thermo.volume module¶

thermo.volume.
Yen_Woods_saturation
(T, Tc, Vc, Zc)[source]¶ Calculates saturation liquid volume, using the Yen and Woods [R14021427] CSP method and a chemical’s critical properties.
The molar volume of a liquid is given by:
\[ \begin{align}\begin{aligned}Vc/Vs = 1 + A(1T_r)^{1/3} + B(1T_r)^{2/3} + D(1T_r)^{4/3}\\D = 0.93B\\A = 17.4425  214.578Z_c + 989.625Z_c^2  1522.06Z_c^3\\B = 3.28257 + 13.6377Z_c + 107.4844Z_c^2384.211Z_c^3 \text{ if } Zc \le 0.26\\B = 60.2091  402.063Z_c + 501.0 Z_c^2 + 641.0 Z_c^3 \text{ if } Zc \ge 0.26\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Vc : float
Critical volume of fluid [m^3/mol]
Zc : float
Critical compressibility of fluid, []
Returns: Vs : float
Saturation liquid volume, [m^3/mol]
Notes
Original equation was in terms of density, but it is converted here.
No example has been found, nor are there points in the article. However, it is believed correct. For compressed liquids with the YenWoods method, see the YenWoods_compressed function.
References
[R14021427] (1, 2) Yen, Lewis C., and S. S. Woods. “A Generalized Equation for Computer Calculation of Liquid Densities.” AIChE Journal 12, no. 1 (1966): 9599. doi:10.1002/aic.690120119 Examples
>>> Yen_Woods_saturation(300, 647.14, 55.45E6, 0.245) 1.7695330765295693e05

thermo.volume.
Rackett
(T, Tc, Pc, Zc)[source]¶ Calculates saturation liquid volume, using Rackett CSP method and critical properties.
The molar volume of a liquid is given by:
\[V_s = \frac{RT_c}{P_c}{Z_c}^{[1+(1{T/T_c})^{2/7} ]}\]Units are all currently in m^3/mol  this can be changed to kg/m^3
Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
Zc : float
Critical compressibility of fluid, []
Returns: Vs : float
Saturation liquid volume, [m^3/mol]
Notes
Units are dependent on gas constant R, imported from scipy According to Reid et. al, underpredicts volume for compounds with Zc < 0.22
References
[R14031428] Rackett, Harold G. “Equation of State for Saturated Liquids.” Journal of Chemical & Engineering Data 15, no. 4 (1970): 514517. doi:10.1021/je60047a012 Examples
Propane, example from the API Handbook
>>> Vm_to_rho(Rackett(272.03889, 369.83, 4248000.0, 0.2763), 44.09562) 531.3223212651092

thermo.volume.
Yamada_Gunn
(T, Tc, Pc, omega)[source]¶ Calculates saturation liquid volume, using Yamada and Gunn CSP method and a chemical’s critical properties and acentric factor.
The molar volume of a liquid is given by:
\[V_s = \frac{RT_c}{P_c}{(0.290560.08775\omega)}^{[1+(1{T/T_c})^{2/7}]}\]Units are in m^3/mol.
Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor for fluid, []
Returns: Vs : float
saturation liquid volume, [m^3/mol]
Notes
This equation is an improvement on the Rackett equation. This is often presented as the Rackett equation. The acentric factor is used here, instead of the critical compressibility A variant using a reference fluid also exists
References
[R14041429] Gunn, R. D., and Tomoyoshi Yamada. “A Corresponding States Correlation of Saturated Liquid Volumes.” AIChE Journal 17, no. 6 (1971): 134145. doi:10.1002/aic.690170613 [R14051429] Yamada, Tomoyoshi, and Robert D. Gunn. “Saturated Liquid Molar Volumes. Rackett Equation.” Journal of Chemical & Engineering Data 18, no. 2 (1973): 23436. doi:10.1021/je60057a006 Examples
>>> Yamada_Gunn(300, 647.14, 22048320.0, 0.245) 2.1882836429895796e05

thermo.volume.
Townsend_Hales
(T, Tc, Vc, omega)[source]¶ Calculates saturation liquid density, using the Townsend and Hales CSP method as modified from the original Riedel equation. Uses chemical critical volume and temperature, as well as acentric factor
The density of a liquid is given by:
\[Vs = V_c/\left(1+0.85(1T_r)+(1.692+0.986\omega)(1T_r)^{1/3}\right)\]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Vc : float
Critical volume of fluid [m^3/mol]
omega : float
Acentric factor for fluid, []
Returns: Vs : float
Saturation liquid volume, [m^3/mol]
Notes
The requirement for critical volume and acentric factor requires all data.
References
[R14061431] Hales, J. L, and R Townsend. “Liquid Densities from 293 to 490 K of Nine Aromatic Hydrocarbons.” The Journal of Chemical Thermodynamics 4, no. 5 (1972): 76372. doi:10.1016/00219614(72)90050X Examples
>>> Townsend_Hales(300, 647.14, 55.95E6, 0.3449) 1.8007361992619923e05

thermo.volume.
Bhirud_normal
(T, Tc, Pc, omega)[source]¶ Calculates saturation liquid density using the Bhirud [R14071432] CSP method. Uses Critical temperature and pressure and acentric factor.
The density of a liquid is given by:
\[ \begin{align}\begin{aligned}&\ln \frac{P_c}{\rho RT} = \ln U^{(0)} + \omega\ln U^{(1)}\\&\ln U^{(0)} = 1.396 44  24.076T_r+ 102.615T_r^2 255.719T_r^3+355.805T_r^4256.671T_r^5 + 75.1088T_r^6\\&\ln U^{(1)} = 13.4412  135.7437 T_r + 533.380T_r^2 1091.453T_r^3+1231.43T_r^4  728.227T_r^5 + 176.737T_r^6\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor for fluid, []
Returns: Vm : float
Saturated liquid molar volume, [mol/m^3]
Notes
Claimed inadequate by others.
An interpolation table for ln U values are used from Tr = 0.98  1.000. Has terrible behavior at low reduced temperatures.
References
[R14071432] (1, 2) Bhirud, Vasant L. “Saturated Liquid Densities of Normal Fluids.” AIChE Journal 24, no. 6 (November 1, 1978): 112731. doi:10.1002/aic.690240630 Examples
Pentane
>>> Bhirud_normal(280.0, 469.7, 33.7E5, 0.252) 0.00011249654029488583

thermo.volume.
COSTALD
(T, Tc, Vc, omega)[source]¶ Calculate saturation liquid density using the COSTALD CSP method.
A popular and accurate estimation method. If possible, fit parameters are used; alternatively critical properties work well.
The density of a liquid is given by:
\[ \begin{align}\begin{aligned}V_s=V^*V^{(0)}[1\omega_{SRK}V^{(\delta)}]\\V^{(0)}=11.52816(1T_r)^{1/3}+1.43907(1T_r)^{2/3}  0.81446(1T_r)+0.190454(1T_r)^{4/3}\\V^{(\delta)}=\frac{0.296123+0.386914T_r0.0427258T_r^20.0480645T_r^3} {T_r1.00001}\end{aligned}\end{align} \]Units are that of critical or fit constant volume.
Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Vc : float
Critical volume of fluid [m^3/mol]. This parameter is alternatively a fit parameter
omega : float
(ideally SRK) Acentric factor for fluid, [] This parameter is alternatively a fit parameter.
Returns: Vs : float
Saturation liquid volume
Notes
196 constants are fit to this function in [R14081433]. Range: 0.25 < Tr < 0.95, often said to be to 1.0
This function has been checked with the API handbook example problem.
References
[R14081433] (1, 2) Hankinson, Risdon W., and George H. Thomson. “A New Correlation for Saturated Densities of Liquids and Their Mixtures.” AIChE Journal 25, no. 4 (1979): 653663. doi:10.1002/aic.690250412 Examples
Propane, from an example in the API Handbook
>>> Vm_to_rho(COSTALD(272.03889, 369.83333, 0.20008161E3, 0.1532), 44.097) 530.3009967969841

thermo.volume.
Campbell_Thodos
(T, Tb, Tc, Pc, M, dipole=None, hydroxyl=False)[source]¶ Calculate saturation liquid density using the CampbellThodos [R14091434] CSP method.
An old and uncommon estimation method.
\[ \begin{align}\begin{aligned}V_s = \frac{RT_c}{P_c}{Z_{RA}}^{[1+(1T_r)^{2/7}]}\\Z_{RA} = \alpha + \beta(1T_r)\\\alpha = 0.38830.0179s\\s = T_{br} \frac{\ln P_c}{(1T_{br})}\\\beta = 0.00318s0.0211+0.625\Lambda^{1.35}\\\Lambda = \frac{P_c^{1/3}} { M^{1/2} T_c^{5/6}}\end{aligned}\end{align} \]For polar compounds:
\[ \begin{align}\begin{aligned}\theta = P_c \mu^2/T_c^2\\\alpha = 0.3883  0.0179s  130540\theta^{2.41}\\\beta = 0.00318s  0.0211 + 0.625\Lambda^{1.35} + 9.74\times 10^6 \theta^{3.38}\end{aligned}\end{align} \]Polar Combounds with hydroxyl groups (water, alcohols)
\[ \begin{align}\begin{aligned}\alpha = \left[0.690T_{br} 0.3342 + \frac{5.79\times 10^{10}} {T_{br}^{32.75}}\right] P_c^{0.145}\\\beta = 0.00318s  0.0211 + 0.625 \Lambda^{1.35} + 5.90\Theta^{0.835}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tb : float
Boiling temperature of the fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
M : float
Molecular weight of the fluid [g/mol]
dipole : float, optional
Dipole moment of the fluid [debye]
hydroxyl : bool, optional
Swith to use the hydroxyl variant for polar fluids
Returns: Vs : float
Saturation liquid volume
Notes
If a dipole is provided, the polar chemical method is used. The paper is an excellent read. Pc is internally converted to atm.
References
[R14091434] (1, 2, 3) Campbell, Scott W., and George Thodos. “Prediction of Saturated Liquid Densities and Critical Volumes for Polar and Nonpolar Substances.” Journal of Chemical & Engineering Data 30, no. 1 (January 1, 1985): 10211. doi:10.1021/je00039a032. Examples
Ammonia, from [R14091434].
>>> Campbell_Thodos(T=405.45, Tb=239.82, Tc=405.45, Pc=111.7*101325, M=17.03, dipole=1.47) 7.347363635885525e05

thermo.volume.
SNM0
(T, Tc, Vc, omega, delta_SRK=None)[source]¶ Calculates saturated liquid density using the Mchaweh, Moshfeghian model [R14101435]. Designed for simple calculations.
\[ \begin{align}\begin{aligned}V_s = V_c/(1+1.169\tau^{1/3}+1.818\tau^{2/3}2.658\tau+2.161\tau^{4/3}\\\tau = 1\frac{(T/T_c)}{\alpha_{SRK}}\\\alpha_{SRK} = [1 + m(1\sqrt{T/T_C}]^2\\m = 0.480+1.574\omega0.176\omega^2\end{aligned}\end{align} \]If the fit parameter delta_SRK is provided, the following is used:
\[V_s = V_C/(1+1.169\tau^{1/3}+1.818\tau^{2/3}2.658\tau+2.161\tau^{4/3}) /\left[1+\delta_{SRK}(\alpha_{SRK}1)^{1/3}\right]\]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Vc : float
Critical volume of fluid [m^3/mol]
omega : float
Acentric factor for fluid, []
delta_SRK : float, optional
Fitting parameter []
Returns: Vs : float
Saturation liquid volume, [m^3/mol]
Notes
73 fit parameters have been gathered from the article.
References
[R14101435] (1, 2) Mchaweh, A., A. Alsaygh, Kh. Nasrifar, and M. Moshfeghian. “A Simplified Method for Calculating Saturated Liquid Densities.” Fluid Phase Equilibria 224, no. 2 (October 1, 2004): 15767. doi:10.1016/j.fluid.2004.06.054 Examples
Argon, without the fit parameter and with it. Tabulated result in Perry’s is 3.4613e05. The fit increases the error on this occasion.
>>> SNM0(121, 150.8, 7.49e05, 0.004) 3.4402256402733416e05 >>> SNM0(121, 150.8, 7.49e05, 0.004, 0.03259620) 3.493288100008123e05

thermo.volume.
CRC_inorganic
(T, rho0, k, Tm)[source]¶ Calculates liquid density of a molten element or salt at temperature above the melting point. Some coefficients are given nearly up to the boiling point.
The mass density of the inorganic liquid is given by:
\[\rho = \rho_{0}  k(TT_m)\]Parameters: T : float
Temperature of the liquid, [K]
rho0 : float
Mass density of the liquid at Tm, [kg/m^3]
k : float
Linear temperature dependence of the mass density, [kg/m^3/K]
Tm : float
The normal melting point, used in the correlation [K]
Returns: rho : float
Mass density of molten metal or salt, [kg/m^3]
Notes
[R14111436] has units of g/mL. While the individual densities could have been converted to molar units, the temperature coefficient could only be converted by refitting to calculated data. To maintain compatibility with the form of the equations, this was not performed.
This linear form is useful only in small temperature ranges. Coefficients for one compound could be used to predict the temperature dependence of density of a similar compound.
References
[R14111436] (1, 2) Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics, 95E. [Boca Raton, FL]: CRC press, 2014. Examples
>>> CRC_inorganic(300, 2370.0, 2.687, 239.08) 2206.30796

thermo.volume.
volume_liquid_methods
= ['PERRYDIPPR', 'VDI_PPDS', 'COOLPROP', 'MMSNM0FIT', 'VDI_TABULAR', 'HTCOSTALDFIT', 'RACKETTFIT', 'CRC_INORG_L', 'CRC_INORG_L_CONST', 'MMSNM0', 'HTCOSTALD', 'YEN_WOODS_SAT', 'RACKETT', 'YAMADA_GUNN', 'BHIRUD_NORMAL', 'TOWNSEND_HALES', 'CAMPBELL_THODOS']¶ Holds all lowpressure methods available for the VolumeLiquid class, for use in iterating over them.

thermo.volume.
volume_liquid_methods_P
= ['COOLPROP', 'COSTALD_COMPRESSED', 'EOS']¶ Holds all highpressure methods available for the VolumeLiquid class, for use in iterating over them.

class
thermo.volume.
VolumeLiquid
(MW=None, Tb=None, Tc=None, Pc=None, Vc=None, Zc=None, omega=None, dipole=None, Psat=None, CASRN='', eos=None)[source]¶ Bases:
thermo.utils.TPDependentProperty
Class for dealing with liquid molar volume as a function of temperature and pressure.
For lowpressure (at 1 atm while under the vapor pressure; along the saturation line otherwise) liquids, there are six coefficientbased methods from five data sources, one source of tabular information, one source of constant values, eight correspondingstates estimators, and the external library CoolProp.
For highpressure liquids (also, <1 atm liquids), there is one correspondingstates estimator, and the external library CoolProp.
Parameters: CASRN : str, optional
The CAS number of the chemical
MW : float, optional
Molecular weight, [g/mol]
Tb : float, optional
Boiling point, [K]
Tc : float, optional
Critical temperature, [K]
Pc : float, optional
Critical pressure, [Pa]
Vc : float, optional
Critical volume, [m^3/mol]
Zc : float, optional
Critical compressibility
omega : float, optional
Acentric factor, []
dipole : float, optional
Dipole, [debye]
Psat : float or callable, optional
Vapor pressure at a given temperature, or callable for the same [Pa]
eos : object, optional
Equation of State object after
thermo.eos.GCEOS
See also
Yen_Woods_saturation
,Rackett
,Yamada_Gunn
,Townsend_Hales
,Bhirud_normal
,COSTALD
,Campbell_Thodos
,SNM0
,CRC_inorganic
,COSTALD_compressed
Notes
A string holding each method’s name is assigned to the following variables in this module, intended as the most convenient way to refer to a method. To iterate over all methods, use the lists stored in
surface_tension_methods
andvolume_liquid_methods_P
for low and high pressure methods respectively.Low pressure methods:
 PERRYDIPPR:
 A simple polynomial as expressed in [R14121437], with data available for 344 fluids. Temperature limits are available for all fluids. Believed very accurate.
 VDI_PPDS:
 Coefficients for a equation form developed by the PPDS, published openly in [R14141437]. Valid up to the critical temperature, and extrapolates to very low temperatures well.
 MMSNM0FIT:
 Uses a fit coefficient for better accuracy in the
SNM0
method, Coefficients available for 73 fluids from [R14131437]. Valid to the critical point.  HTCOSTALDFIT:
 A method with two fit coefficients to the
COSTALD
method. Coefficients available for 192 fluids, from [R14141437]. Valid to the critical point.  RACKETTFIT:
 The
Racket
method, with a fit coefficient Z_RA. Data is available for 186 fluids, from [R14141437]. Valid to the critical point.  CRC_INORG_L:
 Singletemperature coefficient linear model in terms of mass density
for the density of inorganic liquids; converted to molar units
internally. Data is available for 177 fluids normally valid over a
narrow range above the melting point, from [R14151437]; described in
CRC_inorganic
.  MMSNM0:
 CSP method, described in
SNM0
.  HTCOSTALD:
 CSP method, described in
COSTALD
.  YEN_WOODS_SAT:
 CSP method, described in
Yen_Woods_saturation
.  RACKETT:
 CSP method, described in
Rackett
.  YAMADA_GUNN:
 CSP method, described in
Yamada_Gunn
.  BHIRUD_NORMAL:
 CSP method, described in
Bhirud_normal
.  TOWNSEND_HALES:
 CSP method, described in
Townsend_Hales
.  CAMPBELL_THODOS:
 CSP method, described in
Campbell_Thodos
.  COOLPROP:
 CoolProp external library; with select fluids from its library. Range is limited to that of the equations of state it uses, as described in [R14161437]. Very slow.
 CRC_INORG_L_CONST:
 Constant inorganic liquid densities, in [R14151437].
 VDI_TABULAR:
 Tabular data in [R14171437] along the saturation curve; interpolation is as set by the user or the default.
High pressure methods:
 COSTALD_COMPRESSED:
 CSP method, described in
COSTALD_compressed
. Calculates a lowpressure molar volume first, using T_dependent_property.  COOLPROP:
 CoolProp external library; with select fluids from its library. Range is limited to that of the equations of state it uses, as described in [R14161437]. Very slow, but unparalled in accuracy for pressure dependence.
 EOS:
 Equation of state provided by user.
References
[R14121437] (1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, 8E. McGrawHill Professional, 2007. [R14131437] (1, 2) Mchaweh, A., A. Alsaygh, Kh. Nasrifar, and M. Moshfeghian. “A Simplified Method for Calculating Saturated Liquid Densities.” Fluid Phase Equilibria 224, no. 2 (October 1, 2004): 15767. doi:10.1016/j.fluid.2004.06.054 [R14141437] (1, 2, 3, 4) Hankinson, Risdon W., and George H. Thomson. “A New Correlation for Saturated Densities of Liquids and Their Mixtures.” AIChE Journal 25, no. 4 (1979): 653663. doi:10.1002/aic.690250412 [R14151437] (1, 2, 3) Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014. [R14161437] (1, 2, 3) Bell, Ian H., Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. “Pure and PseudoPure Fluid Thermophysical Property Evaluation and the OpenSource Thermophysical Property Library CoolProp.” Industrial & Engineering Chemistry Research 53, no. 6 (February 12, 2014): 24982508. doi:10.1021/ie4033999. http://www.coolprop.org/ [R14171437] (1, 2) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010. Attributes
TP_cached T_cached interpolation_P interpolation_T interpolation_property interpolation_property_inv method method_P Methods
TP_dependent_property
(T, P)Method to calculate the property with sanity checking and without specifying a specific method. TP_dependent_property_derivative_P
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order. TP_dependent_property_derivative_T
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order. TP_or_T_dependent_property
(T, P)T_dependent_property
(T)Method to calculate the property with sanity checking and without specifying a specific method. T_dependent_property_derivative
(T[, order])Method to obtain a derivative of a property with respect to temperature, of a given order. T_dependent_property_integral
(T1, T2)Method to calculate the integral of a property with respect to temperature, using a specified method. T_dependent_property_integral_over_T
(T1, T2)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. __call__
(T, P)Convenience method to calculate the property; calls TP_dependent_property
.calculate
(T, method)Method to calculate lowpressure liquid molar volume at tempearture T with a given method. calculate_P
(T, P, method)Method to calculate pressuredependent liquid molar volume at temperature T and pressure P with a given method. calculate_derivative
(T, method[, order])Method to calculate a derivative of a property with respect to temperature, of a given order using a specified method. calculate_derivative_P
(P, T, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order using a specified method. calculate_derivative_T
(T, P, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order using a specified method. calculate_integral
(T1, T2, method)Method to calculate the integral of a property with respect to temperature, using a specified method. calculate_integral_over_T
(T1, T2, method)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. extrapolate_tabular
(T)interpolate
(T, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data
.interpolate_P
(T, P, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data_P. load_all_methods
()Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. plot_TP_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_T_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature according to either a specified list of methods, or user methods (if set), or all methods. plot_isobar
(P[, Tmin, Tmax, methods_P, pts, ...])Method to create a plot of the property vs temperature at a specific pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T[, Pmin, Pmax, methods_P, ...])Method to create a plot of the property vs pressure at a specified temperature according to either a specified list of methods, or the user methods (if set), or all methods. select_valid_methods
(T)Method to obtain a sorted list of methods which are valid at T according to test_method_validity. select_valid_methods_P
(T, P)Method to obtain a sorted list methods which are valid at T according to test_method_validity. set_tabular_data
(Ts, properties[, name, ...])Method to set tabular data to be used for interpolation. set_tabular_data_P
(Ts, Ps, properties[, ...])Method to set tabular data to be used for interpolation. set_user_methods
(user_methods[, forced])Method used to select certain property methods as having a higher priority than were set by default. set_user_methods_P
(user_methods_P[, forced_P])Method to set the pressuredependent property methods desired for consideration by the user. solve_prop
(goal[, reset_method])Method to solve for the temperature at which a property is at a specified value. test_method_validity
(T, method)Method to check the validity of a method. test_method_validity_P
(T, P, method)Method to check the validity of a highpressure method. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the liquid molar volume above.

Tmin
= None¶ Minimum temperature at which no method can calculate the liquid molar volume under.

all_methods
= None¶ Set of all lowpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

all_methods_P
= None¶ Set of all highpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

calculate
(T, method)[source]¶ Method to calculate lowpressure liquid molar volume at tempearture T with a given method.
This method has no exception handling; see T_dependent_property for that.
Parameters: T : float
Temperature at which to calculate molar volume, [K]
method : str
Name of the method to use
Returns: Vm : float
Molar volume of the liquid at T and a low pressure, [m^3/mol]

calculate_P
(T, P, method)[source]¶ Method to calculate pressuredependent liquid molar volume at temperature T and pressure P with a given method.
This method has no exception handling; see TP_dependent_property for that.
Parameters: T : float
Temperature at which to calculate molar volume, [K]
P : float
Pressure at which to calculate molar volume, [K]
method : str
Name of the method to use
Returns: Vm : float
Molar volume of the liquid at T and P, [m^3/mol]

interpolation_P
= None¶ No interpolation transformation by default.

interpolation_T
= None¶ No interpolation transformation by default.

interpolation_property
= None¶ No interpolation transformation by default.

interpolation_property_inv
= None¶ No interpolation transformation by default.

load_all_methods
()[source]¶ Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. All data is stored as attributes. This method also sets
Tmin
,Tmax
,all_methods
and obj:all_methods_P as a set of methods for which the data exists for.Called on initialization only. See the source code for the variables at which the coefficients are stored. The coefficients can safely be altered once the class is initialized. This method can be called again to reset the parameters.

name
= 'Liquid molar volume'¶

property_max
= 0.002¶ Maximum valid value of liquid molar volume. Generous limit.

property_min
= 0¶ Mimimum valid value of liquid molar volume. It should normally occur at the triple point, and be well above this.

ranked_methods
= ['PERRYDIPPR', 'VDI_PPDS', 'COOLPROP', 'MMSNM0FIT', 'VDI_TABULAR', 'HTCOSTALDFIT', 'RACKETTFIT', 'CRC_INORG_L', 'CRC_INORG_L_CONST', 'MMSNM0', 'HTCOSTALD', 'YEN_WOODS_SAT', 'RACKETT', 'YAMADA_GUNN', 'BHIRUD_NORMAL', 'TOWNSEND_HALES', 'CAMPBELL_THODOS', 'EOS']¶ Default rankings of the lowpressure methods.

ranked_methods_P
= ['COOLPROP', 'COSTALD_COMPRESSED', 'EOS']¶ Default rankings of the highpressure methods.

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by T_dependent_property.

sorted_valid_methods_P
= None¶ sorted_valid_methods_P, list: Stored methods which were found valid at a specific temperature; set by TP_dependent_property.

tabular_data
= None¶ tabular_data, dict: Stored (Ts, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_P
= None¶ tabular_data_P, dict: Stored (Ts, Ps, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_interpolators
= None¶ tabular_data_interpolators, dict: Stored (extrapolator, spline) tuples which are interp1d instances for each set of tabular data; indexed by tuple of (name, interpolation_T, interpolation_property, interpolation_property_inv) to ensure that if an interpolation transform is altered, the old interpolator which had been created is no longer used.

tabular_data_interpolators_P
= None¶ tabular_data_interpolators_P, dict: Stored (extrapolator, spline) tuples which are interp2d instances for each set of tabular data; indexed by tuple of (name, interpolation_T, interpolation_P, interpolation_property, interpolation_property_inv) to ensure that if an interpolation transform is altered, the old interpolator which had been created is no longer used.

tabular_extrapolation_permitted
= True¶ Allow tabular extrapolation by default.

test_method_validity
(T, method)[source]¶ Method to check the validity of a method. Follows the given ranges for all coefficientbased methods. For CSP methods, the models are considered valid from 0 K to the critical point. For tabular data, extrapolation outside of the range is used if
tabular_extrapolation_permitted
is set; if it is, the extrapolation is considered valid for all temperatures.It is not guaranteed that a method will work or give an accurate prediction simply because this method considers the method valid.
BHIRUD_NORMAL behaves poorly at low temperatures and is not used under 0.35Tc. The constant value available for inorganic chemicals, from method CRC_INORG_L_CONST, is considered valid for all temperatures.
Parameters: T : float
Temperature at which to test the method, [K]
method : str
Name of the method to test
Returns: validity : bool
Whether or not a method is valid

test_method_validity_P
(T, P, method)[source]¶ Method to check the validity of a highpressure method. For COOLPROP, the fluid must be both a liquid and under the maximum pressure of the fluid’s EOS. COSTALD_COMPRESSED is considered valid for all values of temperature and pressure. However, it very often will not actually work, due to the form of the polynomial in terms of Tr, the result of which is raised to a negative power. For tabular data, extrapolation outside of the range is used if
tabular_extrapolation_permitted
is set; if it is, the extrapolation is considered valid for all temperatures and pressures.It is not guaranteed that a method will work or give an accurate prediction simply because this method considers the method valid.
Parameters: T : float
Temperature at which to test the method, [K]
P : float
Pressure at which to test the method, [Pa]
method : str
Name of the method to test
Returns: validity : bool
Whether or not a method is valid

units
= 'mol/m^3'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by T_dependent_property.

user_methods_P
= None¶ user_methods_P, list: Stored methods which were specified by the user in a ranked order of preference; set by TP_dependent_property.

thermo.volume.
COSTALD_compressed
(T, P, Psat, Tc, Pc, omega, Vs)[source]¶ Calculates compressedliquid volume, using the COSTALD [R14181443] CSP method and a chemical’s critical properties.
The molar volume of a liquid is given by:
\[ \begin{align}\begin{aligned}V = V_s\left( 1  C \ln \frac{B + P}{B + P^{sat}}\right)\\\frac{B}{P_c} = 1 + a\tau^{1/3} + b\tau^{2/3} + d\tau + e\tau^{4/3}\\e = \exp(f + g\omega_{SRK} + h \omega_{SRK}^2)\\C = j + k \omega_{SRK}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
P : float
Pressure of fluid [Pa]
Psat : float
Saturation pressure of the fluid [Pa]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
(ideally SRK) Acentric factor for fluid, [] This parameter is alternatively a fit parameter.
Vs : float
Saturation liquid volume, [m^3/mol]
Returns: V_dense : float
Highpressure liquid volume, [m^3/mol]
Notes
Original equation was in terms of density, but it is converted here.
The example is from DIPPR, and exactly correct. This is DIPPR Procedure 4C: Method for Estimating the Density of Pure Organic Liquids under Pressure.
References
[R14181443] (1, 2) Thomson, G. H., K. R. Brobst, and R. W. Hankinson. “An Improved Correlation for Densities of Compressed Liquids and Liquid Mixtures.” AIChE Journal 28, no. 4 (July 1, 1982): 67176. doi:10.1002/aic.690280420 Examples
>>> COSTALD_compressed(303., 9.8E7, 85857.9, 466.7, 3640000.0, 0.281, 0.000105047) 9.287482879788506e05

thermo.volume.
Amgat
(xs, Vms)[source]¶ Calculate mixture liquid density using the Amgat mixing rule. Highly inacurate, but easy to use. Assumes idea liquids with no excess volume. Average molecular weight should be used with it to obtain density.
\[V_{mix} = \sum_i x_i V_i\]or in terms of density:
\[\rho_{mix} = \sum\frac{x_i}{\rho_i}\]Parameters: xs : array
Mole fractions of each component, []
Vms : array
Molar volumes of each fluids at conditions [m^3/mol]
Returns: Vm : float
Mixture liquid volume [m^3/mol]
Notes
Units are that of the given volumes. It has been suggested to use this equation with weight fractions, but the results have been less accurate.
Examples
>>> Amgat([0.5, 0.5], [4.057e05, 5.861e05]) 4.9590000000000005e05

thermo.volume.
Rackett_mixture
(T, xs, MWs, Tcs, Pcs, Zrs)[source]¶ Calculate mixture liquid density using the Rackettderived mixing rule as shown in [R14201444].
\[V_m = \sum_i\frac{x_i T_{ci}}{MW_i P_{ci}} Z_{R,m}^{(1 + (1  T_r)^{2/7})} R \sum_i x_i MW_i\]Parameters: T : float
Temperature of liquid [K]
xs: list
Mole fractions of each component, []
MWs : list
Molecular weights of each component [g/mol]
Tcs : list
Critical temperatures of each component [K]
Pcs : list
Critical pressures of each component [Pa]
Zrs : list
Rackett parameters of each component []
Returns: Vm : float
Mixture liquid volume [m^3/mol]
Notes
Model for pure compounds in [R14191444] forms the basis for this model, shown in [R14201444]. Molecular weights are used as weighing by such has been found to provide higher accuracy in [R14201444]. The model can also be used without molecular weights, but results are somewhat different.
As with the Rackett model, critical compressibilities may be used if Rackett parameters have not been regressed.
Critical mixture temperature, and compressibility are all obtained with simple mixing rules.
References
[R14191444] (1, 2) Rackett, Harold G. “Equation of State for Saturated Liquids.” Journal of Chemical & Engineering Data 15, no. 4 (1970): 514517. doi:10.1021/je60047a012 [R14201444] (1, 2, 3, 4, 5) Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982. Examples
Calculation in [R14201444] for methanol and water mixture. Result matches example.
>>> Rackett_mixture(T=298., xs=[0.4576, 0.5424], MWs=[32.04, 18.01], Tcs=[512.58, 647.29], Pcs=[8.096E6, 2.209E7], Zrs=[0.2332, 0.2374]) 2.625288603174508e05

thermo.volume.
COSTALD_mixture
(xs, T, Tcs, Vcs, omegas)[source]¶ Calculate mixture liquid density using the COSTALD CSP method.
A popular and accurate estimation method. If possible, fit parameters are used; alternatively critical properties work well.
The mixing rules giving parameters for the pure component COSTALD equation are:
\[ \begin{align}\begin{aligned}T_{cm} = \frac{\sum_i\sum_j x_i x_j (V_{ij}T_{cij})}{V_m}\\V_m = 0.25\left[ \sum x_i V_i + 3(\sum x_i V_i^{2/3})(\sum_i x_i V_i^{1/3})\right]\\V_{ij}T_{cij} = (V_iT_{ci}V_{j}T_{cj})^{0.5}\\\omega = \sum_i z_i \omega_i\end{aligned}\end{align} \]Parameters: xs: list
Mole fractions of each component
T : float
Temperature of fluid [K]
Tcs : list
Critical temperature of fluids [K]
Vcs : list
Critical volumes of fluids [m^3/mol]. This parameter is alternatively a fit parameter
omegas : list
(ideally SRK) Acentric factor of all fluids, [] This parameter is alternatively a fit parameter.
Returns: Vs : float
Saturation liquid mixture volume
Notes
Range: 0.25 < Tr < 0.95, often said to be to 1.0 No example has been found. Units are that of critical or fit constant volume.
References
[R14211446] Hankinson, Risdon W., and George H. Thomson. “A New Correlation for Saturated Densities of Liquids and Their Mixtures.” AIChE Journal 25, no. 4 (1979): 653663. doi:10.1002/aic.690250412 Examples
>>> COSTALD_mixture([0.4576, 0.5424], 298., [512.58, 647.29],[0.000117, 5.6e05], [0.559,0.344] ) 2.706588773271354e05

thermo.volume.
ideal_gas
(T, P)[source]¶ Calculates ideal gas molar volume. The molar volume of an ideal gas is given by:
\[V = \frac{RT}{P}\]Parameters: T : float
Temperature of fluid [K]
P : float
Pressure of fluid [Pa]
Returns: V : float
Gas volume, [m^3/mol]
Examples
>>> ideal_gas(298.15, 101325.) 0.02446539540458919

thermo.volume.
volume_gas_methods
= ['COOLPROP', 'EOS', 'CRC_VIRIAL', 'TSONOPOULOS_EXTENDED', 'TSONOPOULOS', 'ABBOTT', 'PITZER_CURL', 'IDEAL']¶ Holds all methods available for the VolumeGas class, for use in iterating over them.

class
thermo.volume.
VolumeGas
(CASRN='', MW=None, Tc=None, Pc=None, omega=None, dipole=None, eos=None)[source]¶ Bases:
thermo.utils.TPDependentProperty
Class for dealing with gas molar volume as a function of temperature and pressure.
All considered methods are both temperature and pressure dependent. Included are four CSP methods for calculating second virial coefficients, one source of polynomials for calculating second virial coefficients, one equation of state (PengRobinson), and the ideal gas law.
Parameters: CASRN : str, optional
The CAS number of the chemical
MW : float, optional
Molecular weight, [g/mol]
Tc : float, optional
Critical temperature, [K]
Pc : float, optional
Critical pressure, [Pa]
omega : float, optional
Acentric factor, []
dipole : float, optional
Dipole, [debye]
See also
thermo.virial.BVirial_Pitzer_Curl
,thermo.virial.BVirial_Abbott
,thermo.virial.BVirial_Tsonopoulos
,thermo.virial.BVirial_Tsonopoulos_extended
Notes
A string holding each method’s name is assigned to the following variables in this module, intended as the most convenient way to refer to a method. To iterate over all methods, use the list stored in
volume_gas_methods
. PR:
 PengRobinson Equation of State. See the appropriate module for more information.
 CRC_VIRIAL:
Short polynomials, for 105 fluids from [R14221447]. The full expression is:
\[B = \sum_1^4 a_i\left[T_0/298.151\right]^{i1}\] TSONOPOULOS_EXTENDED:
 CSP method for second virial coefficients, described in
thermo.virial.BVirial_Tsonopoulos_extended
 TSONOPOULOS:
 CSP method for second virial coefficients, described in
thermo.virial.BVirial_Tsonopoulos
 ABBOTT:
 CSP method for second virial coefficients, described in
thermo.virial.BVirial_Abbott
. This method is the simplest CSP method implemented.  PITZER_CURL:
 CSP method for second virial coefficients, described in
thermo.virial.BVirial_Pitzer_Curl
.  COOLPROP:
 CoolProp external library; with select fluids from its library. Range is limited to that of the equations of state it uses, as described in [R14231447]. Very slow, but unparalled in accuracy for pressure dependence.
References
[R14221447] (1, 2) Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014. [R14231447] (1, 2) Bell, Ian H., Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. “Pure and PseudoPure Fluid Thermophysical Property Evaluation and the OpenSource Thermophysical Property Library CoolProp.” Industrial & Engineering Chemistry Research 53, no. 6 (February 12, 2014): 24982508. doi:10.1021/ie4033999. http://www.coolprop.org/ Attributes
TP_cached T_cached interpolation_P interpolation_T interpolation_property interpolation_property_inv method method_P Methods
TP_dependent_property
(T, P)Method to calculate the property with sanity checking and without specifying a specific method. TP_dependent_property_derivative_P
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order. TP_dependent_property_derivative_T
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order. TP_or_T_dependent_property
(T, P)T_dependent_property
(T)Method to calculate the property with sanity checking and without specifying a specific method. T_dependent_property_derivative
(T[, order])Method to obtain a derivative of a property with respect to temperature, of a given order. T_dependent_property_integral
(T1, T2)Method to calculate the integral of a property with respect to temperature, using a specified method. T_dependent_property_integral_over_T
(T1, T2)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. __call__
(T, P)Convenience method to calculate the property; calls TP_dependent_property
.calculate
(T, method)Method to calculate a property with a specified method, with no validity checking or error handling. calculate_P
(T, P, method)Method to calculate pressuredependent gas molar volume at temperature T and pressure P with a given method. calculate_derivative
(T, method[, order])Method to calculate a derivative of a property with respect to temperature, of a given order using a specified method. calculate_derivative_P
(P, T, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order using a specified method. calculate_derivative_T
(T, P, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order using a specified method. calculate_integral
(T1, T2, method)Method to calculate the integral of a property with respect to temperature, using a specified method. calculate_integral_over_T
(T1, T2, method)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. extrapolate_tabular
(T)interpolate
(T, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data
.interpolate_P
(T, P, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data_P. load_all_methods
()Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. plot_TP_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_T_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature according to either a specified list of methods, or user methods (if set), or all methods. plot_isobar
(P[, Tmin, Tmax, methods_P, pts, ...])Method to create a plot of the property vs temperature at a specific pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T[, Pmin, Pmax, methods_P, ...])Method to create a plot of the property vs pressure at a specified temperature according to either a specified list of methods, or the user methods (if set), or all methods. select_valid_methods
(T)Method to obtain a sorted list of methods which are valid at T according to test_method_validity. select_valid_methods_P
(T, P)Method to obtain a sorted list methods which are valid at T according to test_method_validity. set_tabular_data
(Ts, properties[, name, ...])Method to set tabular data to be used for interpolation. set_tabular_data_P
(Ts, Ps, properties[, ...])Method to set tabular data to be used for interpolation. set_user_methods
(user_methods[, forced])Method used to select certain property methods as having a higher priority than were set by default. set_user_methods_P
(user_methods_P[, forced_P])Method to set the pressuredependent property methods desired for consideration by the user. solve_prop
(goal[, reset_method])Method to solve for the temperature at which a property is at a specified value. test_method_validity
(T, method)Method to test the validity of a specified method for a given temperature. test_method_validity_P
(T, P, method)Method to check the validity of a pressure and temperature dependent gas molar volume method. test_property_validity
(prop)Method to test the validity of a calculated property. 
Pmax
= 1000000000.0¶ Maximum pressure at which no method can calculate gas molar volume above.

Pmin
= 0¶ Minimum pressure at which no method can calculate gas molar volume under.

Tmax
= None¶ Maximum temperature at which no method can calculate the gas molar volume above.

Tmin
= None¶ Minimum temperature at which no method can calculate the gas molar volume under.

all_methods_P
= None¶ Set of all highpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

calculate_P
(T, P, method)[source]¶ Method to calculate pressuredependent gas molar volume at temperature T and pressure P with a given method.
This method has no exception handling; see TP_dependent_property for that.
Parameters: T : float
Temperature at which to calculate molar volume, [K]
P : float
Pressure at which to calculate molar volume, [K]
method : str
Name of the method to use
Returns: Vm : float
Molar volume of the gas at T and P, [m^3/mol]

interpolation_P
= None¶ No interpolation transformation by default.

interpolation_T
= None¶ No interpolation transformation by default.

interpolation_property
= None¶ No interpolation transformation by default.

interpolation_property_inv
= None¶ No interpolation transformation by default.

load_all_methods
()[source]¶ Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. All data is stored as attributes. This method also sets obj:all_methods_P as a set of methods for which the data exists for.
Called on initialization only. See the source code for the variables at which the coefficients are stored. The coefficients can safely be altered once the class is initialized. This method can be called again to reset the parameters.

name
= 'Gas molar volume'¶

property_max
= 10000000000.0¶ Maximum valid value of gas molar volume. Set roughly at an ideal gas at 1 Pa and 2 billion K.

property_min
= 0¶ Mimimum valid value of gas molar volume. It should normally be well above this.

ranked_methods
= []¶ Default rankings of the lowpressure methods.

ranked_methods_P
= ['COOLPROP', 'EOS', 'TSONOPOULOS_EXTENDED', 'TSONOPOULOS', 'ABBOTT', 'PITZER_CURL', 'CRC_VIRIAL', 'IDEAL']¶ Default rankings of the pressuredependent methods.

sorted_valid_methods_P
= None¶ sorted_valid_methods_P, list: Stored methods which were found valid at a specific temperature; set by TP_dependent_property.

tabular_data
= None¶ tabular_data, dict: Stored (Ts, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_P
= None¶ tabular_data_P, dict: Stored (Ts, Ps, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_interpolators
= None¶ tabular_data_interpolators, dict: Stored (extrapolator, spline) tuples which are interp1d instances for each set of tabular data; indexed by tuple of (name, interpolation_T, interpolation_property, interpolation_property_inv) to ensure that if an interpolation transform is altered, the old interpolator which had been created is no longer used.

tabular_data_interpolators_P
= None¶ tabular_data_interpolators_P, dict: Stored (extrapolator, spline) tuples which are interp2d instances for each set of tabular data; indexed by tuple of (name, interpolation_T, interpolation_P, interpolation_property, interpolation_property_inv) to ensure that if an interpolation transform is altered, the old interpolator which had been created is no longer used.

tabular_extrapolation_permitted
= True¶ Allow tabular extrapolation by default.

test_method_validity_P
(T, P, method)[source]¶ Method to check the validity of a pressure and temperature dependent gas molar volume method. For the four CSP methods that calculate second virial coefficient, the method is considered valid for all temperatures and pressures, with validity checking based on the result only. For CRC_VIRIAL, there is no limit but there should be one; at some conditions, a negative volume will result! For COOLPROP, the fluid must be both a gas at the given conditions and under the maximum pressure of the fluid’s EOS.
For the equation of state PR, the determined phase must be a gas. For IDEAL, there are no limits.
For tabular data, extrapolation outside of the range is used if
tabular_extrapolation_permitted
is set; if it is, the extrapolation is considered valid for all temperatures and pressures.It is not guaranteed that a method will work or give an accurate prediction simply because this method considers the method valid.
Parameters: T : float
Temperature at which to test the method, [K]
P : float
Pressure at which to test the method, [Pa]
method : str
Name of the method to test
Returns: validity : bool
Whether or not a method is valid

units
= 'mol/m^3'¶

user_methods_P
= None¶ user_methods_P, list: Stored methods which were specified by the user in a ranked order of preference; set by TP_dependent_property.

thermo.volume.
Goodman
(T, Tt, rhol)[source]¶ Calculates solid density at T using the simple relationship by a member of the DIPPR.
The molar volume of a solid is given by:
\[\frac{1}{V_m} = \left( 1.28  0.16 \frac{T}{T_t}\right) \frac{1}{{Vm}_L(T_t)}\]Parameters: T : float
Temperature of fluid [K]
Tt : float
Triple temperature of fluid [K]
rhol : float
Liquid density, [m^3/mol]
Returns: rhos : float
Solid volume, [m^3/mol]
Notes
Works to the next solid transition temperature or to approximately 0.3Tt.
References
[R14241449] Goodman, Benjamin T., W. Vincent Wilding, John L. Oscarson, and Richard L. Rowley. “A Note on the Relationship between Organic Solid Density and Liquid Density at the Triple Point.” Journal of Chemical & Engineering Data 49, no. 6 (2004): 151214. doi:10.1021/je034220e. Examples
>>> Goodman(281.46, 353.43, 7.6326) 8.797191839062899

thermo.volume.
volume_solid_methods
= ['GOODMAN', 'CRC_INORG_S']¶ Holds all methods available for the VolumeSolid class, for use in iterating over them.

class
thermo.volume.
VolumeSolid
(CASRN='', MW=None, Tt=None, Vml_Tt=None)[source]¶ Bases:
thermo.utils.TDependentProperty
Class for dealing with solid molar volume as a function of temperature. Consists of one constant value source, and one simple estimator based on liquid molar volume.
Parameters: CASRN : str, optional
CAS number
MW : float, optional
Molecular weight, [g/mol]
Tt : float, optional
Triple temperature
Vml_Tt : float, optional
Liquid molar volume at the triple point
See also
Notes
A string holding each method’s name is assigned to the following variables in this module, intended as the most convenient way to refer to a method. To iterate over all methods, use the list stored in
volume_solid_methods
. CRC_INORG_S:
 Constant values in [R14251450], for 1872 chemicals.
 GOODMAN:
 Simple method using the liquid molar volume. Good up to 0.3*Tt.
See
Goodman
for details.
References
[R14251450] (1, 2) Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014. Attributes
T_cached interpolation_T interpolation_property interpolation_property_inv method Methods
T_dependent_property
(T)Method to calculate the property with sanity checking and without specifying a specific method. T_dependent_property_derivative
(T[, order])Method to obtain a derivative of a property with respect to temperature, of a given order. T_dependent_property_integral
(T1, T2)Method to calculate the integral of a property with respect to temperature, using a specified method. T_dependent_property_integral_over_T
(T1, T2)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. __call__
(T)Convenience method to calculate the property; calls T_dependent_property
.calculate
(T, method)Method to calculate the molar volume of a solid at tempearture T with a given method. calculate_derivative
(T, method[, order])Method to calculate a derivative of a property with respect to temperature, of a given order using a specified method. calculate_integral
(T1, T2, method)Method to calculate the integral of a property with respect to temperature, using a specified method. calculate_integral_over_T
(T1, T2, method)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. extrapolate_tabular
(T)interpolate
(T, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data
.load_all_methods
()Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. plot_T_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature according to either a specified list of methods, or user methods (if set), or all methods. select_valid_methods
(T)Method to obtain a sorted list of methods which are valid at T according to test_method_validity. set_tabular_data
(Ts, properties[, name, ...])Method to set tabular data to be used for interpolation. set_user_methods
(user_methods[, forced])Method used to select certain property methods as having a higher priority than were set by default. solve_prop
(goal[, reset_method])Method to solve for the temperature at which a property is at a specified value. test_method_validity
(T, method)Method to check the validity of a method. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the solid molar volume above; assumed 10 000 K even under ultrahigh pressure.

Tmin
= None¶ Minimum temperature at which no method can calculate the solid molar volume under.

all_methods
= None¶ Set of all methods available for a given CASRN and properties; filled by
load_all_methods
.

calculate
(T, method)[source]¶ Method to calculate the molar volume of a solid at tempearture T with a given method.
This method has no exception handling; see T_dependent_property for that.
Parameters: T : float
Temperature at which to calculate molar volume, [K]
method : str
Name of the method to use
Returns: Vms : float
Molar volume of the solid at T, [m^3/mol]

interpolation_T
= None¶ No interpolation transformation by default.

interpolation_property
= None¶ No interpolation transformation by default.

interpolation_property_inv
= None¶ No interpolation transformation by default.

load_all_methods
()[source]¶ Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. All data is stored as attributes. This method also sets
Tmin
,Tmax
, andall_methods
as a set of methods for which the data exists for.Called on initialization only. See the source code for the variables at which the coefficients are stored. The coefficients can safely be altered once the class is initialized. This method can be called again to reset the parameters.

name
= 'Solid molar volume'¶

property_max
= 0.002¶ Maximum value of Heat capacity; arbitrarily set to 0.002, as the largest in the data is 0.00136.

property_min
= 0¶ Molar volume cannot be under 0.

ranked_methods
= ['CRC_INORG_S']¶ Default rankings of the available methods.

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by T_dependent_property.

tabular_data
= None¶ tabular_data, dict: Stored (Ts, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_interpolators
= None¶ tabular_data_interpolators, dict: Stored (extrapolator, spline) tuples which are interp1d instances for each set of tabular data; indexed by tuple of (name, interpolation_T, interpolation_property, interpolation_property_inv) to ensure that if an interpolation transform is altered, the old interpolator which had been created is no longer used.

tabular_extrapolation_permitted
= True¶ Allow tabular extrapolation by default.

test_method_validity
(T, method)[source]¶ Method to check the validity of a method. Follows the given ranges for all coefficientbased methods. For tabular data, extrapolation outside of the range is used if
tabular_extrapolation_permitted
is set; if it is, the extrapolation is considered valid for all temperatures.It is not guaranteed that a method will work or give an accurate prediction simply because this method considers the method valid.
Parameters: T : float
Temperature at which to test the method, [K]
method : str
Name of the method to test
Returns: validity : bool
Whether or not a method is valid

units
= 'mol/m^3'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by T_dependent_property.

class
thermo.volume.
VolumeLiquidMixture
(MWs=[], Tcs=[], Pcs=[], Vcs=[], Zcs=[], omegas=[], CASs=[], VolumeLiquids=[])[source]¶ Bases:
thermo.utils.MixtureProperty
Class for dealing with the molar volume of a liquid mixture as a function of temperature, pressure, and composition. Consists of one electrolytespecific method, four corresponding states methods which do not use purecomponent volumes, and one moleweighted averaging method.
Prefered method is SIMPLE, or Laliberte if the mixture is aqueous and has electrolytes.
Parameters: MWs : list[float], optional
Molecular weights of all species in the mixture, [g/mol]
Tcs : list[float], optional
Critical temperatures of all species in the mixture, [K]
Pcs : list[float], optional
Critical pressures of all species in the mixture, [Pa]
Vcs : list[float], optional
Critical molar volumes of all species in the mixture, [m^3/mol]
Zcs : list[float], optional
Critical compressibility factors of all species in the mixture, [Pa]
omegas : list[float], optional
Accentric factors of all species in the mixture, []
CASs : list[str], optional
The CAS numbers of all species in the mixture
VolumeLiquids : list[VolumeLiquid], optional
VolumeLiquid objects created for all species in the mixture, normally created by
thermo.chemical.Chemical
.Notes
To iterate over all methods, use the list stored in
volume_liquid_mixture_methods
. Laliberte:
 Aqueous electrolyte model equation with coefficients; see
thermo.electrochem.Laliberte_density
for more details.  COSTALD mixture:
 CSP method described in
COSTALD_mixture
.  COSTALD mixture parameters:
 CSP method described in
COSTALD_mixture
, with two mixture composition independent fit coefficients, Vc and omega.  RACKETT:
 CSP method described in
Rackett_mixture
.  RACKETT Parameters:
 CSP method described in
Rackett_mixture
, but with a mixture independent fit coefficient for compressibility factor for each species.  SIMPLE:
 Linear mole fraction mixing rule described in
thermo.utils.mixing_simple
; also known as Amgat’s law.
References
[R14261451] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Attributes
method prop_cached Methods
__call__
(T, P, zs, ws)Convenience method to calculate the property; calls mixture_property
.calculate
(T, P, zs, ws, method)Method to calculate molar volume of a liquid mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method. calculate_derivative_P
(P, T, zs, ws, method)Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition of a given order using a specified method. calculate_derivative_T
(T, P, zs, ws, method)Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition of a given order using a specified method. load_all_methods
()Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. mixture_property
(T, P, zs, ws)Method to calculate the property with sanity checking and without specifying a specific method. plot_isobar
(P, zs, ws[, Tmin, Tmax, ...])Method to create a plot of the property vs temperature at a specific pressure and composition according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T, zs, ws[, Pmin, Pmax, ...])Method to create a plot of the property vs pressure at a specified temperature and composition according to either a specified list of methods, or the user methods (if set), or all methods. plot_property
(zs, ws[, Tmin, Tmax, Pmin, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. property_derivative_P
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition, of a given order. property_derivative_T
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition, of a given order. select_valid_methods
(T, P, zs, ws)Method to obtain a sorted list of methods which are valid at T, P, zs, ws, and possibly Vfls, according to test_method_validity. set_user_method
(user_methods[, forced])Method to set the T, P, and composition dependent property methods desired for consideration by the user. test_method_validity
(T, P, zs, ws, method)Method to test the validity of a specified method for the given conditions. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the liquid molar volume above.

Tmin
= None¶ Minimum temperature at which no method can calculate the liquid molar volume under.

all_methods
= None¶ Set of all methods available for a given set of information; filled by
load_all_methods
.

calculate
(T, P, zs, ws, method)[source]¶ Method to calculate molar volume of a liquid mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method.
This method has no exception handling; see mixture_property for that.
Parameters: T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Name of the method to use
Returns: Vm : float
Molar volume of the liquid mixture at the given conditions, [m^3/mol]

load_all_methods
()[source]¶ Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. All data are stored as attributes. This method also sets
Tmin
,Tmax
, andall_methods
as a set of methods which should work to calculate the property.Called on initialization only. See the source code for the variables at which the coefficients are stored. The coefficients can safely be altered once the class is initialized. This method can be called again to reset the parameters.

name
= 'Liquid volume'¶

property_max
= 0.002¶ Maximum valid value of liquid molar volume. Generous limit.

property_min
= 0¶ Mimimum valid value of liquid molar volume. It should normally occur at the triple point, and be well above this.

ranked_methods
= ['Laliberte', 'SIMPLE', 'COSTALD mixture parameters', 'RACKETT Parameters', 'COSTALD mixture', 'RACKETT']¶

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by mixture_property.

test_method_validity
(T, P, zs, ws, method)[source]¶ Method to test the validity of a specified method for the given conditions. No methods have implemented checks or strict ranges of validity.
Parameters: T : float
Temperature at which to check method validity, [K]
P : float
Pressure at which to check method validity, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Method name to use
Returns: validity : bool
Whether or not a specifid method is valid

units
= 'm^3/mol'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by mixture_property.

class
thermo.volume.
VolumeGasMixture
(eos=None, CASs=[], VolumeGases=[])[source]¶ Bases:
thermo.utils.MixtureProperty
Class for dealing with the molar volume of a gas mixture as a function of temperature, pressure, and composition. Consists of an equation of state, the ideal gas law, and one moleweighted averaging method.
Prefered method is EOS, or IDEAL if critical properties of components are unavailable.
Parameters: CASs : list[str], optional
The CAS numbers of all species in the mixture
VolumeGases : list[VolumeGas], optional
VolumeGas objects created for all species in the mixture, normally created by
thermo.chemical.Chemical
.eos : container[EOS Object], optional
Equation of state object, normally created by
thermo.chemical.Mixture
.See also
Notes
To iterate over all methods, use the list stored in
volume_gas_mixture_methods
. EOS:
 Equation of State object, normally provided by
thermo.chemical.Mixture
. Seethermo.eos_mix
for more details.  SIMPLE:
 Linear mole fraction mixing rule described in
thermo.utils.mixing_simple
; more correct than the ideal gas law.  IDEAL:
 The ideal gas law.
References
[R14271452] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Attributes
method prop_cached Methods
__call__
(T, P, zs, ws)Convenience method to calculate the property; calls mixture_property
.calculate
(T, P, zs, ws, method)Method to calculate molar volume of a gas mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method. calculate_derivative_P
(P, T, zs, ws, method)Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition of a given order using a specified method. calculate_derivative_T
(T, P, zs, ws, method)Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition of a given order using a specified method. load_all_methods
()Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. mixture_property
(T, P, zs, ws)Method to calculate the property with sanity checking and without specifying a specific method. plot_isobar
(P, zs, ws[, Tmin, Tmax, ...])Method to create a plot of the property vs temperature at a specific pressure and composition according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T, zs, ws[, Pmin, Pmax, ...])Method to create a plot of the property vs pressure at a specified temperature and composition according to either a specified list of methods, or the user methods (if set), or all methods. plot_property
(zs, ws[, Tmin, Tmax, Pmin, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. property_derivative_P
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition, of a given order. property_derivative_T
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition, of a given order. select_valid_methods
(T, P, zs, ws)Method to obtain a sorted list of methods which are valid at T, P, zs, ws, and possibly Vfls, according to test_method_validity. set_user_method
(user_methods[, forced])Method to set the T, P, and composition dependent property methods desired for consideration by the user. test_method_validity
(T, P, zs, ws, method)Method to test the validity of a specified method for the given conditions. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the gas molar volume above.

Tmin
= None¶ Minimum temperature at which no method can calculate the gas molar volume under.

all_methods
= None¶ Set of all methods available for a given set of information; filled by
load_all_methods
.

calculate
(T, P, zs, ws, method)[source]¶ Method to calculate molar volume of a gas mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method.
This method has no exception handling; see mixture_property for that.
Parameters: T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Name of the method to use
Returns: Vm : float
Molar volume of the gas mixture at the given conditions, [m^3/mol]

load_all_methods
()[source]¶ Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. All data are stored as attributes. This method also sets
Tmin
,Tmax
, andall_methods
as a set of methods which should work to calculate the property.Called on initialization only. See the source code for the variables at which the coefficients are stored. The coefficients can safely be altered once the class is initialized. This method can be called again to reset the parameters.

name
= 'Gas volume'¶

property_max
= 10000000000.0¶ Maximum valid value of gas molar volume. Set roughly at an ideal gas at 1 Pa and 2 billion K.

property_min
= 0¶ Mimimum valid value of gas molar volume. It should normally be well above this.

ranked_methods
= ['EOS', 'SIMPLE', 'IDEAL']¶

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by mixture_property.

test_method_validity
(T, P, zs, ws, method)[source]¶ Method to test the validity of a specified method for the given conditions. No methods have implemented checks or strict ranges of validity.
Parameters: T : float
Temperature at which to check method validity, [K]
P : float
Pressure at which to check method validity, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Method name to use
Returns: validity : bool
Whether or not a specifid method is valid

units
= 'm^3/mol'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by mixture_property.

class
thermo.volume.
VolumeSolidMixture
(CASs=[], VolumeSolids=[])[source]¶ Bases:
thermo.utils.MixtureProperty
Class for dealing with the molar volume of a solid mixture as a function of temperature, pressure, and composition. Consists of only moleweighted averaging.
Parameters: CASs : list[str], optional
The CAS numbers of all species in the mixture
VolumeSolids : list[VolumeSolid], optional
VolumeSolid objects created for all species in the mixture, normally created by
thermo.chemical.Chemical
.Notes
To iterate over all methods, use the list stored in
volume_solid_mixture_methods
. SIMPLE:
 Linear mole fraction mixing rule described in
thermo.utils.mixing_simple
.
Attributes
method prop_cached Methods
__call__
(T, P, zs, ws)Convenience method to calculate the property; calls mixture_property
.calculate
(T, P, zs, ws, method)Method to calculate molar volume of a solid mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method. calculate_derivative_P
(P, T, zs, ws, method)Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition of a given order using a specified method. calculate_derivative_T
(T, P, zs, ws, method)Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition of a given order using a specified method. load_all_methods
()Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. mixture_property
(T, P, zs, ws)Method to calculate the property with sanity checking and without specifying a specific method. plot_isobar
(P, zs, ws[, Tmin, Tmax, ...])Method to create a plot of the property vs temperature at a specific pressure and composition according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T, zs, ws[, Pmin, Pmax, ...])Method to create a plot of the property vs pressure at a specified temperature and composition according to either a specified list of methods, or the user methods (if set), or all methods. plot_property
(zs, ws[, Tmin, Tmax, Pmin, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. property_derivative_P
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition, of a given order. property_derivative_T
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition, of a given order. select_valid_methods
(T, P, zs, ws)Method to obtain a sorted list of methods which are valid at T, P, zs, ws, and possibly Vfls, according to test_method_validity. set_user_method
(user_methods[, forced])Method to set the T, P, and composition dependent property methods desired for consideration by the user. test_method_validity
(T, P, zs, ws, method)Method to test the validity of a specified method for the given conditions. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the solid molar volume above; assumed 10 000 K even under ultrahigh pressure.

Tmin
= None¶ Minimum temperature at which no method can calculate the solid molar volume under.

all_methods
= None¶ Set of all methods available for a given set of information; filled by
load_all_methods
.

calculate
(T, P, zs, ws, method)[source]¶ Method to calculate molar volume of a solid mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method.
This method has no exception handling; see mixture_property for that.
Parameters: T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Name of the method to use
Returns: Vm : float
Molar volume of the solid mixture at the given conditions, [m^3/mol]

load_all_methods
()[source]¶ Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. All data are stored as attributes. This method also sets
Tmin
,Tmax
, andall_methods
as a set of methods which should work to calculate the property.Called on initialization only. See the source code for the variables at which the coefficients are stored. The coefficients can safely be altered once the class is initialized. This method can be called again to reset the parameters.

name
= 'Solid molar volume'¶

property_max
= 0.002¶ Maximum value of Heat capacity; arbitrarily set to 0.002, as the largest in the data is 0.00136.

property_min
= 0¶ Molar volume cannot be under 0.

ranked_methods
= ['SIMPLE']¶

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by mixture_property.

test_method_validity
(T, P, zs, ws, method)[source]¶ Method to test the validity of a specified method for the given conditions. No methods have implemented checks or strict ranges of validity.
Parameters: T : float
Temperature at which to check method validity, [K]
P : float
Pressure at which to check method validity, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Method name to use
Returns: validity : bool
Whether or not a specifid method is valid

units
= 'm^3/mol'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by mixture_property.