# thermo.permittivity module¶

thermo.permittivity.permittivity_IAPWS(T, rho)[source]

Calculate the relative permittivity of pure water as a function of. temperature and density. Assumes the 1997 IAPWS [R10001001] formulation.

\begin{align}\begin{aligned}\epsilon(\rho, T) =\frac{1 + A + 5B + (9 + 2A + 18B + A^2 + 10AB + 9B^2)^{0.5}}{4(1-B)}\\A(\rho, T) = \frac{N_A\mu^2\rho g}{M\epsilon_0 kT}\\B(\rho) = \frac{N_A\alpha\rho}{3M\epsilon_0}\\g(\delta,\tau) = 1 + \sum_{i=1}^{11}n_i\delta^{I_i}\tau^{J_i} + n_{12}\delta\left(\frac{647.096}{228}\tau^{-1} - 1\right)^{-1.2}\\\delta = \rho/(322 \text{ kg/m}^3)\\\tau = T/647.096\text{K}\end{aligned}\end{align}
Parameters: T : float Temperature of water [K] rho : float Mass density of water at T and P [kg/m^3] epsilon : float Relative permittivity of water at T and rho, [-]

Notes

Validity:

273.15 < T < 323.15 K for 0 < P < iceVI melting pressure at T or 1000 MPa, whichever is smaller.

323.15 < T < 873.15 K 0 < p < 600 MPa.

Coefficients:

ih = [1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 10]; jh = [0.25, 1, 2.5, 1.5, 1.5, 2.5, 2, 2, 5, 0.5, 10]; Nh = [0.978224486826, -0.957771379375, 0.237511794148, 0.714692244396,

-0.298217036956, -0.108863472196, 0.949327488264E-1, -.980469816509E-2, 0.165167634970E-4, 0.937359795772E-4, -0.12317921872E-9];

polarizability = 1.636E-40 dipole = 6.138E-30

References

 [R10001001] (1, 2) IAPWS. 1997. Release on the Static Dielectric Constant of Ordinary Water Substance for Temperatures from 238 K to 873 K and Pressures up to 1000 MPa.

Examples

>>> permittivity_IAPWS(373., 958.46)
55.56584297721836

class thermo.permittivity.Permittivity(CASRN='')[source]

Class for dealing with liquid permittivity as a function of temperature. Consists of one temperature-dependent simple expression and one constant value source.

Parameters: CASRN : str, optional The CAS number of the chemical

Notes

To iterate over all methods, use the list stored in permittivity_methods.

CRC:

Simple polynomials for calculating permittivity over a specified temperature range only. The full expression is:

$\epsilon_r = A + BT + CT^2 + DT^3$

Not all chemicals use all terms; in fact, few do. Data is available for 759 liquids, from [R10011002].

CRC_CONSTANT:
Constant permittivity values at specified temperatures only. Data is from [R10011002], and is available for 1303 liquids.

References

 [R10011002] (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.

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 permittivity of a liquid at temperature 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 permittivity above.

Tmin = None

Minimum temperature at which no method can calculate the permittivity 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 permittivity of a liquid at temperature 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 relative permittivity, [K] method : str Name of the method to use epsilon : float Relative permittivity of the liquid at T, [-]
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, and all_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 = 'relative permittivity'
property_max = 1000

Maximum valid of permittivity; highest in the data available is ~240.

property_min = 1

Relative permittivity must always be larger than 1; nothing is better than a vacuum.

ranked_methods = ['CRC', 'CRC_CONSTANT']

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 coefficient-based 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 validity : bool Whether or not a method is valid
units = '-'
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.