatorname{Cp}{\left(P \right)} V^{2}{\left(P \right)} \frac{d} {d P} \operatorname{dPdV_{T}}{\left(P \right)}}{2 \operatorname{Cv} {\left(P \right)}} - \frac{\operatorname{Cp}{\left(P \right)} V{\left(P \right)} \operatorname{dPdV_{T}}{\left(P \right)} \frac{d}{d P} V{\left(P \right)}}{\operatorname{Cv}{\left(P \right) }} + \frac{\operatorname{Cp}{\left(P \right)} V^{2}{\left(P \right) } \operatorname{dPdV_{T}}{\left(P \right)} \frac{d}{d P} \operatorname{Cv}{\left(P \right)}}{2 \operatorname{Cv}^{2}{\left(P \right)}} - \frac{V^{2}{\left(P \right)} \operatorname{dPdV_{T}} {\left(P \right)} \frac{d}{d P} \operatorname{Cp}{\left(P \right)}} {2 \operatorname{Cv}{\left(P \right)}}\right) \operatorname{Cv} {\left(P \right)}}{\operatorname{Cp}{\left(P \right)} V^{2}{\left(P \right)} \operatorname{dPdV_{T}}{\left(P \right)}}

Returns

dspeed_of_sound_dP_Tfloat: Pressure derivative of speed of sound at constant temperature, [m*kg^0.5/s/mol^0.5/Pa]

dspeed_of_sound_dT_P()[source]¶

Method to calculate the temperature derivative of speed of sound at constant pressure in molar units.

\left(\frac{\partial c}{\partial T}\right)_P = - \frac{\sqrt{- \frac{\operatorname{Cp}{\left(T \right)} V^{2} {\left(T \right)} \operatorname{dPdV_{T}}{\left(T \right)}} {\operatorname{Cv}{\left(T \right)}}} \left(- \frac{\operatorname{Cp} {\left(T \right)} V^{2}{\left(T \right)} \frac{d}{d T} \operatorname{dPdV_{T}}{\left(T \right)}}{2 \operatorname{Cv}{\left(T \right)}} - \frac{\operatorname{Cp}{\left(T \right)} V{\left(T \right)} \operatorname{dPdV_{T}}{\left(T \right)} \frac{d}{d T} V{\left(T \right)}}{\operatorname{Cv}{\left(T \right)}} + \frac{\operatorname{Cp}{\left(T \right)} V^{2}{\left(T \right)} \operatorname{dPdV_{T}}{\left(T \right)} \frac{d}{d T} \operatorname{Cv}{\left(T \right)}}{2 \operatorname{Cv}^{2} {\left(T \right)}} - \frac{V^{2}{\left(T \right)} \operatorname{ dPdV_{T}}{\left(T \right)} \frac{d}{d T} \operatorname{Cp}{\left(T \right)}}{2 \operatorname{Cv}{\left(T \right)}}\right) \operatorname{Cv}{\left(T \right)}}{\operatorname{Cp}{\left(T \right)} V^{2}{\left(T \right)} \operatorname{dPdV_{T}}{\left(T \right)}}

Returns

dspeed_of_sound_dT_Pfloat: Temperature derivative of speed of sound at constant pressure, [m*kg^0.5/s/mol^0.5/K]

Notes

Requires the temperature derivative of Cp and Cv both at constant pressure, as wel as the volume and temperature derivative of pressure, calculated at constant temperature and then pressure respectively. These can be tricky to obtain.

property economic_statuses¶

Status of each component in in relation to import and export from various regions, [-].

Returns

economic_statuseslist[dict]: Status of each component in in relation to import and export from various regions, [-].

property energy¶

Method to return the energy (enthalpy times flow rate) of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

energyfloat: Enthalpy flow rate, [W]

property energy_calc¶

Method to return the energy (enthalpy times flow rate) of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

energyfloat: Enthalpy flow rate, [W]

property energy_reactive¶

Method to return the reactive energy (reactive enthalpy times flow rate) of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

energy_reactivefloat: Reactive enthalpy flow rate, [W]

property energy_reactive_calc¶

Method to return the reactive energy (reactive enthalpy times flow rate) of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

energy_reactivefloat: Reactive enthalpy flow rate, [W]

force_phase = None¶: Attribute which can be set to a global Phase object to force the phases identification routines to label it a certain phase. Accepts values of (‘g’, ‘l’, ‘s’).

property formulas¶

Formulas of each component, [-].

Returns

formulaslist[str]: Formulas of each component, [-].

classmethod from_json(json_repr)[source]¶

Method to create a phase from a JSON serialization of another phase.

Parameters

json_reprdict: JSON-friendly representation, [-]

Returns

phasePhase: Newly created phase object from the json serialization, [-]

Notes

It is important that the input string be in the same format as that created by Phase.as_json.

fugacities()[source]¶

Method to calculate and return the fugacities of the phase.

f_i = P z_i \exp(\ln \phi_i)

Returns

fugacitieslist[float]: Fugacities, [Pa]

fugacities_at_zs(zs, most_stable=False)[source]¶

Method to directly calculate the figacities at a different composition than the current phase. This is implemented to allow for the possibility of more direct calls to obtain fugacities than is possible with the phase interface. This base method simply creates a new phase, gets its log fugacity coefficients, exponentiates them, and multiplies them by P and compositions.

Returns

fugacitieslist[float]: Fugacities, [Pa]

fugacities_lowest_Gibbs()¶

Method to calculate and return the fugacities of the phase.

f_i = P z_i \exp(\ln \phi_i)

Returns

fugacitieslist[float]: Fugacities, [Pa]

fugacity()[source]¶

Method to calculate and return the fugacity of the phase; provided the phase is 1 component.

Returns

fugacitylist[float]: Fugacity, [Pa]

gammas()[source]¶

Method to calculate and return the activity coefficients of the phase, [-].

Activity coefficients are defined as the ratio of the actual fugacity coefficients times the pressure to the reference pure fugacity coefficients times the reference pressure. The reference pressure can be set to the actual pressure (the Lewis Randall standard state) which makes the pressures cancel.

\gamma_i(T, P, x; f_i^0(T, P_i^0)) = \frac{\phi_i(T, P, x)P}{\phi_i^0(T, P_i^0) P_i^0}

Returns

gammaslist[float]: Activity coefficients, [-]

gammas_infinite_dilution()[source]¶

Calculate and return the infinite dilution activity coefficients of each component.

Returns

gammas_infinitelist[float]: Infinite dilution activity coefficients, [-]

Notes

The algorithm is as follows. For each component, set its composition to zero. Normalize the remaining compositions to 1. Create a new object with that composition, and calculate the activity coefficient of the component whose concentration was set to zero.

helium_molar_weight()¶

Method to calculate and return the effective quantiy of helium in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the helium component.

helium_partial_pressure()¶: Method to calculate and return the ideal partial pressure of helium, [Pa]

humidity_ratio()¶

Method to calculate and return the humidity ratio of the phase; normally defined as the kg water/kg dry air, the definition here is kg water/(kg rest of the phase) [-]

\text{humidity ratio} = \text{HR} = \frac{w_{H2O}}{1 - w_{H2O}}

Returns

humidity_ratiofloat: Humidity ratio, [-]

hydrogen_molar_weight()¶

Method to calculate and return the effective quantiy of hydrogen in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the hydrogen component.

hydrogen_partial_pressure()¶: Method to calculate and return the ideal partial pressure of hydrogen, [Pa]

hydrogen_sulfide_molar_weight()¶

Method to calculate and return the effective quantiy of hydrogen_sulfide in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the hydrogen_sulfide component.

hydrogen_sulfide_partial_pressure()¶: Method to calculate and return the ideal partial pressure of hydrogen_sulfide, [Pa]

ideal_gas_basis = False¶

is_same_model(other_phase, ignore_phase=False)[source]¶

Method to check whether or not a model is the exact same as another. In the case ignore_phase is True, whether the model is liquid or gas is omitted as in the case of CEOSGas and CEOSLiquid.

Parameters

other_phasePhase: The phase to compare against, [-]
ignore_phasebool: Whether or not to include the specifc class of the model in the hash

Returns

samebool: Whether they are the same or not

Notes

This may be quicker to calculate than the model hash.

is_solid = False¶

isentropic_exponent()¶

Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $PV^k = \text{const}$ .

k = -\frac{V}{P}\frac{C_p}{C_v}\left(\frac{\partial P}{\partial V}\right)_T

Returns

k_PVfloat: Isentropic exponent of a real fluid, [-]

isentropic_exponent_PT()[source]¶

Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $P^{(1-k)}T^k = \text{const}$ .

k = \frac{1}{1 - \frac{P}{C_p}\left(\frac{\partial V}{\partial T}\right)_P}

Returns

k_PTfloat: Isentropic exponent of a real fluid, [-]

isentropic_exponent_PV()[source]¶

Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $PV^k = \text{const}$ .

k = -\frac{V}{P}\frac{C_p}{C_v}\left(\frac{\partial P}{\partial V}\right)_T

Returns

k_PVfloat: Isentropic exponent of a real fluid, [-]

isentropic_exponent_TV()[source]¶

Method to calculate and return the real gas isentropic exponent of the phase, which satisfies the relationship $TV^{k-1} = \text{const}$ .

k = 1 + \frac{V}{C_v} \left(\frac{\partial P}{\partial T}\right)_V

Returns

k_TVfloat: Isentropic exponent of a real fluid, [-]

isobaric_expansion()[source]¶

Method to calculate and return the isobatic expansion coefficient of the phase.

\beta = \frac{1}{V}\left(\frac{\partial V}{\partial T} \right)_P

Returns

betafloat: Isobaric coefficient of a thermal expansion, [1/K]

isothermal_bulk_modulus()[source]¶

Method to calculate and return the isothermal bulk modulus of the phase.

K_T = -V\left(\frac{\partial P}{\partial V} \right)_T

Returns

isothermal_bulk_modulusfloat: Isothermal bulk modulus, [Pa]

isothermal_compressibility()¶

Method to calculate and return the isothermal compressibility of the phase.

\kappa = -\frac{1}{V}\left(\frac{\partial V}{\partial P} \right)_T

Returns

kappafloat: Isothermal coefficient of compressibility, [1/Pa]

kappa()[source]¶

Method to calculate and return the isothermal compressibility of the phase.

\kappa = -\frac{1}{V}\left(\frac{\partial V}{\partial P} \right)_T

Returns

kappafloat: Isothermal coefficient of compressibility, [1/Pa]

kgs()¶

Method to calculate and return the pure-component gas temperature-dependent thermal conductivity of each species from the thermo.thermal_conductivity.ThermalConductivityGas objects.

These values are normally at low pressure, not along the saturation line.

Returns

kgslist[float]: Pure component temperature dependent gas thermal conductivities, [W/(m*K)]

kinematic_viscosity()¶

Method to calculate and return the kinematic viscosity of the phase, [m^2/s]

Returns

nufloat: Kinematic viscosity, [m^2/s]

kls()¶

Method to calculate and return the pure-component liquid temperature-dependent thermal conductivity of each species from the thermo.thermal_conductivity.ThermalConductivityLiquid objects.

These values are normally at low pressure, not along the saturation line.

Returns

klslist[float]: Pure component temperature dependent liquid thermal conductivities, [W/(m*K)]

property legal_statuses¶

Status of each component in in relation to import and export rules from various regions, [-].

Returns

legal_statuseslist[dict]: Status of each component in in relation to import and export rules from various regions, [-].

lnfugacities()[source]¶

Method to calculate and return the log of fugacities of the phase.

\ln f_i = \ln\left( P z_i \exp(\ln \phi_i)\right) = \ln(P) + \ln(z_i) + \ln \phi_i

Returns

lnfugacitieslist[float]: Log fugacities, [log(Pa)]

lnphi()[source]¶

Method to calculate and return the log of fugacity coefficient of the phase; provided the phase is 1 component.

Returns

lnphilist[float]: Log fugacity coefficient, [-]

lnphis()[source]¶

Method to calculate and return the log of fugacity coefficients of each component in the phase.

Returns

lnphislist[float]: Log fugacity coefficients, [-]

lnphis_G_min()[source]¶

Method to calculate and return the log fugacity coefficients of the phase. If the phase can have multiple solutions at its T and P, this method should return those with the lowest Gibbs energy. This needs to be implemented on phases with that criteria like cubic EOSs.

Returns

lnphislist[float]: Log fugacity coefficients, [-]

lnphis_at_zs(zs, most_stable=False)[source]¶

Method to directly calculate the log fugacity coefficients at a different composition than the current phase. This is implemented to allow for the possibility of more direct calls to obtain fugacities than is possible with the phase interface. This base method simply creates a new phase, gets its log fugacity coefficients, and returns them.

Returns

lnphislist[float]: Log fugacity coefficients, [-]

lnphis_lowest_Gibbs()[source]¶

property logPs¶

Octanol-water partition coefficients for each component, [-].

Returns

logPslist[float]: Octanol-water partition coefficients for each component, [-].

log_zs()[source]¶

Method to calculate and return the log of mole fractions specified. These are used in calculating entropy and in many other formulas.

\ln z_i

Returns

log_zslist[float]: Log of mole fractions, [-]

property m¶

Method to return the mass flow rate of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

mfloat: Mass flow of the phase, [kg/s]

property m_calc¶

methane_molar_weight()¶

Method to calculate and return the effective quantiy of methane in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the methane component.

methane_partial_pressure()¶: Method to calculate and return the ideal partial pressure of methane, [Pa]

model_hash(ignore_phase=False)[source]¶

Method to compute a hash of a phase.

Parameters

ignore_phasebool: Whether or not to include the specifc class of the model in the hash

Returns

hashint: Hash representing the settings of the phase; phases with all identical model parameters should have the same hash.

molar_water_content()¶

property molecular_diameters¶

Lennard-Jones molecular diameters for each component, [angstrom].

Returns

molecular_diameterslist[float]: Lennard-Jones molecular diameters for each component, [angstrom].

property ms¶

Method to return the mass flow rates of each component in this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

msfloat: Mass flow of the components in the phase, [kg/s]

property ms_calc¶

Method to return the mass flow rates of each component in this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

msfloat: Mass flow of the components in the phase, [kg/s]

mu()[source]¶

mugs()¶

Method to calculate and return the pure-component gas temperature-dependent viscosity of each species from the thermo.viscosity.ViscosityGas objects.

These values are normally at low pressure, not along the saturation line.

Returns

mugslist[float]: Pure component temperature dependent gas viscosities, [Pa*s]

muls()¶

Method to calculate and return the pure-component liquid temperature-dependent viscosity of each species from the thermo.viscosity.ViscosityLiquid objects.

These values are normally at low pressure, not along the saturation line.

Returns

mulslist[float]: Pure component temperature dependent liquid viscosities, [Pa*s]

property n¶

Method to return the molar flow rate of this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

nfloat: Molar flow of the phase, [mol/s]

property n_calc¶

property names¶

Names for each component, [-].

Returns

nameslist[str]: Names for each component, [-].

nitrogen_molar_weight()¶

Method to calculate and return the effective quantiy of nitrogen in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the nitrogen component.

nitrogen_partial_pressure()¶: Method to calculate and return the ideal partial pressure of nitrogen, [Pa]

property ns¶

Method to return the molar flow rates of each component in this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

nsfloat: Molar flow of the components in the phase, [mol/s]

property ns_calc¶

Method to return the molar flow rates of each component in this phase. This method is only available when the phase is linked to an EquilibriumStream.

Returns

nsfloat: Molar flow of the components in the phase, [mol/s]

nu()[source]¶

Method to calculate and return the kinematic viscosity of the phase, [m^2/s]

Returns

nufloat: Kinematic viscosity, [m^2/s]

obj_references = ()¶: Tuple of object instances which should be stored as json using their own as_json method.

property omegas¶

Acentric factors for each component, [-].

Returns

omegaslist[float]: Acentric factors for each component, [-].

oxygen_molar_weight()¶

Method to calculate and return the effective quantiy of oxygen in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the oxygen component.

oxygen_partial_pressure()¶: Method to calculate and return the ideal partial pressure of oxygen, [Pa]

partial_pressures()[source]¶

Method to return the partial pressures of each component in the phase. Note that this is the conventional definition assumed in almost every source; there is also a non-ideal definition.

P_i = z_i P

Returns

partial_pressureslist[float]: Partial pressures of all the components in the phase, [Pa]

property phase_STPs¶

Standard states (‘g’, ‘l’, or ‘s’) for each component, [-].

Returns

phase_STPslist[str]: Standard states (‘g’, ‘l’, or ‘s’) for each component, [-].

phi()[source]¶

Method to calculate and return the fugacity coefficient of the phase; provided the phase is 1 component.

Returns

philist[float]: Fugacity coefficient, [-]

phis()[source]¶

Method to calculate and return the fugacity coefficients of the phase.

\phi_i = \exp (\ln \phi_i)

Returns

phislist[float]: Fugacity coefficients, [-]

pointer_reference_dicts = ()¶: Tuple of dictionaries for string -> object

pointer_references = ()¶: Tuple of attributes which should be stored by converting them to a string, and then they will be looked up in their corresponding pointer_reference_dicts entry.

pseudo_Pc()¶

Method to calculate and return the pseudocritical pressure calculated using Kay’s rule (linear mole fractions):

P_{c, pseudo} = \sum_i z_i P_{c,i}

Returns

pseudo_Pcfloat: Pseudocritical pressure of the phase, [Pa]

pseudo_Tc()¶

Method to calculate and return the pseudocritical temperature calculated using Kay’s rule (linear mole fractions):

T_{c, pseudo} = \sum_i z_i T_{c,i}

Returns

pseudo_Tcfloat: Pseudocritical temperature of the phase, [K]

pseudo_Vc()¶

Method to calculate and return the pseudocritical volume calculated using Kay’s rule (linear mole fractions):

V_{c, pseudo} = \sum_i z_i V_{c,i}

Returns

pseudo_Vcfloat: Pseudocritical volume of the phase, [m^3/mol]

pseudo_Zc()¶

Method to calculate and return the pseudocritical compressibility calculated using Kay’s rule (linear mole fractions):

Z_{c, pseudo} = \sum_i z_i Z_{c,i}

Returns

pseudo_Zcfloat: Pseudocritical compressibility of the phase, [-]

pseudo_omega()¶

Method to calculate and return the pseudocritical acentric factor calculated using Kay’s rule (linear mole fractions):

\omega_{pseudo} = \sum_i z_i \omega_{i}

Returns

pseudo_omegafloat: Pseudo acentric factor of the phase, [-]

pure_reference_types = ()¶: Tuple of types of thermo.utils.TDependentProperty or thermo.utils.TPDependentProperty corresponding to pure_references.

pure_references = ()¶: Tuple of attribute names which hold lists of thermo.utils.TDependentProperty or thermo.utils.TPDependentProperty instances.

reference_pointer_dicts = ()¶: Tuple of dictionaries for object -> string

result¶

rho()[source]¶

Method to calculate and return the molar density of the phase.

\rho = frac{1}{V}

Returns

rhofloat: Molar density, [mol/m^3]

rho_gas()¶

Method to calculate and return the ideal-gas molar density of the phase at the chosen reference temperature and pressure, according to the temperature variable T_gas_ref and pressure variable P_gas_ref of the thermo.bulk.BulkSettings.

Returns

rho_gasfloat: Ideal gas molar density at the reference temperature and pressure, [mol/m^3]

rho_gas_normal()¶

Method to calculate and return the ideal-gas molar density of the phase at the normal temperature and pressure, according to the temperature variable T_normal and pressure variable P_normal of the thermo.bulk.BulkSettings.

Returns

rho_gas_normalfloat: Ideal gas molar density at normal temperature and pressure, [mol/m^3]

rho_gas_standard()¶

Method to calculate and return the ideal-gas molar density of the phase at the standard temperature and pressure, according to the temperature variable T_standard and pressure variable P_standard of the thermo.bulk.BulkSettings.

Returns

rho_gas_standardfloat: Ideal gas molar density at standard temperature and pressure, [mol/m^3]

rho_mass()[source]¶

Method to calculate and return mass density of the phase.

\rho = \frac{MW}{1000\cdot VM}

Returns

rho_massfloat: Mass density, [kg/m^3]

rho_mass_gas()¶

Method to calculate and return the ideal-gas mass density of the phase at the chosen reference temperature and pressure, according to the temperature variable T_gas_ref and pressure variable P_gas_ref of the thermo.bulk.BulkSettings.

Returns

rho_mass_gasfloat: Ideal gas molar density at the reference temperature and pressure, [kg/m^3]

rho_mass_gas_normal()¶

Method to calculate and return the ideal-gas mass density of the phase at the normal temperature and pressure, according to the temperature variable T_normal and pressure variable P_normal of the thermo.bulk.BulkSettings.

Returns

rho_mass_gas_normalfloat: Ideal gas molar density at normal temperature and pressure, [kg/m^3]

rho_mass_gas_standard()¶

Method to calculate and return the ideal-gas mass density of the phase at the standard temperature and pressure, according to the temperature variable T_standard and pressure variable P_standard of the thermo.bulk.BulkSettings.

Returns

rho_mass_gas_standardfloat: Ideal gas molar density at standard temperature and pressure, [kg/m^3]

rho_mass_liquid_ref()¶

Method to calculate and return the liquid reference mass density according to the temperature variable T_liquid_volume_ref of thermo.bulk.BulkSettings and the composition of the phase.

Returns

rho_mass_liquid_reffloat: Liquid mass density at the reference condition, [kg/m^3]

property rhocs¶

Molar densities at the critical point for each component, [mol/m^3].

Returns

rhocslist[float]: Molar densities at the critical point for each component, [mol/m^3].

property rhocs_mass¶

Densities at the critical point for each component, [kg/m^3].

Returns

rhocs_masslist[float]: Densities at the critical point for each component, [kg/m^3].

property rhog_STPs¶

Molar gas densities at STP for each component; metastable if normally another state, [mol/m^3].

Returns

rhog_STPslist[float]: Molar gas densities at STP for each component; metastable if normally another state, [mol/m^3].

property rhog_STPs_mass¶

Gas densities at STP for each component; metastable if normally another state, [kg/m^3].

Returns

rhog_STPs_masslist[float]: Gas densities at STP for each component; metastable if normally another state, [kg/m^3].

property rhol_60Fs¶

Liquid molar densities for each component at 60 °F, [mol/m^3].

Returns

rhol_60Fslist[float]: Liquid molar densities for each component at 60 °F, [mol/m^3].

property rhol_60Fs_mass¶

Liquid mass densities for each component at 60 °F, [kg/m^3].

Returns

rhol_60Fs_masslist[float]: Liquid mass densities for each component at 60 °F, [kg/m^3].

property rhol_STPs¶

Molar liquid densities at STP for each component, [mol/m^3].

Returns

rhol_STPslist[float]: Molar liquid densities at STP for each component, [mol/m^3].

property rhol_STPs_mass¶

Liquid densities at STP for each component, [kg/m^3].

Returns

rhol_STPs_masslist[float]: Liquid densities at STP for each component, [kg/m^3].

property rhos_Tms¶

Solid molar densities for each component at their respective melting points, [mol/m^3].

Returns

rhos_Tmslist[float]: Solid molar densities for each component at their respective melting points, [mol/m^3].

property rhos_Tms_mass¶

Solid mass densities for each component at their melting point, [kg/m^3].

Returns

rhos_Tms_masslist[float]: Solid mass densities for each component at their melting point, [kg/m^3].

scalar = True¶

sigma()[source]¶

Calculate and return the surface tension of the phase. For details of the implementation, see SurfaceTensionMixture.

This property is strictly the ideal-gas to liquid surface tension, not a true inter-phase property.

Returns

sigmafloat: Surface tension, [N/m]

property sigma_STPs¶

Liquid-air surface tensions at 298.15 K and the higher of 101325 Pa or the saturation pressure, [N/m].

Returns

sigma_STPslist[float]: Liquid-air surface tensions at 298.15 K and the higher of 101325 Pa or the saturation pressure, [N/m].

property sigma_Tbs¶

Liquid-air surface tensions at the normal boiling point and 101325 Pa, [N/m].

Returns

sigma_Tbslist[float]: Liquid-air surface tensions at the normal boiling point and 101325 Pa, [N/m].

property sigma_Tms¶

Liquid-air surface tensions at the melting point and 101325 Pa, [N/m].

Returns

sigma_Tmslist[float]: Liquid-air surface tensions at the melting point and 101325 Pa, [N/m].

sigmas()¶

Method to calculate and return the pure-component surface tensions of each species from the thermo.interface.SurfaceTension objects.

Returns

sigmaslist[float]: Surface tensions, [N/m]

property similarity_variables¶

Similarity variables for each component, [mol/g].

Returns

similarity_variableslist[float]: Similarity variables for each component, [mol/g].

property smiless¶

SMILES identifiers for each component, [-].

Returns

smilesslist[str]: SMILES identifiers for each component, [-].

property solubility_parameters¶

Solubility parameters for each component at 298.15 K, [Pa^0.5].

Returns

solubility_parameterslist[float]: Solubility parameters for each component at 298.15 K, [Pa^0.5].

speed_of_sound()[source]¶

Method to calculate and return the molar speed of sound of the phase.

w = \left[-V^2 \left(\frac{\partial P}{\partial V}\right)_T \frac{C_p} {C_v}\right]^{1/2}

A similar expression based on molar density is:

w = \left[\left(\frac{\partial P}{\partial \rho}\right)_T \frac{C_p} {C_v}\right]^{1/2}

Returns

wfloat: Speed of sound for a real gas, [m*kg^0.5/(s*mol^0.5)]

speed_of_sound_ideal_gas()[source]¶

Method to calculate and return the molar speed of sound of an ideal gas phase at the current conditions.

w = \left[-V^2 \left(\frac{\partial P}{\partial V}\right)_T \frac{C_p} {C_v}\right]^{1/2}

\left(\frac{\partial P}{\partial V}\right)_T = \frac{-P^2}{RT}

Returns

wfloat: Speed of sound for a real gas, [m*kg^0.5/(s*mol^0.5)]

speed_of_sound_ideal_gas_mass()[source]¶

Method to calculate and return the mass speed of sound of an ideal gas phase at the current conditions.

c = \sqrt{kR_{specific, ideal gas}T}

Returns

wfloat: Speed of sound for an ideal gas, [m/s]

speed_of_sound_mass()[source]¶

Method to calculate and return the speed of sound of the phase.

w = \left[-V^2 \frac{1000}{MW}\left(\frac{\partial P}{\partial V} \right)_T \frac{C_p}{C_v}\right]^{1/2}

Returns

wfloat: Speed of sound for a real gas, [m/s]

state_hash()[source]¶

Basic method to calculate a hash of the state of the phase and its model parameters.

Note that the hashes should only be compared on the same system running in the same process!

Returns

state_hashint: Hash of the object’s model parameters and state, [-]

supports_lnphis_args = False¶

thermal_diffusivity()¶

Method to calculate and return the thermal diffusivity of the phase.

\alpha = \frac{k}{\rho Cp}

Returns

alphafloat: Thermal diffusivity, [m^2/s]

to(zs, T=None, P=None, V=None)[source]¶

Method to create a new Phase object with the same constants as the existing Phase but at different conditions. Mole fractions zs are always required and any two of T, P, and V are required.

Parameters

zslist[float]: Molar composition of the new phase, [-]
Tfloat, optional: Temperature of the new phase, [K]
Pfloat, optional: Pressure of the new phase, [Pa]
Vfloat, optional: Molar volume of the new phase, [m^3/mol]

Returns

new_phasePhase: New phase at the specified conditions, [-]

Examples

These sample cases illustrate the three combinations of inputs. Note that some thermodynamic models may have multiple solutions for some inputs!

>>> from thermo import IdealGas
>>> phase = IdealGas(T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=[])
>>> phase.to(T=1e5, P=1e3, zs=[.5, .5])
IdealGas(HeatCapacityGases=[], T=100000.0, P=1000.0, zs=[0.5, 0.5])
>>> phase.to(V=1e-4, P=1e3, zs=[.1, .9])
IdealGas(HeatCapacityGases=[], T=0.012027235504, P=1000.0, zs=[0.1, 0.9])
>>> phase.to(T=1e5, V=1e12, zs=[.2, .8])
IdealGas(HeatCapacityGases=[], T=100000.0, P=8.31446261e-07, zs=[0.2, 0.8])

to_TP_zs(T, P, zs)[source]¶

Method to create a new Phase object with the same constants as the existing Phase but at a different T and P.

Parameters

zslist[float]: Molar composition of the new phase, [-]
Tfloat: Temperature of the new phase, [K]
Pfloat: Pressure of the new phase, [Pa]

Returns

new_phasePhase: New phase at the specified conditions, [-]

Notes

This method is marginally faster than Phase.to as it does not need to check what the inputs are.

Examples

>>> from thermo import IdealGas
>>> phase = IdealGas(T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=[])
>>> phase.to_TP_zs(T=1e5, P=1e3, zs=[.5, .5])
IdealGas(HeatCapacityGases=[], T=100000.0, P=1000.0, zs=[0.5, 0.5])

value(name)[source]¶

Method to retrieve a property from a string. This more or less wraps getattr.

name could be a python property like ‘Tms’ or a callable method like ‘H’.

Parameters

namestr: String representing the property, [-]

Returns

valuevarious: Value specified, [various]

water_molar_weight()¶

Method to calculate and return the effective quantiy of water in the phase as a molar weight, [g/mol].

This is the molecular weight of the phase times the mass fraction of the water component.

water_partial_pressure()¶: Method to calculate and return the ideal partial pressure of water, [Pa]

ws()[source]¶

Method to calculate and return the mass fractions of the phase, [-]

Returns

wslist[float]: Mass fractions, [-]

property ws_calc¶

ws_no_water()¶

Method to calculate and return the mass fractions of all species in the phase, normalized to a water-free basis (the mass fraction of water returned is zero).

Returns

ws_no_waterlist[float]: Mass fractions on a water free basis, [-]

property zs_calc¶

zs_no_water()¶

Method to calculate and return the mole fractions of all species in the phase, normalized to a water-free basis (the mole fraction of water returned is zero).

Returns

zs_no_waterlist[float]: Mole fractions on a water free basis, [-]

Ideal Gas Equation of State ¶

class thermo.phases.IdealGas(HeatCapacityGases=None, Hfs=None, Gfs=None, T=None, P=None, zs=None)[source]¶

Bases: thermo.phases.phase.Phase

Class for representing an ideal gas as a phase object. All departure properties are zero.

P = \frac{RT}{V}

Parameters

HeatCapacityGaseslist[HeatCapacityGas]: Objects proiding pure-component heat capacity correlations, [-]
Hfslist[float]: Molar ideal-gas standard heats of formation at 298.15 K and 1 atm, [J/mol]
Gfslist[float]: Molar ideal-gas standard Gibbs energies of formation at 298.15 K and 1 atm, [J/mol]
Tfloat, optional: Temperature, [K]
Pfloat, optional: Pressure, [Pa]
zslist[float], optional: Mole fractions of each component, [-]

Examples

T-P initialization for oxygen and nitrogen, using Poling’s polynomial heat capacities:

>>> from scipy.constants import R
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63]))]
>>> phase = IdealGas(T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=HeatCapacityGases)
>>> phase.Cp()
29.1733530

Methods

`Cp`()	Method to calculate and return the molar heat capacity of the phase.
`H`()	Method to calculate and return the enthalpy of the phase.
`S`()	Method to calculate and return the entropy of the phase.
`d2H_dP2`()	Method to calculate and return the second pressure derivative of molar enthalpy of the phase.
`d2H_dT2`()	Method to calculate and return the first temperature derivative of molar heat capacity of the phase.
`d2P_dT2`()	Method to calculate and return the second temperature derivative of pressure of the phase.
`d2P_dTdV`()	Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.
`d2P_dV2`()	Method to calculate and return the second volume derivative of pressure of the phase.
`d2S_dP2`()	Method to calculate and return the second pressure derivative of molar entropy of the phase.
`dH_dP`()	Method to calculate and return the first pressure derivative of molar enthalpy of the phase.
`dH_dP_V`()	Method to calculate and return the pressure derivative of molar enthalpy at constant volume of the phase.
`dH_dT_V`()	Method to calculate and return the molar heat capacity of the phase.
`dH_dV_P`()	Method to calculate and return the volume derivative of molar enthalpy at constant pressure of the phase.
`dH_dV_T`()	Method to calculate and return the volume derivative of molar enthalpy at constant temperature of the phase.
`dP_dT`()	Method to calculate and return the first temperature derivative of pressure of the phase.
`dP_dV`()	Method to calculate and return the first volume derivative of pressure of the phase.
`dS_dP`()	Method to calculate and return the first pressure derivative of molar entropy of the phase.
`dS_dP_V`()	Method to calculate and return the first pressure derivative of molar entropy at constant volume of the phase.
`dS_dT`()	Method to calculate and return the first temperature derivative of molar entropy of the phase.
`dS_dT_V`()	Method to calculate and return the first temperature derivative of molar entropy at constant volume of the phase.
`dlnphis_dP`()	Method to calculate and return the pressure derivative of the log of fugacity coefficients of each component in the phase.
`dlnphis_dT`()	Method to calculate and return the temperature derivative of the log of fugacity coefficients of each component in the phase.
`dphis_dP`()	Method to calculate and return the pressure derivative of fugacity coefficients of each component in the phase.
`dphis_dT`()	Method to calculate and return the temperature derivative of fugacity coefficients of each component in the phase.
`fugacities`()	Method to calculate and return the fugacities of each component in the phase.
`lnphis`()	Method to calculate and return the log of fugacity coefficients of each component in the phase.
`phis`()	Method to calculate and return the fugacity coefficients of each component in the phase.

Cp()[source]¶

Method to calculate and return the molar heat capacity of the phase.

C_p = \sum_i z_i C_{p,i}^{ig}

Returns

Cpfloat: Molar heat capacity, [J/(mol*K)]

H()[source]¶

Method to calculate and return the enthalpy of the phase.

H = \sum_i z_i H_{i}^{ig}

Returns

Hfloat: Molar enthalpy, [J/(mol)]

S()[source]¶

Method to calculate and return the entropy of the phase.

S = \sum_i z_i S_{i}^{ig} - R\ln\left(\frac{P}{P_{ref}}\right) - R\sum_i z_i \ln(z_i)

Returns

Sfloat: Molar entropy, [J/(mol*K)]

__repr__()[source]¶

Method to create a string representation of the phase object, with the goal of making it easy to obtain standalone code which reproduces the current state of the phase. This is extremely helpful in creating new test cases.

Returns

recreationstr: String which is valid Python and recreates the current state of the object if ran, [-]

Examples

>>> from thermo import HeatCapacityGas, IdealGas
>>> from scipy.constants import R
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63]))]
>>> phase = IdealGas(T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=HeatCapacityGases)
>>> phase
IdealGas(HeatCapacityGases=[HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [-8.23131799e-12, 1.30537063e-08, 5.82012383e-07, -0.0021700747, 29.42488320])), HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [1.48828880e-11, -4.988677570e-08, 5.470916402e-05, -0.01491614593, 30.1814993]))], T=300, P=100000.0, zs=[0.79, 0.21])

d2H_dP2()[source]¶

Method to calculate and return the second pressure derivative of molar enthalpy of the phase.

\frac{\partial^2 H}{\partial P^2} = 0

Returns

d2H_dP2float: Second pressure derivative of molar enthalpy, [J/(mol*Pa^2)]

d2H_dT2()[source]¶

Method to calculate and return the first temperature derivative of molar heat capacity of the phase.

\frac{\partial C_p}{\partial T} = \sum_i z_i \frac{\partial C_{p,i}^{ig}}{\partial T}

Returns

d2H_dT2float: Second temperature derivative of enthalpy, [J/(mol*K^2)]

d2P_dT2()[source]¶

Method to calculate and return the second temperature derivative of pressure of the phase.

\frac{\partial^2 P}{\partial T^2} = 0

Returns

d2P_dT2float: Second temperature derivative of pressure, [Pa/K^2]

d2P_dTdV()[source]¶

Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.

\frac{\partial^2 P}{\partial V \partial T} = \frac{-P^2}{RT^2}

Returns

d2P_dTdVfloat: Second volume derivative of pressure, [mol*Pa^2/(J*K)]

d2P_dV2()[source]¶

Method to calculate and return the second volume derivative of pressure of the phase.

\frac{\partial^2 P}{\partial V^2} = \frac{2P^3}{R^2T^2}

Returns

d2P_dV2float: Second volume derivative of pressure, [Pa*mol^2/m^6]

d2S_dP2()[source]¶

Method to calculate and return the second pressure derivative of molar entropy of the phase.

\frac{\partial^2 S}{\partial P^2} = \frac{R}{P^2}

Returns

d2S_dP2float: Second pressure derivative of molar entropy, [J/(mol*K*Pa^2)]

dH_dP()[source]¶

Method to calculate and return the first pressure derivative of molar enthalpy of the phase.

\frac{\partial H}{\partial P} = 0

Returns

dH_dPfloat: First pressure derivative of molar enthalpy, [J/(mol*Pa)]

dH_dP_V()[source]¶

Method to calculate and return the pressure derivative of molar enthalpy at constant volume of the phase.

\left(\frac{\partial H}{\partial P}\right)_{V} = C_p \left(\frac{\partial T}{\partial P}\right)_{V}

Returns

dH_dP_Vfloat: First pressure derivative of molar enthalpy at constant volume, [J/(mol*Pa)]

dH_dT_V()¶

Method to calculate and return the molar heat capacity of the phase.

C_p = \sum_i z_i C_{p,i}^{ig}

Returns

Cpfloat: Molar heat capacity, [J/(mol*K)]

dH_dV_P()[source]¶

Method to calculate and return the volume derivative of molar enthalpy at constant pressure of the phase.

\left(\frac{\partial H}{\partial V}\right)_{P} = C_p \left(\frac{\partial T}{\partial V}\right)_{P}

Returns

dH_dV_Tfloat: First pressure derivative of molar enthalpy at constant volume, [J/(m^3)]

dH_dV_T()[source]¶

Method to calculate and return the volume derivative of molar enthalpy at constant temperature of the phase.

\left(\frac{\partial H}{\partial V}\right)_{T} = 0

Returns

dH_dV_Tfloat: First pressure derivative of molar enthalpy at constant volume, [J/(m^3)]

dP_dT()[source]¶

Method to calculate and return the first temperature derivative of pressure of the phase.

\frac{\partial P}{\partial T} = \frac{P}{T}

Returns

dP_dTfloat: First temperature derivative of pressure, [Pa/K]

dP_dV()[source]¶

Method to calculate and return the first volume derivative of pressure of the phase.

\frac{\partial P}{\partial V} = \frac{-P^2}{RT}

Returns

dP_dVfloat: First volume derivative of pressure, [Pa*mol/m^3]

dS_dP()[source]¶

Method to calculate and return the first pressure derivative of molar entropy of the phase.

\frac{\partial S}{\partial P} = -\frac{R}{P}

Returns

dS_dPfloat: First pressure derivative of molar entropy, [J/(mol*K*Pa)]

dS_dP_V()[source]¶

Method to calculate and return the first pressure derivative of molar entropy at constant volume of the phase.

\left(\frac{\partial S}{\partial P}\right)_V = \frac{-R}{P} + \frac{C_p}{T}\frac{\partial T}{\partial P}

Returns

dS_dP_Vfloat: First pressure derivative of molar entropy at constant volume, [J/(mol*K*Pa)]

dS_dT()[source]¶

Method to calculate and return the first temperature derivative of molar entropy of the phase.

\frac{\partial S}{\partial T} = \frac{C_p}{T}

Returns

dS_dTfloat: First temperature derivative of molar entropy, [J/(mol*K^2)]

dS_dT_V()[source]¶

Method to calculate and return the first temperature derivative of molar entropy at constant volume of the phase.

\left(\frac{\partial S}{\partial T}\right)_V = \frac{C_p}{T} - \frac{R}{P}\frac{\partial P}{\partial T}

Returns

dS_dT_Vfloat: First temperature derivative of molar entropy at constant volume, [J/(mol*K^2)]

dlnphis_dP()[source]¶

Method to calculate and return the pressure derivative of the log of fugacity coefficients of each component in the phase.

\frac{\partial \ln \phi_i}{\partial P} = 0

Returns

dlnphis_dPlist[float]: Log fugacity coefficients, [1/Pa]

dlnphis_dT()[source]¶

Method to calculate and return the temperature derivative of the log of fugacity coefficients of each component in the phase.

\frac{\partial \ln \phi_i}{\partial T} = 0

Returns

dlnphis_dTlist[float]: Log fugacity coefficients, [1/K]

dphis_dP()[source]¶

Method to calculate and return the pressure derivative of fugacity coefficients of each component in the phase.

\frac{\partial \phi_i}{\partial P} = 0

Returns

dphis_dPlist[float]: Pressure derivative of fugacity fugacity coefficients, [1/Pa]

dphis_dT()[source]¶

Method to calculate and return the temperature derivative of fugacity coefficients of each component in the phase.

\frac{\partial \phi_i}{\partial T} = 0

Returns

dphis_dTlist[float]: Temperature derivative of fugacity fugacity coefficients, [1/K]

fugacities()[source]¶

Method to calculate and return the fugacities of each component in the phase.

\text{fugacitiy}_i = z_i P

Returns

fugacitieslist[float]: Fugacities, [Pa]

Examples

>>> from scipy.constants import R
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63]))]
>>> phase = IdealGas(T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=HeatCapacityGases)
>>> phase.fugacities()
[79000.0, 21000.0]

lnphis()[source]¶

Method to calculate and return the log of fugacity coefficients of each component in the phase.

\ln \phi_i = 0.0

Returns

lnphislist[float]: Log fugacity coefficients, [-]

phis()[source]¶

Method to calculate and return the fugacity coefficients of each component in the phase.

\phi_i = 1

Returns

phislist[float]: Fugacity fugacity coefficients, [-]

Cubic Equations of State ¶

Gas Phases ¶

class thermo.phases.CEOSGas(eos_class, eos_kwargs, HeatCapacityGases=None, Hfs=None, Gfs=None, Sfs=None, T=None, P=None, zs=None)[source]¶

Bases: thermo.phases.ceos.CEOSPhase

Class for representing a cubic equation of state gas phase as a phase object. All departure properties are actually calculated by the code in thermo.eos and thermo.eos_mix.

P=\frac{RT}{V-b}-\frac{a\alpha(T)}{V^2 + \delta V + \epsilon}

Parameters

eos_classGCEOSMIX: EOS class, [-]
eos_kwargsdict: Parameters to be passed to the created EOS, [-]
HeatCapacityGaseslist[HeatCapacityGas]: Objects proiding pure-component heat capacity correlations, [-]
Hfslist[float]: Molar ideal-gas standard heats of formation at 298.15 K and 1 atm, [J/mol]
Gfslist[float]: Molar ideal-gas standard Gibbs energies of formation at 298.15 K and 1 atm, [J/mol]
Tfloat, optional: Temperature, [K]
Pfloat, optional: Pressure, [Pa]
zslist[float], optional: Mole fractions of each component, [-]

Examples

T-P initialization for oxygen and nitrogen with the PR EOS, using Poling’s polynomial heat capacities:

>>> from scipy.constants import R
>>> from thermo import HeatCapacityGas, PRMIX, CEOSGas
>>> eos_kwargs = dict(Tcs=[154.58, 126.2], Pcs=[5042945.25, 3394387.5], omegas=[0.021, 0.04], kijs=[[0.0, -0.0159], [-0.0159, 0.0]])
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63]))]
>>> phase = CEOSGas(eos_class=PRMIX, eos_kwargs=eos_kwargs, T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=HeatCapacityGases)
>>> phase.Cp()
29.2285050

Methods

`Cp`()	Method to calculate and return the constant-pressure heat capacity of the phase.
`Cv`()	Method to calculate and return the constant-volume heat capacity Cv of the phase.
`H`()	Method to calculate and return the enthalpy of the phase.
`S`()	Method to calculate and return the entropy of the phase.
`V_iter`([force])	Method to calculate and return the volume of the phase in a way suitable for a TV resolution to converge on the same pressure.
`d2P_dT2`()	Method to calculate and return the second temperature derivative of pressure of the phase.
`d2P_dTdV`()	Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.
`d2P_dV2`()	Method to calculate and return the second volume derivative of pressure of the phase.
`dP_dT`()	Method to calculate and return the first temperature derivative of pressure of the phase.
`dP_dV`()	Method to calculate and return the first volume derivative of pressure of the phase.
`dS_dT_V`()	Method to calculate and return the first temperature derivative of molar entropy at constant volume of the phase.
`dlnphis_dP`()	Method to calculate and return the first pressure derivative of the log of fugacity coefficients of each component in the phase.
`dlnphis_dT`()	Method to calculate and return the first temperature derivative of the log of fugacity coefficients of each component in the phase.
`lnphis`()	Method to calculate and return the log of fugacity coefficients of each component in the phase.
`to_TP_zs`(T, P, zs[, other_eos])	Method to create a new Phase object with the same constants as the existing Phase but at a different T and P.

Cp()¶

Method to calculate and return the constant-pressure heat capacity of the phase.

Returns

Cpfloat: Molar heat capacity, [J/(mol*K)]

Cv()¶

Method to calculate and return the constant-volume heat capacity Cv of the phase.

C_v = T\left(\frac{\partial P}{\partial T}\right)_V^2/ \left(\frac{\partial P}{\partial V}\right)_T + Cp

Returns

Cvfloat: Constant volume molar heat capacity, [J/(mol*K)]

H()¶

Method to calculate and return the enthalpy of the phase. The reference state for most subclasses is an ideal-gas enthalpy of zero at 298.15 K and 101325 Pa.

Returns

Hfloat: Molar enthalpy, [J/(mol)]

S()¶

Method to calculate and return the entropy of the phase. The reference state for most subclasses is an ideal-gas entropy of zero at 298.15 K and 101325 Pa.

Returns

Sfloat: Molar entropy, [J/(mol*K)]

V_iter(force=False)¶

Method to calculate and return the volume of the phase in a way suitable for a TV resolution to converge on the same pressure. This often means the return value of this method is an mpmath mpf. This dummy method simply returns the implemented V method.

Returns

Vfloat or mpf: Molar volume, [m^3/mol]

__repr__()¶

Method to create a string representation of the phase object, with the goal of making it easy to obtain standalone code which reproduces the current state of the phase. This is extremely helpful in creating new test cases.

Returns

recreationstr: String which is valid Python and recreates the current state of the object if ran, [-]

d2P_dT2()[source]¶

Method to calculate and return the second temperature derivative of pressure of the phase.

\left(\frac{\partial^2 P}{\partial T^2}\right)_V = - \frac{a \frac{d^{2} \alpha{\left (T \right )}}{d T^{2}}}{V^{2} + V \delta + \epsilon}

Returns

d2P_dT2float: Second temperature derivative of pressure, [Pa/K^2]

d2P_dTdV()[source]¶

Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.

\left(\frac{\partial^2 P}{\partial T \partial V}\right) = - \frac{ R}{\left(V - b\right)^{2}} + \frac{a \left(2 V + \delta\right) \frac{d \alpha{\left (T \right )}}{d T}}{\left(V^{2} + V \delta + \epsilon\right)^{2}}

Returns

d2P_dTdVfloat: Second volume derivative of pressure, [mol*Pa^2/(J*K)]

d2P_dV2()[source]¶

Method to calculate and return the second volume derivative of pressure of the phase.

\left(\frac{\partial^2 P}{\partial V^2}\right)_T = 2 \left(\frac{ R T}{\left(V - b\right)^{3}} - \frac{a \left(2 V + \delta\right)^{ 2} \alpha{\left (T \right )}}{\left(V^{2} + V \delta + \epsilon \right)^{3}} + \frac{a \alpha{\left (T \right )}}{\left(V^{2} + V \delta + \epsilon\right)^{2}}\right)

Returns

d2P_dV2float: Second volume derivative of pressure, [Pa*mol^2/m^6]

dP_dT()[source]¶

Method to calculate and return the first temperature derivative of pressure of the phase.

\left(\frac{\partial P}{\partial T}\right)_V = \frac{R}{V - b} - \frac{a \frac{d \alpha{\left (T \right )}}{d T}}{V^{2} + V \delta + \epsilon}

Returns

dP_dTfloat: First temperature derivative of pressure, [Pa/K]

dP_dV()[source]¶

Method to calculate and return the first volume derivative of pressure of the phase.

\left(\frac{\partial P}{\partial V}\right)_T = - \frac{R T}{\left( V - b\right)^{2}} - \frac{a \left(- 2 V - \delta\right) \alpha{ \left (T \right )}}{\left(V^{2} + V \delta + \epsilon\right)^{2}}

Returns

dP_dVfloat: First volume derivative of pressure, [Pa*mol/m^3]

dS_dT_V()¶

Method to calculate and return the first temperature derivative of molar entropy at constant volume of the phase.

\left(\frac{\partial S}{\partial T}\right)_V = \frac{C_p^{ig}}{T} - \frac{R}{P}\frac{\partial P}{\partial T} + \left(\frac{\partial S_{dep}}{\partial T}\right)_V

Returns

dS_dT_Vfloat: First temperature derivative of molar entropy at constant volume, [J/(mol*K^2)]

dlnphis_dP()[source]¶

Method to calculate and return the first pressure derivative of the log of fugacity coefficients of each component in the phase. The calculation is performed by thermo.eos_mix.GCEOSMIX.dlnphis_dP or a simpler formula in the case of most specific models.

Returns

dlnphis_dPlist[float]: First pressure derivative of log fugacity coefficients, [1/Pa]

dlnphis_dT()[source]¶

Method to calculate and return the first temperature derivative of the log of fugacity coefficients of each component in the phase. The calculation is performed by thermo.eos_mix.GCEOSMIX.dlnphis_dT or a simpler formula in the case of most specific models.

Returns

dlnphis_dTlist[float]: First temperature derivative of log fugacity coefficients, [1/K]

lnphis()[source]¶

Method to calculate and return the log of fugacity coefficients of each component in the phase. The calculation is performed by thermo.eos_mix.GCEOSMIX.fugacity_coefficients or a simpler formula in the case of most specific models.

Returns

lnphislist[float]: Log fugacity coefficients, [-]

to_TP_zs(T, P, zs, other_eos=None)¶

Method to create a new Phase object with the same constants as the existing Phase but at a different T and P. This method has a special parameter other_eos.

This is added to allow a gas-type phase to be created from a liquid-type phase at the same conditions (and vice-versa), as GCEOSMIX objects were designed to have vapor and liquid properties in the same phase. This argument is mostly for internal use.

Parameters

zslist[float]: Molar composition of the new phase, [-]
Tfloat: Temperature of the new phase, [K]
Pfloat: Pressure of the new phase, [Pa]
other_eosobj:GCEOSMIX <thermo.eos_mix.GCEOSMIX> object: Other equation of state object at the same conditions, [-]

Returns

new_phasePhase: New phase at the specified conditions, [-]

Notes

This method is marginally faster than Phase.to as it does not need to check what the inputs are.

Examples

>>> from thermo.eos_mix import PRMIX
>>> eos_kwargs = dict(Tcs=[305.32, 369.83], Pcs=[4872000.0, 4248000.0], omegas=[0.098, 0.152])
>>> gas = CEOSGas(PRMIX, T=300.0, P=1e6, zs=[.2, .8], eos_kwargs=eos_kwargs)
>>> liquid = CEOSLiquid(PRMIX, T=500.0, P=1e7, zs=[.3, .7], eos_kwargs=eos_kwargs)
>>> new_liq = liquid.to_TP_zs(T=gas.T, P=gas.P, zs=gas.zs, other_eos=gas.eos_mix)
>>> new_liq
CEOSLiquid(eos_class=PRMIX, eos_kwargs={"Tcs": [305.32, 369.83], "Pcs": [4872000.0, 4248000.0], "omegas": [0.098, 0.152]}, HeatCapacityGases=[], T=300.0, P=1000000.0, zs=[0.2, 0.8])
>>> new_liq.eos_mix is gas.eos_mix
True

Liquid Phases ¶

class thermo.phases.CEOSLiquid(eos_class, eos_kwargs, HeatCapacityGases=None, Hfs=None, Gfs=None, Sfs=None, T=None, P=None, zs=None)[source]¶

Bases: thermo.phases.ceos.CEOSPhase

Class for representing a cubic equation of state gas phase as a phase object. All departure properties are actually calculated by the code in thermo.eos and thermo.eos_mix.

P=\frac{RT}{V-b}-\frac{a\alpha(T)}{V^2 + \delta V + \epsilon}

Parameters

eos_classGCEOSMIX: EOS class, [-]
eos_kwargsdict: Parameters to be passed to the created EOS, [-]
HeatCapacityGaseslist[HeatCapacityGas]: Objects proiding pure-component heat capacity correlations, [-]
Hfslist[float]: Molar ideal-gas standard heats of formation at 298.15 K and 1 atm, [J/mol]
Gfslist[float]: Molar ideal-gas standard Gibbs energies of formation at 298.15 K and 1 atm, [J/mol]
Tfloat, optional: Temperature, [K]
Pfloat, optional: Pressure, [Pa]
zslist[float], optional: Mole fractions of each component, [-]

Examples

T-P initialization for oxygen and nitrogen with the PR EOS, using Poling’s polynomial heat capacities:

>>> from scipy.constants import R
>>> from thermo import HeatCapacityGas, PRMIX, CEOSGas
>>> eos_kwargs = dict(Tcs=[154.58, 126.2], Pcs=[5042945.25, 3394387.5], omegas=[0.021, 0.04], kijs=[[0.0, -0.0159], [-0.0159, 0.0]])
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63]))]
>>> phase = CEOSGas(eos_class=PRMIX, eos_kwargs=eos_kwargs, T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=HeatCapacityGases)
>>> phase.Cp()
29.2285050

Virial Equations of State ¶

Gas Phase Object ¶

class thermo.phases.VirialGas(model, HeatCapacityGases=None, Hfs=None, Gfs=None, T=None, P=None, zs=None, cross_B_model='theory', cross_C_model='Orentlicher-Prausnitz')[source]¶

Bases: thermo.phases.phase.IdealGasDeparturePhase

Class for representing a real gas defined by the virial equation of state (density form), as a phase object. The equation includes the B and C coefficients but not further coefficients as they cannot be accurately estimated. Only limited experimental data for third virial coefficients is available.

This model is generic, and allows any source of virial coefficients to be plugged it, so long as it provides the right methods. See VirialCSP.

Z = \frac{PV}{RT} = 1 + \frac{B}{V} + \frac{C}{V^2}

Parameters

modelobject

Object which provides pure component and interaction second and third virial coefficients; VirialCSP, [-]

HeatCapacityGaseslist[HeatCapacityGas]

Objects proiding pure-component heat capacity correlations, [-]

Hfslist[float]

Molar ideal-gas standard heats of formation at 298.15 K and 1 atm, [J/mol]

Gfslist[float]

Molar ideal-gas standard Gibbs energies of formation at 298.15 K and 1 atm, [J/mol]

Tfloat, optional

Temperature, [K]

Pfloat, optional

Pressure, [Pa]

zslist[float], optional

Mole fractions of each component, [-]

cross_B_modelstr, optional

The method used to combine the pure and/or interaction second B virial coefficients into a single B coefficient.

‘linear’: $B = \sum_i y_i B_i$
‘theory’: :math:` B = sum_i sum_j y_i y_j B(T)`

cross_C_modelstr, optional

The method used to combine the pure and/or interaction third C virial coefficients into a single C coefficient.

‘linear’: $C = \sum_i y_i C_i$ ; this is considerably faster
‘Orentlicher-Prausnitz’: $C = \sum_i \sum_j \sum_k y_i y_j y_k C_{ijk}(T)$ where $C_{ijk} = \left(C_{ij}C_{jk}C_{ik}\right)^{1/3}$

Examples

T-P initialization for nitrogen, oxygen, and argon, using Poling’s polynomial heat capacities:

>>> Tcs=[126.2, 154.58, 150.8]
>>> Pcs=[3394387.5, 5042945.25, 4873732.5]
>>> Vcs=[8.95e-05, 7.34e-05, 7.49e-05]
>>> omegas=[0.04, 0.021, -0.004]
>>> model = VirialCSP(Tcs=Tcs, Pcs=Pcs, Vcs=Vcs, omegas=omegas, B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA')
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
...                      HeatCapacityGas(poly_fit=(50.0, 1000.0, [0,0,0,0, R*2.5]))]
>>> phase = VirialGas(model=model, T=300, P=1e5, zs=[.78, .21, .01], HeatCapacityGases=HeatCapacityGases, cross_B_model='theory', cross_C_model='Orentlicher-Prausnitz')
>>> phase.V(), phase.isothermal_compressibility(), phase.speed_of_sound()
(0.02493687, 1.00025907e-05, 59.081947)
>>> phase
VirialGas(model=VirialCSP(Tcs=[126.2, 154.58, 150.8], Pcs=[3394387.5, 5042945.25, 4873732.5], Vcs=[8.95e-05, 7.34e-05, 7.49e-05], omegas=[0.04, 0.021, -0.004], B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA', T=300), HeatCapacityGases=[HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [1.48828880864943e-11, -4.9886775708919434e-08, 5.4709164027448316e-05, -0.014916145936966912, 30.18149930389626])), HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [-8.231317991971707e-12, 1.3053706310500586e-08, 5.820123832707268e-07, -0.0021700747433379955, 29.424883205644317])), HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [0, 0, 0, 0, 20.7861565453831]))], cross_B_model='theory', cross_C_model='Orentlicher-Prausnitz', T=300, P=100000.0, zs=[0.78, 0.21, 0.01])

Methods

`B`()	Method to calculate and return the B second virial coefficient.
`C`()	Method to calculate and return the C third virial coefficient.
`H_dep`()	Method to calculate and return the molar departure enthalpy.
`S_dep`()	Method to calculate and return the molar departure entropy.
`V`()	Method to calculate and return the molar volume.
`d2B_dT2`()	Method to calculate and return the second temperature derivative of the B second virial coefficient.
`d2B_dTdzs`()	Method to calculate and return the temperature derivative of the first mole fraction derivatives of the B second virial coefficient.
`d2B_dzizjs`()	Method to calculate and return the second mole fraction derivatives of the B second virial coefficient.
`d2C_dT2`()	Method to calculate and return the second temperature derivative of the C third virial coefficient.
`d2C_dTdzs`()	Method to calculate and return the first temperature derivative of the first mole fraction derivatives of the C third virial coefficient.
`d2C_dzizjs`()	Method to calculate and return the second mole fraction derivatives of the C third virial coefficient.
`d2P_dT2`()	Method to calculate and return the second derivative of pressure with respect to temperature.
`d2P_dTdV`()	Method to calculate and return the second derivative of pressure with respect to volume and temperature.
`d2P_dV2`()	Method to calculate and return the second derivative of pressure with respect to volume.
`d2V_dzizjs`()	Method to calculate and return the second mole fraction derivatives of the molar volume.
`d3B_dT3`()	Method to calculate and return the third temperature derivative of the B second virial coefficient.
`d3C_dT3`()	Method to calculate and return the third temperature derivative of the C third virial coefficient.
`dB_dT`()	Method to calculate and return the first temperature derivative of the B second virial coefficient.
`dB_dzs`()	Method to calculate and return the first mole fraction derivatives of the B second virial coefficient.
`dC_dT`()	Method to calculate and return the first temperature derivative of the C third virial coefficient.
`dC_dzs`()	Method to calculate and return the first mole fraction derivatives of the C third virial coefficient.
`dG_dep_dzs`()	Method to calculate and return the first mole fraction derivatives of the departure Gibbs energy.
`dH_dep_dT`()	Method to calculate and return the first temperature derivative of molar departure enthalpy.
`dP_dT`()	Method to calculate and return the first derivative of pressure with respect to temperature.
`dP_dV`()	Method to calculate and return the first derivative of pressure with respect to volume.
`dS_dep_dT`()	Method to calculate and return the first temperature derivative of molar departure entropy.
`dV_dzs`()	Method to calculate and return the first mole fraction derivatives of the molar volume.
`lnphis`()	Method to calculate and return the log fugacity coefficients of the phase.

B()[source]¶

Method to calculate and return the B second virial coefficient.

Returns

Bfloat: Second molar virial coefficient [m^3/mol]

C()[source]¶

Method to calculate and return the C third virial coefficient.

Returns

Cfloat: Third molar virial coefficient [m^6/mol^2]

H_dep()[source]¶

Method to calculate and return the molar departure enthalpy.

H_{dep} = \frac{R T^{2} \left(2 V \frac{d}{d T} B{\left(T \right)} + \frac{d}{d T} C{\left(T \right)}\right)}{2 V^{2}} - R T \left(-1 + \frac{V^{2} + V B{\left(T \right)} + C{\left(T \right)}}{V^{2}} \right)

Returns

H_depfloat: Departure enthalpy [J/mol]

S_dep()[source]¶

Method to calculate and return the molar departure entropy.

S_{dep} = \frac{R \left(- T \frac{d}{d T} C{\left(T \right)} + 2 V^{2} \ln{\left(\frac{V^{2} + V B{\left(T \right)} + C{\left(T \right)}} {V^{2}} \right)} - 2 V \left(T \frac{d}{d T} B{\left(T \right)} + B{\left(T \right)}\right) - C{\left(T \right)}\right)}{2 V^{2}}

Returns

S_depfloat: Departure enthalpy [J/(mol*K)]

V()[source]¶

Method to calculate and return the molar volume.

Returns

Vfloat: Molar volume [m^3/mol]

__repr__()[source]¶

Method to create a string representation of the phase object, with the goal of making it easy to obtain standalone code which reproduces the current state of the phase. This is extremely helpful in creating new test cases.

Returns

recreationstr: String which is valid Python and recreates the current state of the object if ran, [-]

d2B_dT2()[source]¶

Method to calculate and return the second temperature derivative of the B second virial coefficient.

Returns

d2B_dT2float: Second temperature derivative of second molar virial coefficient [m^3/(mol*K^2)]

d2B_dTdzs()[source]¶

Method to calculate and return the temperature derivative of the first mole fraction derivatives of the B second virial coefficient.

Returns

d2B_dTdzslist[float]: First temperature derivative of first mole fraction derivatives of second molar virial coefficient [m^3/(mol*K)]

d2B_dzizjs()[source]¶

Method to calculate and return the second mole fraction derivatives of the B second virial coefficient.

Returns

d2B_dzizjslist[list[float]]: Second mole fraction derivatives of second molar virial coefficient [m^3/(mol)]

d2C_dT2()[source]¶

Method to calculate and return the second temperature derivative of the C third virial coefficient.

Returns

d2C_dT2float: Second temperature derivative of third molar virial coefficient [m^6/(mol^2*K^2)]

d2C_dTdzs()[source]¶

Method to calculate and return the first temperature derivative of the first mole fraction derivatives of the C third virial coefficient.

Returns

d2C_dTdzslist[float]: First temperature derivative of the first mole fraction derivatives of third molar virial coefficient [m^6/(mol^2*K)]

d2C_dzizjs()[source]¶

Method to calculate and return the second mole fraction derivatives of the C third virial coefficient.

Returns

d2C_dzizjslist[list[float]]: Second mole fraction derivatives of third molar virial coefficient [m^6/(mol^2)]

d2P_dT2()[source]¶

Method to calculate and return the second derivative of pressure with respect to temperature.

\left(\frac{\partial^2 P}{\partial T^2}\right)_{V} = \frac{R \left(T \left(V \frac{d^{2}}{d T^{2}} B{\left(T \right)} + \frac{d^{2}}{d T^{2}} C{\left(T \right)}\right) + 2 V \frac{d}{d T} B{\left(T \right)} + 2 \frac{d}{d T} C{\left(T \right)}\right)}{V^{3}}

Returns

d2P_dT2float: Second derivative of pressure with respect to temperature at constant volume [Pa/K^2]

d2P_dTdV()[source]¶

Method to calculate and return the second derivative of pressure with respect to volume and temperature.

\left(\frac{\partial^2 P}{\partial V\partial T}\right)_{T} = - \frac{R \left(2 T V \frac{d}{d T} B{\left(T \right)} + 3 T \frac{d}{d T} C{\left(T \right)} + V^{2} + 2 V B{\left(T \right)} + 3 C{\left(T \right)}\right)}{V^{4}}

Returns

d2P_dTdVfloat: Second derivative of pressure with respect to volume at and temperature [Pa*mol/(m^3*K)]

d2P_dV2()[source]¶

Method to calculate and return the second derivative of pressure with respect to volume.

\left(\frac{\partial^2 P}{\partial V^2}\right)_{T} = \frac{2 R T \left(V^{2} + 3 V B{\left(T \right)} + 6 C{\left(T \right)}\right)}{V^{5}}

Returns

d2P_dV2float: Second derivative of pressure with respect to volume at constant temperature [Pa*mol^2/(m^6)]

d2V_dzizjs()[source]¶

Method to calculate and return the second mole fraction derivatives of the molar volume. See chemicals.virial.d2V_dzizjs_virial for further details.

Returns

d2V_dzizjslist[float]: Second mole fraction derivatives of molar volume [m^3/mol]

d3B_dT3()[source]¶

Method to calculate and return the third temperature derivative of the B second virial coefficient.

Returns

d3B_dT3float: Third temperature derivative of second molar virial coefficient [m^3/(mol*K^3)]

d3C_dT3()[source]¶

Method to calculate and return the third temperature derivative of the C third virial coefficient.

Returns

d3C_dT3float: Second temperature derivative of third molar virial coefficient [m^6/(mol^2*K^3)]

dB_dT()[source]¶

Method to calculate and return the first temperature derivative of the B second virial coefficient.

Returns

dB_dTfloat: First temperature derivative of second molar virial coefficient [m^3/(mol*K)]

dB_dzs()[source]¶

Method to calculate and return the first mole fraction derivatives of the B second virial coefficient.

Returns

dB_dzslist[float]: First mole fraction derivatives of second molar virial coefficient [m^3/(mol)]

dC_dT()[source]¶

Method to calculate and return the first temperature derivative of the C third virial coefficient.

Returns

dC_dTfloat: First temperature derivative of third molar virial coefficient [m^6/(mol^2*K)]

dC_dzs()[source]¶

Method to calculate and return the first mole fraction derivatives of the C third virial coefficient.

Returns

dC_dzslist[float]: First mole fraction derivatives of third molar virial coefficient [m^6/(mol^2)]

dG_dep_dzs()[source]¶

Method to calculate and return the first mole fraction derivatives of the departure Gibbs energy.

Returns

dG_dep_dzslist[float]: First mole fraction derivatives of departure Gibbs energy [J/mol]

dH_dep_dT()[source]¶

Method to calculate and return the first temperature derivative of molar departure enthalpy.

\frac{\partial H_{dep}}{\partial T} = \frac{R \left(2 T^{2} V \frac{d^{2}}{d T^{2}} B{\left(T \right)} + T^{2} \frac{d^{2}}{d T^{2}} C{\left(T \right)} + 2 T V \frac{d}{d T} B{\left(T \right)} - 2 V B{\left(T \right)} - 2 C{\left(T \right)}\right)}{2 V^{2}}

Returns

dH_dep_dTfloat: First temperature derivative of departure enthalpy [J/(mol*K)]

dP_dT()[source]¶

Method to calculate and return the first derivative of pressure with respect to temperature.

\left(\frac{\partial P}{\partial T}\right)_{V} = \frac{R \left(T \left(V \frac{d}{d T} B{\left(T \right)} + \frac{d}{d T} C{\left(T \right)}\right) + V^{2} + V B{\left(T \right)} + C{\left(T \right)} \right)}{V^{3}}

Returns

dP_dTfloat: First derivative of pressure with respect to temperature at constant volume [Pa/K]

dP_dV()[source]¶

Method to calculate and return the first derivative of pressure with respect to volume.

\left(\frac{\partial P}{\partial V}\right)_{T} = - \frac{R T \left(V^{2} + 2 V B{\left(T \right)} + 3 C{\left(T \right)}\right)}{V^{4}}

Returns

dP_dVfloat: First derivative of pressure with respect to volume at constant temperature [Pa*mol/(m^3)]

dS_dep_dT()[source]¶

Method to calculate and return the first temperature derivative of molar departure entropy.

\frac{\partial S_{dep}}{\partial T} = \frac{R \left(2 V^{2} \left(V \frac{d}{d T} B{\left(T \right)} + \frac{d}{d T} C{\left(T \right)} \right) - \left(V^{2} + V B{\left(T \right)} + C{\left(T \right)} \right) \left(T \frac{d^{2}}{d T^{2}} C{\left(T \right)} + 2 V \left(T \frac{d^{2}}{d T^{2}} B{\left(T \right)} + 2 \frac{d}{d T} B{\left(T \right)}\right) + 2 \frac{d}{d T} C{\left(T \right)} \right)\right)}{2 V^{2} \left(V^{2} + V B{\left(T \right)} + C{\left(T \right)}\right)}

Returns

dS_dep_dTfloat: First temperature derivative of departure enthalpy [J/(mol*K^2)]

dV_dzs()[source]¶

Method to calculate and return the first mole fraction derivatives of the molar volume. See chemicals.virial.dV_dzs_virial for further details.

Returns

dV_dzslist[float]: First mole fraction derivatives of molar volume [m^3/mol]

lnphis()[source]¶

Method to calculate and return the log fugacity coefficients of the phase.

Returns

lnphislist[float]: Log fugacity coefficients, [-]

Corresponding States Virial Model ¶

class thermo.phases.VirialCSP(Tcs, Pcs, Vcs, omegas, B_model='VIRIAL_B_XIANG', cross_B_model='Tarakad-Danner', cross_B_model_kijs=None, C_model='VIRIAL_C_XIANG', B_model_Meng_as=None, B_model_Tsonopoulos_extended_as=None, B_model_Tsonopoulos_extended_bs=None, T=None)[source]¶

Bases: object

Class for calculating the B virial coefficients of pure components and their B interaction matrix, and the C virial coefficients of pure components and their mixtures. It is configurable which corresponding states model is used. Either the B or C model can be disabled; if both are off, this will revert to the ideal-gas equation of state.

Parameters

Tcslist[float]

Critical temperatures of all components, [K]

Pcslist[float]

Critical pressures of all components, [Pa]

Vcslist[float]

Critical volumes of all components, [m^3/mol]

omegaslist[float]

Acentric factors of all components, [-]

B_modelstr, optional

The model used to calculate the B pure component and interaction virial coefficients, [-]

VIRIAL_B_ZERO: The B virial coefficient is always zero
VIRIAL_B_PITZER_CURL The model of [2], chemicals.virial.BVirial_Pitzer_Curl
VIRIAL_B_ABBOTT The model of [3], chemicals.virial.BVirial_Abbott
VIRIAL_B_TSONOPOULOS The model of [4], chemicals.virial.BVirial_Tsonopoulos
VIRIAL_B_TSONOPOULOS_EXTENDED The model of [5] and [6], chemicals.virial.BVirial_Tsonopoulos_extended
VIRIAL_B_OCONNELL_PRAUSNITZ The model of [1], chemicals.virial.BVirial_Oconnell_Prausnitz
VIRIAL_B_XIANG The model of [7], chemicals.virial.BVirial_Xiang
VIRIAL_B_MENG The model of [8], chemicals.virial.BVirial_Meng

cross_B_modelstr, optional

The model used to calculate the B cross virial coefficient

VIRIAL_CROSS_B_TARAKAD_DANNER : This model uses the mixing rules for estimating interaction critical components according to the rules chemicals.virial.Tarakad_Danner_virial_CSP_Tcijs, chemicals.virial.Tarakad_Danner_virial_CSP_Pcijs, chemicals.virial.Lee_Kesler_virial_CSP_Vcijs and chemicals.virial.Tarakad_Danner_virial_CSP_omegaijs; note that this mixing rule has an interaction parameter for the interaction critical temperature, which defaults to zero and can be provided. chemicals.virial.Meng_Duan_2005_virial_CSP_kijs or chemicals.virial.Tarakad_Danner_virial_CSP_kijs are two sample models for estimating these parameters; additional models are available in the literature and also the value can be regressed from experimental values.

cross_B_model_kijslist[list[float]], optional

Cross parameters kijs for VIRIAL_CROSS_B_TARAKAD_DANNER cross rule; specified or set to zero [-]

C_modelstr, optional

The model used to calculate the C pure component and interaction virial coefficients, [-]

VIRIAL_C_ZERO: The C virial coefficient is always zero
VIRIAL_C_ORBEY_VERA The model of [9], chemicals.virial.CVirial_Orbey_Vera
VIRIAL_C_XIANG The model of [10], chemicals.virial.CVirial_Liu_Xiang

B_model_Meng_aslist[list[float]], optional

Meng a parameters; this is essentially a correction for polar behavior, and must be provided for all components as well as their interactions; see chemicals.virial.Meng_virial_a. This is used only for the model VIRIAL_B_MENG [-]

B_model_Tsonopoulos_extended_aslist[list[float]], optional

Tsonopoulos extended a parameters; this is essentially a correction for polar behavior, and must be provided for all components as well as their interactions; see thermo.functional_groups.BVirial_Tsonopoulos_extended_ab. This is used only for the model VIRIAL_B_TSONOPOULOS_EXTENDED [-]

B_model_Tsonopoulos_extended_bslist[list[float]], optional

Meng a parameters; this is essentially a correction for polar behavior, and must be provided for all components as well as their interactions; see thermo.functional_groups.BVirial_Tsonopoulos_extended_ab. This is used only for the model VIRIAL_B_TSONOPOULOS_EXTENDED [-]

Tfloat, optional

The specified temperature for the model; the calculations are cached based only on temperature, use VirialCSP.to to obtain a new object at a different temperature, [K]

References

1: O`Connell, J. P., and J. M. Prausnitz. “Empirical Correlation of Second Virial Coefficients for Vapor-Liquid Equilibrium Calculations.” Industrial & Engineering Chemistry Process Design and Development 6, no. 2 (April 1, 1967): 245-50. https://doi.org/10.1021/i260022a016.
2: Pitzer, Kenneth S., and R. F. Curl. “The Volumetric and Thermodynamic Properties of Fluids. III. Empirical Equation for the Second Virial Coefficient1.” Journal of the American Chemical Society 79, no. 10 (May 1, 1957): 2369-70. doi:10.1021/ja01567a007.
3: Smith, H. C. Van Ness Joseph M. Introduction to Chemical Engineering Thermodynamics 4E 1987.
4: Tsonopoulos, Constantine. “An Empirical Correlation of Second Virial Coefficients.” AIChE Journal 20, no. 2 (March 1, 1974): 263-72. doi:10.1002/aic.690200209.
5: Tsonopoulos, C., and J. L. Heidman. “From the Virial to the Cubic Equation of State.” Fluid Phase Equilibria 57, no. 3 (1990): 261-76. doi:10.1016/0378-3812(90)85126-U
6: Tsonopoulos, Constantine, and John H. Dymond. “Second Virial Coefficients of Normal Alkanes, Linear 1-Alkanols (and Water), Alkyl Ethers, and Their Mixtures.” Fluid Phase Equilibria, International Workshop on Vapour-Liquid Equilibria and Related Properties in Binary and Ternary Mixtures of Ethers, Alkanes and Alkanols, 133, no. 1-2 (June 1997): 11-34. doi:10.1016/S0378-3812(97)00058-7.
7: Xiang, H. W. “The New Simple Extended Corresponding-States Principle: Vapor Pressure and Second Virial Coefficient.” Chemical Engineering Science 57, no. 8 (April 2002): 1439049. https://doi.org/10.1016/S0009-2509(02)00017-9.
8: Meng, Long, Yuan-Yuan Duan, and Lei Li. “Correlations for Second and Third Virial Coefficients of Pure Fluids.” Fluid Phase Equilibria 226 (December 10, 2004): 109-20. https://doi.org/10.1016/j.fluid.2004.09.023.
9: Orbey, Hasan, and J. H. Vera. “Correlation for the Third Virial Coefficient Using Tc, Pc and ω as Parameters.” AIChE Journal 29, no. 1 (January 1, 1983): 107-13. https://doi.org/10.1002/aic.690290115.
10: Liu, D. X., and H. W. Xiang. “Corresponding-States Correlation and Prediction of Third Virial Coefficients for a Wide Range of Substances.” International Journal of Thermophysics 24, no. 6 (November 1, 2003): 1667-80. https://doi.org/10.1023/B:IJOT.0000004098.98614.38.

Methods

`B_interactions`()	Method to calculate and return the matrix of interaction component virial coefficients at the specified temperature.
`B_pures`()	Method to calculate and return the pure component virial coefficients at the specified temperature.
`C_interactions`()	Method to calculate and return the matrix of interaction third virial coefficients at the specified temperature.
`C_pures`()	Method to calculate and return the pure component third virial coefficients at the specified temperature.
`d2B_dT2_interactions`()	Method to calculate and return the second temperature derivative of the B virial interaction coefficients at the specified temperature.
`d2B_dT2_pures`()	Method to calculate and return the second temperature derivative of pure component virial coefficients at the specified temperature.
`d2C_dT2_interactions`()	Method to calculate and return the matrix of second temperature derivatives of interaction third virial coefficients at the specified temperature.
`d2C_dT2_pures`()	Method to calculate and return the second temperature derivative of pure component third virial coefficients at the specified temperature.
`d3B_dT3_interactions`()	Method to calculate and return the third temperature derivative of the B virial interaction coefficients at the specified temperature.
`d3B_dT3_pures`()	Method to calculate and return the third temperature derivative of pure component virial coefficients at the specified temperature.
`d3C_dT3_interactions`()	Method to calculate and return the matrix of third temperature derivatives of interaction third virial coefficients at the specified temperature.
`d3C_dT3_pures`()	Method to calculate and return the third temperature derivative of pure component third virial coefficients at the specified temperature.
`dB_dT_interactions`()	Method to calculate and return the first temperature derivative of the B virial interaction coefficients at the specified temperature.
`dB_dT_pures`()	Method to calculate and return the first temperature derivative of pure component virial coefficients at the specified temperature.
`dC_dT_interactions`()	Method to calculate and return the matrix of first temperature derivatives of interaction third virial coefficients at the specified temperature.
`dC_dT_pures`()	Method to calculate and return the first temperature derivative of pure component third virial coefficients at the specified temperature.
`to`([T])	Method to construct a new object at a new temperature.

B_interactions()[source]¶

Method to calculate and return the matrix of interaction component virial coefficients at the specified temperature.

Returns

B_interactionslist[list[float]]: Second B virial coefficients interaction matrix, [m^3/mol]

B_pures()[source]¶

Method to calculate and return the pure component virial coefficients at the specified temperature.

Returns

B_pureslist[float]: Second B virial coefficients, [m^3/mol]

C_interactions()[source]¶

Method to calculate and return the matrix of interaction third virial coefficients at the specified temperature.

Returns

C_interactionslist[list[float]]: Interaction third C virial coefficients, [m^6/mol^2]

C_pures()[source]¶

Method to calculate and return the pure component third virial coefficients at the specified temperature.

Returns

C_pureslist[float]: Third C virial coefficients, [m^6/mol^2]

__repr__()[source]¶

Method to create a string representation of the VirialCSP object, with the goal of making it easy to obtain standalone code which reproduces the current state of the phase. This is extremely helpful in creating new test cases.

Returns

recreationstr: String which is valid Python and recreates the current state of the object if ran, [-]

Examples

>>> from thermo import VirialCSP
>>> model = VirialCSP(Tcs=[126.2, 154.58, 150.8], Pcs=[3394387.5, 5042945.25, 4873732.5], Vcs=[8.95e-05, 7.34e-05, 7.49e-05], omegas=[0.04, 0.021, -0.004], B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA')
>>> model
VirialCSP(Tcs=[126.2, 154.58, 150.8], Pcs=[3394387.5, 5042945.25, 4873732.5], Vcs=[8.95e-05, 7.34e-05, 7.49e-05], omegas=[0.04, 0.021, -0.004], B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA')

d2B_dT2_interactions()[source]¶

Method to calculate and return the second temperature derivative of the B virial interaction coefficients at the specified temperature.

Returns

d2B_dT2_interactionslist[list[float]]: Second temperature derivative of second B virial interaction coefficients, [m^3/(mol*K^2)]

d2B_dT2_pures()[source]¶

Method to calculate and return the second temperature derivative of pure component virial coefficients at the specified temperature.

Returns

d2B_dT2_pureslist[float]: Second temperature derivative of second B virial coefficients, [m^3/(mol*K^2)]

d2C_dT2_interactions()[source]¶

Method to calculate and return the matrix of second temperature derivatives of interaction third virial coefficients at the specified temperature.

Returns

d2C_dT2_interactionslist[list[float]]: Interaction second temperature derivatives of third C virial coefficients, [m^6/(mol^2*K^2)]

d2C_dT2_pures()[source]¶

Method to calculate and return the second temperature derivative of pure component third virial coefficients at the specified temperature.

Returns

d2C_dT2_pureslist[float]: Second temperature derivative of third C virial coefficients, [m^6/(mol^2*K^2)]

d3B_dT3_interactions()[source]¶

Method to calculate and return the third temperature derivative of the B virial interaction coefficients at the specified temperature.

Returns

d3B_dT3_interactionslist[list[float]]: Third temperature derivative of second B virial interaction coefficients, [m^3/(mol*K^3)]

d3B_dT3_pures()[source]¶

Method to calculate and return the third temperature derivative of pure component virial coefficients at the specified temperature.

Returns

d3B_dT3_pureslist[float]: Third temperature derivative of second B virial coefficients, [m^3/(mol*K^3)]

d3C_dT3_interactions()[source]¶

Method to calculate and return the matrix of third temperature derivatives of interaction third virial coefficients at the specified temperature.

Returns

d3C_dT3_interactionslist[list[float]]: Interaction third temperature derivatives of third C virial coefficients, [m^6/(mol^2*K^2)]

d3C_dT3_pures()[source]¶

Method to calculate and return the third temperature derivative of pure component third virial coefficients at the specified temperature.

Returns

d3C_dT3_pureslist[float]: Third temperature derivative of third C virial coefficients, [m^6/(mol^2*K^3)]

dB_dT_interactions()[source]¶

Method to calculate and return the first temperature derivative of the B virial interaction coefficients at the specified temperature.

Returns

dB_dT_interactionslist[list[float]]: Second temperature derivative of second B virial interaction coefficients, [m^3/(mol*K)]

dB_dT_pures()[source]¶

Method to calculate and return the first temperature derivative of pure component virial coefficients at the specified temperature.

Returns

dB_dT_pureslist[float]: Second temperature derivative of second B virial coefficients, [m^3/(mol*K)]

dC_dT_interactions()[source]¶

Method to calculate and return the matrix of first temperature derivatives of interaction third virial coefficients at the specified temperature.

Returns

dC_dT_interactionslist[list[float]]: Interaction first temperature derivatives of third C virial coefficients, [m^6/(mol^2*K)]

dC_dT_pures()[source]¶

Method to calculate and return the first temperature derivative of pure component third virial coefficients at the specified temperature.

Returns

dC_dT_pureslist[float]: First temperature derivative of third C virial coefficients, [m^6/(mol^2*K)]

to(T=None)[source]¶

Method to construct a new object at a new temperature.

Parameters

Tfloat: Temperature, [K]

Returns

objVirialCSP: Object at new temperature, [-]

Activity Based Liquids ¶

class thermo.phases.GibbsExcessLiquid(VaporPressures, VolumeLiquids=None, HeatCapacityGases=None, GibbsExcessModel=None, eos_pure_instances=None, EnthalpyVaporizations=None, HeatCapacityLiquids=None, VolumeSupercriticalLiquids=None, use_Hvap_caloric=False, use_Poynting=False, use_phis_sat=False, use_Tait=False, use_eos_volume=False, Hfs=None, Gfs=None, Sfs=None, henry_components=None, henry_abcdef=None, henry_as=None, henry_bs=None, henry_cs=None, henry_ds=None, henry_es=None, henry_fs=None, henry_mode='solvents_with_parameters', T=None, P=None, zs=None, Psat_extrpolation='AB', equilibrium_basis=None, caloric_basis=None)[source]¶

Bases: thermo.phases.phase.Phase

Phase based on combining Raoult’s law with a GibbsExcess model, optionally including saturation fugacity coefficient corrections (if the vapor phase is a cubic equation of state) and Poynting correction factors (if more accuracy is desired).

The equilibrium equation options (controlled by equilibrium_basis) are as follows:

‘Psat’: $\phi_i = \frac{\gamma_i P_{i}^{sat}}{P}$
‘Poynting&PhiSat’: $\phi_i = \frac{\gamma_i P_{i}^{sat} \phi_i^{sat} \text{Poynting}_i}{P}$
‘Poynting’: $\phi_i = \frac{\gamma_i P_{i}^{sat}\text{Poynting}_i}{P}$
‘PhiSat’: $\phi_i = \frac{\gamma_i P_{i}^{sat} \phi_i^{sat}}{P}$

In all cases, the activity coefficient is derived from the GibbsExcess model specified as input; use the IdealSolution class as an input to set the activity coefficients to one.

The enthalpy H and entropy S (and other caloric properties U, G, A) equation options are similar to the equilibrium ones. If the same option is selected for equilibrium_basis and caloric_basis, the phase will be thermodynamically consistent. This is recommended for many reasons. The full ‘Poynting&PhiSat’ equations for H and S are as follows; see GibbsExcessLiquid.H and GibbsExcessLiquid.S for all of the other equations:

H = H_{\text{excess}} + \sum_i z_i \left[-RT^2\left( \frac{\frac{\partial \phi_{\text{sat},i}}{\partial T}}{\phi_{\text{sat},i}} + \frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + \frac{\frac{\text{Poynting}}{\partial T}}{\text{Poynting}} \right) + \int_{T,ref}^T C_{p,ig} dT \right]

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left( T \frac{\frac{\partial \phi_{\text{sat},i}}{\partial T}}{\phi_{\text{sat},i}} + T\frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + T\frac{\frac{\text{Poynting}}{\partial T}}{\text{Poynting}} + \ln(P_{\text{sat},i}) + \ln\left(\frac{\text{Poynting}\cdot\phi_{\text{sat},i}}{P}\right) \right) - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

An additional caloric mode is Hvap, which uses enthalpy of vaporization; this mode can never be thermodynamically consistent, but is still widely used.

H = H_{\text{excess}} + \sum_i z_i\left[-H_{vap,i} + \int_{T,ref}^T C_{p,ig} dT \right]

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left(\ln P_{\text{sat},i} + \ln\left(\frac{1}{P}\right)\right) + \frac{H_{vap,i}}{T} - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

Warning

Note that above the critical point, there is no definition for what vapor pressure is. The vapor pressure also tends to reach zero at temperatures in the 4-20 K range. These aspects mean extrapolation in the supercritical and very low temperature region is critical to ensure the equations will still converge. Extrapolation can be performed using either the equation $P^{\text{sat}} = \exp\left(A - \frac{B}{T}\right)$ or $P^{\text{sat}} = \exp\left(A + \frac{B}{T} + C\cdot \ln T\right)$ by setting Psat_extrpolation to either ‘AB’ or ‘ABC’ respectively. The extremely low temperature region’s issue is solved by calculating the logarithm of vapor pressures instead of the actual value. While floating point values in Python (doubles) can reach a minimum value of around 1e-308, if only the logarithm of that number is computed no issues arise. Both of these features only work when the vapor pressure correlations are polynomials.

Warning

When using ‘PhiSat’ as an option, note that the factor cannot be calculated when a compound is supercritical, as there is no longer any vapor-liquid pure-component equilibrium (by definition).

Parameters

VaporPressureslist[thermo.vapor_pressure.VaporPressure]: Objects holding vapor pressure data and methods, [-]
VolumeLiquidslist[thermo.volume.VolumeLiquid], optional: Objects holding liquid volume data and methods; required for Poynting factors and volumetric properties, [-]
HeatCapacityGaseslist[thermo.heat_capacity.HeatCapacityGas], optional: Objects proiding pure-component heat capacity correlations; required for caloric properties, [-]
GibbsExcessModelGibbsExcess, optional: Configured instance for calculating activity coefficients and excess properties; set to IdealSolution if not provided, [-]
eos_pure_instanceslist[thermo.eos.GCEOS], optional: Cubic equation of state object instances for each pure component, [-]
EnthalpyVaporizationslist[thermo.phase_change.EnthalpyVaporization], optional: Objects holding enthalpy of vaporization data and methods; used only with the ‘Hvap’ optional, [-]
HeatCapacityLiquidslist[thermo.heat_capacity.HeatCapacityLiquid], optional: Objects holding liquid heat capacity data and methods; not used at present, [-]
VolumeSupercriticalLiquidslist[thermo.volume.VolumeLiquid], optional: Objects holding liquid volume data and methods but that are used for supercritical temperatures on a per-component basis only; required for Poynting factors and volumetric properties at supercritical conditions; VolumeLiquids is used if not provided, [-]
Hfslist[float], optional: Molar ideal-gas standard heats of formation at 298.15 K and 1 atm, [J/mol]
Gfslist[float], optional: Molar ideal-gas standard Gibbs energies of formation at 298.15 K and 1 atm, [J/mol]
Tfloat, optional: Temperature, [K]
Pfloat, optional: Pressure, [Pa]
zslist[float], optional: Mole fractions of each component, [-]
equilibrium_basisstr, optional: Which set of equilibrium equations to use when calculating fugacities and related properties; valid options are ‘Psat’, ‘Poynting&PhiSat’, ‘Poynting’, ‘PhiSat’, [-]
caloric_basisstr, optional: Which set of caloric equations to use when calculating fugacities and related properties; valid options are ‘Psat’, ‘Poynting&PhiSat’, ‘Poynting’, ‘PhiSat’, ‘Hvap’ [-]
Psat_extrpolationstr, optional: One of ‘AB’ or ‘ABC’; configures extrapolation for vapor pressure, [-]
henry_abcdeftuple[list[list[float]], 6], optional: Contains the parameters used for henry’s law constant, [-]
henry_aslist[list[float]], optional: a parameters used in calculating henry’s law constant, [-]
henry_bslist[list[float]], optional: b parameters used in calculating henry’s law constant, [K]
henry_cslist[list[float]], optional: c parameters used in calculating henry’s law constant, [-]
henry_dslist[list[float]], optional: d paraemeters used in calculating henry’s law constant, [1/K]
henry_eslist[list[float]], optional: e parameters used in calculating henry’s law constant, [K^2]
henry_fslist[list[float]], optional: f parameters used in calculating henry’s law constant, [1/K^2]
henry_modestr: The setting for henry’s law. ‘solvents’ to consider all components set not to be henry’s law components a solvent (if any parameters are missing this will not make sense at all); ‘solvents_with_parameters’ to consider only the solvents with parameters (vapor pressures will be used if a component has no solvents whatsoever)
use_Hvap_caloricbool, optional: If True, enthalpy and entropy will be calculated using ideal-gas heat capacity and the heat of vaporization of the fluid only. This forces enthalpy to be pressure-independent. This supersedes other options which would otherwise impact these properties. The molar volume of the fluid has no impact on enthalpy or entropy if this option is True. This option is not thermodynamically consistent, but is still often an assumption that is made.

Methods

`Cp`()	Method to calculate and return the constant-pressure heat capacity of the phase.
`H`()	Method to calculate the enthalpy of the `GibbsExcessLiquid` phase.
`Poyntings`()	Method to calculate and return the Poynting pressure correction factors of the phase, [-].
`S`()	Method to calculate the entropy of the `GibbsExcessLiquid` phase.
`d2lnHenry_matrix_dT2`()	Method to calculate and return the second temperature derivative of the matrix of log Henry's law constants as required by the traditional mixing rule, [-].
`dlnHenry_matrix_dT`()	Method to calculate and return the first temperature derivative of the matrix of log Henry's law constants as required by the traditional mixing rule, [-].
`gammas`()	Method to calculate and return the activity coefficients of the phase, [-].
`lnHenry_matrix`()	Method to calculate and return the matrix of log Henry's law constants as required by the traditional mixing rule, [-].
`phis_sat`()	Method to calculate and return the saturation fugacity coefficient correction factors of the phase, [-].

Cp()[source]¶

Method to calculate and return the constant-pressure heat capacity of the phase.

Returns

Cpfloat: Molar heat capacity, [J/(mol*K)]

H()[source]¶

Method to calculate the enthalpy of the GibbsExcessLiquid phase. Depending on the settings of the phase, this can include the effects of activity coefficients gammas, pressure correction terms Poyntings, and pure component saturation fugacities phis_sat as well as the pure component vapor pressures.

When caloric_basis is ‘Poynting&PhiSat’:

H = H_{\text{excess}} + \sum_i z_i \left[-RT^2\left( \frac{\frac{\partial \phi_{\text{sat},i}}{\partial T}}{\phi_{\text{sat},i}} + \frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + \frac{\frac{\text{Poynting}}{\partial T}}{\text{Poynting}} \right) + \int_{T,ref}^T C_{p,ig} dT \right]

When caloric_basis is ‘PhiSat’:

H = H_{\text{excess}} + \sum_i z_i \left[-RT^2\left( \frac{\frac{\partial \phi_{\text{sat},i}}{\partial T}}{\phi_{\text{sat},i}} + \frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} \right) + \int_{T,ref}^T C_{p,ig} dT \right]

When caloric_basis is ‘Poynting’:

H = H_{\text{excess}} + \sum_i z_i \left[-RT^2\left( + \frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + \frac{\frac{\text{Poynting}}{\partial T}}{\text{Poynting}} \right) + \int_{T,ref}^T C_{p,ig} dT \right]

When caloric_basis is ‘Psat’:

H = H_{\text{excess}} + \sum_i z_i \left[-RT^2\left( + \frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} \right) + \int_{T,ref}^T C_{p,ig} dT \right]

When caloric_basis is ‘Hvap’:

H = H_{\text{excess}} + \sum_i z_i\left[-H_{vap,i} + \int_{T,ref}^T C_{p,ig} dT \right]

Returns

Hfloat: Enthalpy of the phase, [J/(mol)]

Poyntings()[source]¶

Method to calculate and return the Poynting pressure correction factors of the phase, [-].

\text{Poynting}_i = \exp\left(\frac{V_{m,i}(P-P_{sat})}{RT}\right)

Returns

Poyntingslist[float]: Poynting pressure correction factors, [-]

Notes

The above formula is correct for pressure-independent molar volumes. When the volume does depend on pressure, the full expression is:

\text{Poynting} = \exp\left[\frac{\int_{P_i^{sat}}^P V_i^l dP}{RT}\right]

When a specified model e.g. the Tait equation is used, an analytical integral of this term is normally available.

S()[source]¶

Method to calculate the entropy of the GibbsExcessLiquid phase. Depending on the settings of the phase, this can include the effects of activity coefficients gammas, pressure correction terms Poyntings, and pure component saturation fugacities phis_sat as well as the pure component vapor pressures.

When caloric_basis is ‘Poynting&PhiSat’:

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left( T \frac{\frac{\partial \phi_{\text{sat},i}}{\partial T}}{\phi_{\text{sat},i}} + T\frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + T\frac{\frac{\text{Poynting}}{\partial T}}{\text{Poynting}} + \ln(P_{\text{sat},i}) + \ln\left(\frac{\text{Poynting}\cdot\phi_{\text{sat},i}}{P}\right) \right) - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

When caloric_basis is ‘PhiSat’:

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left( T \frac{\frac{\partial \phi_{\text{sat},i}}{\partial T}}{\phi_{\text{sat},i}} + T\frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + \ln(P_{\text{sat},i}) + \ln\left(\frac{\phi_{\text{sat},i}}{P}\right) \right) - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

When caloric_basis is ‘Poynting’:

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left( T\frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + T\frac{\frac{\text{Poynting}}{\partial T}}{\text{Poynting}} + \ln(P_{\text{sat},i}) + \ln\left(\frac{\text{Poynting}}{P}\right) \right) - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

When caloric_basis is ‘Psat’:

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left( T\frac{\frac{\partial P_{\text{sat},i}}{\partial T}}{P_{\text{sat},i}} + \ln(P_{\text{sat},i}) + \ln\left(\frac{1}{P}\right) \right) - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

When caloric_basis is ‘Hvap’:

S = S_{\text{excess}} - R\sum_i z_i\ln z_i - R\ln\left(\frac{P}{P_{ref}}\right) - \sum_i z_i\left[R\left(\ln P_{\text{sat},i} + \ln\left(\frac{1}{P}\right)\right) + \frac{H_{vap,i}}{T} - \int_{T,ref}^T \frac{C_{p,ig,i}}{T} dT \right]

Returns

Sfloat: Entropy of the phase, [J/(mol*K)]

d2lnHenry_matrix_dT2()[source]¶

Method to calculate and return the second temperature derivative of the matrix of log Henry’s law constants as required by the traditional mixing rule, [-].

Returns

d2lnHenry_matrix_dT2list[list[float]]: Second temperature derivative of Henry’s law interaction parameters, [log(Pa)/K]

dlnHenry_matrix_dT()[source]¶

Method to calculate and return the first temperature derivative of the matrix of log Henry’s law constants as required by the traditional mixing rule, [-].

Returns

dlnHenry_matrix_dTlist[list[float]]: First temperature derivative of Henry’s law interaction parameters, [log(Pa)/K]

gammas()[source]¶

Method to calculate and return the activity coefficients of the phase, [-]. This is a direct call to GibbsExcess.gammas.

Returns

gammaslist[float]: Activity coefficients, [-]

lnHenry_matrix()[source]¶

Method to calculate and return the matrix of log Henry’s law constants as required by the traditional mixing rule, [-].

\ln \text{H}_{i,j} = A_{ij}+\frac{B_{ij}}{T}+C_{ij}\ln T + D_{ij}T + \frac{E_{ij}}{T^2} + F_{ij}{T^2}

Returns

lnHenry_matrixlist[list[float]]: Henry’s law interaction parameters, [log(Pa)]

Notes

Solvent/solvent and gas/gas values are all 0.

phis_sat()[source]¶

Method to calculate and return the saturation fugacity coefficient correction factors of the phase, [-].

These are calculated from the provided pure-component equations of state. This term should only be used with a consistent vapor-phase cubic equation of state.

Returns

phis_satlist[float]: Saturation fugacity coefficient correction factors, [-]

Notes

Warning

This factor cannot be calculated when a compound is supercritical, as there is no longer any vapor-liquid pure-component equilibrium (by definition).

Fundamental Equations of State ¶

HelmholtzEOS is the base class for all Helmholtz energy fundamental equations of state.

class thermo.phases.HelmholtzEOS[source]¶

Bases: thermo.phases.phase.Phase

Methods

`Cp`()	Method to calculate and return the constant-pressure heat capacity of the phase.
`Cv`()	Method to calculate and return the constant-volume heat capacity Cv of the phase.
`H`()	Method to calculate and return the enthalpy of the phase.
`S`()	Method to calculate and return the entropy of the phase.
`V_iter`([force])	Method to calculate and return the volume of the phase in a way suitable for a TV resolution to converge on the same pressure.
`d2P_dT2`()	Method to calculate and return the second temperature derivative of pressure of the phase.
`d2P_dTdV`()	Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.
`d2P_dV2`()	Method to calculate and return the second volume derivative of pressure of the phase.
`dH_dP`()	Method to calculate and return the pressure derivative of enthalpy of the phase at constant pressure.
`dP_dT`()	Method to calculate and return the first temperature derivative of pressure of the phase.
`dP_dV`()	Method to calculate and return the first volume derivative of pressure of the phase.
`dS_dP`()	Method to calculate and return the pressure derivative of entropy of the phase at constant pressure.
`lnphis`()	Method to calculate and return the log of fugacity coefficients of each component in the phase.
`to_TP_zs`(T, P, zs)	Method to create a new Phase object with the same constants as the existing Phase but at a different T and P.

Cp()[source]¶

Method to calculate and return the constant-pressure heat capacity of the phase.

Returns

Cpfloat: Molar heat capacity, [J/(mol*K)]

Cv()[source]¶

Method to calculate and return the constant-volume heat capacity Cv of the phase.

C_v = T\left(\frac{\partial P}{\partial T}\right)_V^2/ \left(\frac{\partial P}{\partial V}\right)_T + Cp

Returns

Cvfloat: Constant volume molar heat capacity, [J/(mol*K)]

H()[source]¶

Method to calculate and return the enthalpy of the phase. The reference state for most subclasses is an ideal-gas enthalpy of zero at 298.15 K and 101325 Pa.

Returns

Hfloat: Molar enthalpy, [J/(mol)]

S()[source]¶

Method to calculate and return the entropy of the phase. The reference state for most subclasses is an ideal-gas entropy of zero at 298.15 K and 101325 Pa.

Returns

Sfloat: Molar entropy, [J/(mol*K)]

V_iter(force=False)¶

Method to calculate and return the volume of the phase in a way suitable for a TV resolution to converge on the same pressure. This often means the return value of this method is an mpmath mpf. This dummy method simply returns the implemented V method.

Returns

Vfloat or mpf: Molar volume, [m^3/mol]

__repr__()[source]¶

Method to create a string representation of the phase object, with the goal of making it easy to obtain standalone code which reproduces the current state of the phase. This is extremely helpful in creating new test cases.

Returns

recreationstr: String which is valid Python and recreates the current state of the object if ran, [-]

Examples

>>> from thermo import IAPWS95Gas
>>> phase = IAPWS95Gas(T=300, P=1e5, zs=[1])
>>> phase
IAPWS95Gas(T=300, P=100000.0, zs=[1.0])

d2P_dT2()[source]¶

Method to calculate and return the second temperature derivative of pressure of the phase.

Returns

d2P_dT2float: Second temperature derivative of pressure, [Pa/K^2]

d2P_dTdV()[source]¶

Method to calculate and return the second derivative of pressure with respect to temperature and volume of the phase.

Returns

d2P_dTdVfloat: Second volume derivative of pressure, [mol*Pa^2/(J*K)]

d2P_dV2()[source]¶

Method to calculate and return the second volume derivative of pressure of the phase.

Returns

d2P_dV2float: Second volume derivative of pressure, [Pa*mol^2/m^6]

dH_dP()¶

Method to calculate and return the pressure derivative of enthalpy of the phase at constant pressure.

Returns

dH_dP_Tfloat: Pressure derivative of enthalpy, [J/(mol*Pa)]

dP_dT()[source]¶

Method to calculate and return the first temperature derivative of pressure of the phase.

Returns

dP_dTfloat: First temperature derivative of pressure, [Pa/K]

dP_dV()[source]¶

Method to calculate and return the first volume derivative of pressure of the phase.

Returns

dP_dVfloat: First volume derivative of pressure, [Pa*mol/m^3]

dS_dP()¶

Method to calculate and return the pressure derivative of entropy of the phase at constant pressure.

Returns

dS_dP_Tfloat: Pressure derivative of entropy, [J/(mol*K*Pa)]

lnphis()[source]¶

Method to calculate and return the log of fugacity coefficients of each component in the phase.

Returns

lnphislist[float]: Log fugacity coefficients, [-]

to_TP_zs(T, P, zs)¶

Method to create a new Phase object with the same constants as the existing Phase but at a different T and P.

Parameters

zslist[float]: Molar composition of the new phase, [-]
Tfloat: Temperature of the new phase, [K]
Pfloat: Pressure of the new phase, [Pa]

Returns

new_phasePhase: New phase at the specified conditions, [-]

Notes

This method is marginally faster than Phase.to as it does not need to check what the inputs are.

Examples

>>> from thermo import IdealGas
>>> phase = IdealGas(T=300, P=1e5, zs=[.79, .21], HeatCapacityGases=[])
>>> phase.to_TP_zs(T=1e5, P=1e3, zs=[.5, .5])
IdealGas(HeatCapacityGases=[], T=100000.0, P=1000.0, zs=[0.5, 0.5])

IAPWS95 is the base class for the IAPWS-95 formulation for water; IAPWS95Gas and IAPWS95Liquid are the gas and liquid sub-phases respectively.

class thermo.phases.IAPWS95(T=None, P=None, zs=None)[source]¶

Bases: thermo.phases.helmholtz_eos.HelmholtzEOS

Methods

`k`()	Calculate and return the thermal conductivity of water according to the IAPWS.
`mu`()	Calculate and return the viscosity of water according to the IAPWS.

k()[source]¶

Calculate and return the thermal conductivity of water according to the IAPWS. For details, see chemicals.thermal_conductivity.k_IAPWS.

Returns

kfloat: Thermal conductivity of water, [W/m/K]

mu()[source]¶

Calculate and return the viscosity of water according to the IAPWS. For details, see chemicals.viscosity.mu_IAPWS.

Returns

mufloat: Viscosity of water, [Pa*s]

class thermo.phases.IAPWS95Gas(T=None, P=None, zs=None)[source]¶: Bases: thermo.phases.iapws_phase.IAPWS95

class thermo.phases.IAPWS95Liquid(T=None, P=None, zs=None)[source]¶: Bases: thermo.phases.iapws_phase.IAPWS95

DryAirLemmon is an implementation of thermophysical properties of air by Lemmon (2000).

class thermo.phases.DryAirLemmon(T=None, P=None, zs=None)[source]¶

Bases: thermo.phases.helmholtz_eos.HelmholtzEOS

Methods

`k`()	Calculate and return the thermal conductivity of air according to Lemmon and Jacobsen (2004) For details, see `chemicals.thermal_conductivity.k_air_lemmon`.
`mu`()	Calculate and return the viscosity of air according to the Lemmon and Jacobsen (2003) .

k()[source]¶

Calculate and return the thermal conductivity of air according to Lemmon and Jacobsen (2004) For details, see chemicals.thermal_conductivity.k_air_lemmon.

Returns

kfloat: Thermal conductivity of air, [W/m/K]

mu()[source]¶

Calculate and return the viscosity of air according to the Lemmon and Jacobsen (2003) . For details, see chemicals.viscosity.mu_air_lemmon.

Returns

mufloat: Viscosity of air, [Pa*s]

CoolProp Wrapper ¶

class thermo.phases.CoolPropGas(backend, fluid, T=None, P=None, zs=None, Hfs=None, Gfs=None, Sfs=None)[source]¶: Bases: thermo.phases.coolprop_phase.CoolPropPhase

class thermo.phases.CoolPropLiquid(backend, fluid, T=None, P=None, zs=None, Hfs=None, Gfs=None, Sfs=None)[source]¶: Bases: thermo.phases.coolprop_phase.CoolPropPhase

Phase Models (thermo.phases)¶

Base Class ¶

Ideal Gas Equation of State ¶

Cubic Equations of State ¶

Gas Phases ¶

Liquid Phases ¶

Virial Equations of State ¶

Gas Phase Object ¶

Corresponding States Virial Model ¶

Activity Based Liquids ¶

Fundamental Equations of State ¶

CoolProp Wrapper ¶

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