pmutt.empirical.shomate.Shomate

class pmutt.empirical.shomate.Shomate(name, T_low, T_high, a, units='J/mol/K', n_sites=None, **kwargs)

Bases: EmpiricalBase

Stores the information for an individual Shomate specie Inherits from EmpiricalBase

The thermodynamic properties are calculated using the following form:

\(\frac{c_P}{R}=\frac{1}{R}\bigg(A+Bt+Ct^2+Dt^3+\frac{E}{t^2} \bigg)\)

\(\frac{H}{RT}=\frac{1}{RT}\bigg(At+B\frac{t^2}{2}+C\frac{t^3}{3} +D\frac{t^4}{4}-\frac{E}{t}+F\bigg)\)

\(\frac{S}{R}=\frac{1}{R}\bigg(A\ln(t)+Bt+C\frac{t^2}{2}+D \frac{t^3}{3}-\frac{E}{2t^2}+G\bigg)\)

where \(t=\frac{T}{1000}\) in K

T_low

Lower temperature bound (in K)

Type:: float

T_high

High temperature bound (in K)

Type:: float

a

Shomate polynomial to use between T_low and T_high

Type:: (8,) numpy.ndarray

units

Units used to fit the Shomate polynomial. Units should be supported by R (e.g. J/mol/K, cal/mol/K, eV/K). Default is J/mol/K.

Type:: str, optional

__init__(name, T_low, T_high, a, units='J/mol/K', n_sites=None, **kwargs)

Methods

`__init__`(name, T_low, T_high, a[, units, ...])
`compare_CpoR`([T])	Compares the dimensionless heat capacity of the statistical model and the empirical model
`compare_GoRT`([T])	Compares the dimensionless Gibbs energy of the statistical model and the empirical model
`compare_HoRT`([T])	Compares the dimensionless enthalpy of the statistical model and the empirical model
`compare_SoR`([T])	Compares the dimensionless entropy of the statistical model and the empirical model
`from_data`(name, T, CpoR, T_ref, HoRT_ref, ...)	Calculates the Shomate polynomials using thermodynamic data
`from_dict`(json_obj)	Recreate an object from the JSON representation.
`from_model`(model[, name, T_low, T_high, ...])	Calculates the NASA polynomials using the model passed
`from_statmech`(name, statmech_model, T_low, ...)	Calculates the Shomate polynomial using statistical mechanic models.
`get_Cp`(T, units[, raise_error, raise_warning])	Calculate the heat capacity
`get_CpoR`(T[, raise_error, raise_warning])	Calculate the dimensionless heat capacity
`get_Cv`(units, **kwargs)	Calculate the heat capacity (constant V)
`get_CvoR`()	Default method to calculate the dimensionless heat capacity at constant volume.
`get_F`(units[, T])	Calculate the Helmholtz energy
`get_FoRT`(**kwargs)	Calculates the dimensionless Helmholtz energy
`get_G`(T, units[, raise_error, ...])	Calculate the Gibbs energy
`get_GoRT`(T[, raise_error, raise_warning, ...])	Calculate the dimensionless Gibbs free energy
`get_H`(T, units[, raise_error, raise_warning])	Calculate the enthalpy
`get_HoRT`(T[, raise_error, raise_warning])	Calculate the dimensionless enthalpy
`get_S`(T, units[, raise_error, ...])	Calculate the entropy
`get_Selements`()	Calculate the dimensionless entropy of the elements in the molecule
`get_SoR`(T[, raise_error, raise_warning, ...])	Calculate the dimensionless entropy
`get_U`(units[, T])	Calculate the internal energy
`get_UoRT`()	Default method to calculate the dimensionless internal energy.
`get_q`()	Default method to calculate the partition coefficient.
`plot_empirical`([T_low, T_high, Cp_units, ...])	Plots the thermodynamic profiles between `T_low` and `T_high` using empirical relationship
`plot_statmech`([T_low, T_high, Cp_units, ...])	Plots the thermodynamic profiles between `T_low` and `T_high` using empirical relationship
`plot_statmech_and_empirical`([T_low, T_high, ...])	Plots the thermodynamic profiles between `T_low` and `T_high` using empirical relationship
`to_cti`()	Writes the object in Cantera's CTI format.
`to_dict`()	Represents object as dictionary with JSON-accepted datatypes
`to_omkm_yaml`()	Returns a dictionary compatible with Cantera's YAML format

Attributes

units

compare_CpoR(T=None)

Compares the dimensionless heat capacity of the statistical model and the empirical model

Parameters:

T ((N,) numpy.ndarray or float, optional) – Temperatures (in K) to calculate CpoR. If None, generates a list of temperatures between self.T_low and self.T_high

Returns:

T ((N,) numpy.ndarray or float) – Temperatures in K
CpoR_model ((N,) numpy.ndarray or float) – Dimensionless heat capacity of original model
CpoR_empirical (((N,) numpy.ndarray or float) – Dimensionless heat capacity of empirical model

compare_GoRT(T=None)

Compares the dimensionless Gibbs energy of the statistical model and the empirical model

Parameters:

T ((N,) numpy.ndarray or float, optional) – Temperatures (in K) to calculate CpoR. If None, generates a list of temperatures between self.T_low and self.T_high

Returns:

T ((N,) numpy.ndarray or float) – Temperatures in K
CpoR_model ((N,) numpy.ndarray or float) – Dimensionless heat capacity of original model
CpoR_empirical ((N,) numpy.ndarray or float) – Dimensionless heat capacity of empirical model

compare_HoRT(T=None)

Compares the dimensionless enthalpy of the statistical model and the empirical model

Parameters:

T ((N,) numpy.ndarray or float, optional) – Temperatures (in K) to calculate CpoR. If None, generates a list of temperatures between self.T_low and self.T_high

Returns:

T ((N,) numpy.ndarray or float) – Temperatures in K
CpoR_model ((N,) numpy.ndarray or float) – Dimensionless heat capacity of original model
CpoR_empirical (((N,) numpy.ndarray or float) – Dimensionless heat capacity of empirical model

compare_SoR(T=None)

Compares the dimensionless entropy of the statistical model and the empirical model

Parameters:

T ((N,) numpy.ndarray or float, optional) – Temperatures (in K) to calculate CpoR. If None, generates a list of temperatures between self.T_low and self.T_high

Returns:

T ((N,) numpy.ndarray or float) – Temperatures in K
CpoR_model ((N,) numpy.ndarray or float) – Dimensionless heat capacity of original model
CpoR_empirical (((N,) numpy.ndarray or float) – Dimensionless heat capacity of empirical model

classmethod from_data(name, T, CpoR, T_ref, HoRT_ref, SoR_ref, units='J/mol/K', **kwargs)

Calculates the Shomate polynomials using thermodynamic data

Parameters:

name (str) – Name of the species
T ((N,) numpy.ndarray) – Temperatures in K used for fitting CpoR.
CpoR ((N,) numpy.ndarray) – Dimensionless heat capacity corresponding to T.
T_ref (float) – Reference temperature in K used fitting empirical coefficients.
HoRT_ref (float) – Dimensionless reference enthalpy that corresponds to T_ref.
SoR_ref (float) – Dimensionless entropy that corresponds to T_ref.
units (str, optional) – Units used to fit the Shomate polynomial. Units should be supported by R (e.g. J/mol/K, cal/mol/K, eV/K). Default is J/mol/K.

Returns:

shomate – Shomate object with polynomial terms fitted to data.

Return type:

Shomate object

classmethod from_dict(json_obj)

Recreate an object from the JSON representation.

Parameters:: json_obj (dict) – JSON representation
Returns:: shomate
Return type:: Shomate object

classmethod from_model(model, name=None, T_low=None, T_high=None, elements=None, n_T=50, units='J/mol/K', **kwargs)

Calculates the NASA polynomials using the model passed

Parameters:

model (Model object or class) – Model to generate data. Must contain the methods get_CpoR, get_HoRT and get_SoR
name (str, optional) – Name of the species. If not passed, model.name will be used.
T_low (float, optional) – Lower limit temerature in K. If not passed, model.T_low will be used.
T_high (float, optional) – Higher limit temperature in K. If not passed, model.T_high will be used.
elements (dict, optional) – Composition of the species. If not passed, model.elements will be used. Keys of dictionary are elements, values are stoichiometric values in a formula unit. e.g. CH3OH can be represented as: {‘C’: 1, ‘H’: 4, ‘O’: 1,}.
n_T (int, optional) – Number of data points between T_low and T_high for fitting heat capacity. Default is 50.
units (str, optional) – Units used to fit the Shomate polynomial. Units should be supported by R (e.g. J/mol/K, cal/mol/K, eV/K). Default is J/mol/K.
kwargs (keyword arguments) – Used to initalize model if a class is passed.

Returns:

Shomate – Shomate object with polynomial terms fitted to data.

Return type:

Shomate object

classmethod from_statmech(name, statmech_model, T_low, T_high, references=None, elements=None, **kwargs)

Calculates the Shomate polynomial using statistical mechanic models. Deprecated as of Version 1.2.13. Please use from_model instead.

Parameters:

name (str) – Name of the species
statmech_model (pmutt.statmech.StatMech object or class) – Statistical Mechanics model to generate data
T_low (float) – Lower limit temerature in K
T_high (float) – Higher limit temperature in K
references (pmutt.empirical.references.References object) – Reference to adjust enthalpy
**kwargs (keyword arguments) – Used to initalize statmech_model or EmpiricalBase attributes to be stored.

Returns:

shomate – Shomate object with polynomial terms fitted to data.

Return type:

Shomate object

get_Cp(T, units, raise_error=True, raise_warning=True, **kwargs)

Calculate the heat capacity

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
units (str) – Units as string. See R() for accepted units.
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

Cp – Heat capacity

Return type:

float or (N,) numpy.ndarray

get_CpoR(T, raise_error=True, raise_warning=True, **kwargs)

Calculate the dimensionless heat capacity

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

CpoR – Dimensionless heat capacity

Return type:

float or (N,) numpy.ndarray

get_Cv(units, **kwargs)

Calculate the heat capacity (constant V)

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_CvoR

Returns:

Cv – Heat capacity (constant V) in appropriate units

Return type:

float

get_CvoR()

Default method to calculate the dimensionless heat capacity at constant volume.

Returns:: CvoR – Returns 0
Return type:: float

get_F(units, T=298.15, **kwargs)

Calculate the Helmholtz energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_FoRT

Returns:

F – Hemholtz energy in appropriate units

Return type:

float

get_FoRT(**kwargs)

Calculates the dimensionless Helmholtz energy

Parameters:: kwargs (keyword arguments) – Parameters needed by get_UoRT and get_SoR
Returns:: FoRT – Dimensionless Helmholtz energy
Return type:: float

get_G(T, units, raise_error=True, raise_warning=True, S_elements=None, **kwargs)

Calculate the Gibbs energy

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
S_elements (bool, optional) – Includes the entropy of the elements to compute an entropy of formation. Defauly is None
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

G – Gibbs energy

Return type:

float or (N,) numpy.ndarray

get_GoRT(T, raise_error=True, raise_warning=True, S_elements=None, **kwargs)

Calculate the dimensionless Gibbs free energy

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
S_elements (bool, optional) – Includes the entropy of the elements to compute an entropy of formation. Defauly is None
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

GoRT – Dimensionless Gibbs free energy

Return type:

float or (N,) numpy.ndarray

get_H(T, units, raise_error=True, raise_warning=True, **kwargs)

Calculate the enthalpy

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

H – Enthalpy

Return type:

float or (N,) numpy.ndarray

get_HoRT(T, raise_error=True, raise_warning=True, **kwargs)

Calculate the dimensionless enthalpy

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

HoRT – Dimensionless enthalpy

Return type:

float or (N,) numpy.ndarray

get_S(T, units, raise_error=True, raise_warning=True, S_elements=None, **kwargs)

Calculate the entropy

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
units (str) – Units as string. See R() for accepted units.
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
S_elements (bool, optional) – Includes the entropy of the elements to compute an entropy of formation. Defauly is None
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

S – Entropy

Return type:

float or (N,) numpy.ndarray

get_Selements()

Calculate the dimensionless entropy of the elements in the molecule

Parameters:: None –
Returns:: SoR – Entropy
Return type:: float

get_SoR(T, raise_error=True, raise_warning=True, S_elements=None, **kwargs)

Calculate the dimensionless entropy

Parameters:

T (float or (N,) numpy.ndarray) – Temperature(s) in K
raise_error (bool, optional) – If True, raises an error if any of the modes do not have the quantity of interest. Default is True
raise_warning (bool, optional) – Only relevant if raise_error is False. Raises a warning if any of the modes do not have the quantity of interest. Default is True
S_elements (bool, optional) – Includes the entropy of the elements to compute an entropy of formation. Defauly is None
kwargs (key-word arguments) – Arguments to calculate mixture model properties, if any

Returns:

SoR – Dimensionless entropy

Return type:

float or (N,) numpy.ndarray

get_U(units, T=298.15, **kwargs)

Calculate the internal energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_UoRT

Returns:

U – Internal energy in appropriate units

Return type:

float

get_UoRT()

Default method to calculate the dimensionless internal energy.

Returns:: UoRT – Returns 0
Return type:: float

get_q()

Default method to calculate the partition coefficient.

Returns:: q – Returns 1
Return type:: float

plot_empirical(T_low=None, T_high=None, Cp_units=None, H_units=None, S_units=None, G_units=None)

Plots the thermodynamic profiles between T_low and T_high using empirical relationship

Parameters:

T_low (float) – Lower temperature in K. If not specified, T_low attribute used.
T_high (float) – Upper temperature in K. If not specified, T_high attribute used.
Cp_units (str) – Units to plot heat capacity. See R() for accepted units. If not specified, dimensionless units used.
H_units (str) – Units to plot enthalpy. See R() for accepted units but omit the ‘/K’ (e.g. J/mol). If not specified, dimensionless units used.
S_units (str) – Units to plot entropy. See R() for accepted units. If not specified, dimensionless units used.
G_units (str) – Units to plot Gibbs free energy. See R() for accepted units but omit the ‘/K’ (e.g. J/mol). If not specified, dimensionless units used.

Returns:

figure (matplotlib.figure.Figure) – Figure
axes (tuple of matplotlib.axes.Axes.axis) – Axes of the plots. 0. Cp 1. H 2. S 3. G

plot_statmech(T_low=None, T_high=None, Cp_units=None, H_units=None, S_units=None, G_units=None, use_references=True)

Plots the thermodynamic profiles between T_low and T_high using empirical relationship

Parameters:

T_low (float) – Lower temperature in K. If not specified, T_low attribute used
T_high (float) – Upper temperature in K. If not specified, T_high attribute used
Cp_units (str) – Units to plot heat capacity. See R() for accepted units. If not specified, dimensionless units used.
H_units (str) – Units to plot enthalpy. See R() for accepted units but omit the ‘/K’ (e.g. J/mol). If not specified, dimensionless units used.
S_units (str) – Units to plot entropy. See R() for accepted units. If not specified, dimensionless units used.
G_units (str) – Units to plot Gibbs free energy. See R() for accepted units but omit the ‘/K’ (e.g. J/mol). If not specified, dimensionless units used.

Returns:

figure (matplotlib.figure.Figure) – Figure
axes (tuple of matplotlib.axes.Axes.axis) – Axes of the plots. 0. Cp 1. H 2. S 3. G

plot_statmech_and_empirical(T_low=None, T_high=None, Cp_units=None, H_units=None, S_units=None, G_units=None, use_references=True)

Plots the thermodynamic profiles between T_low and T_high using empirical relationship

Parameters:

T_low (float) – Lower temperature in K. If not specified, T_low attribute used
T_high (float) – Upper temperature in K. If not specified, T_high attribute used
Cp_units (str) – Units to plot heat capacity. See R() for accepted units. If not specified, dimensionless units used.
H_units (str) – Units to plot enthalpy. See R() for accepted units but omit the ‘/K’ (e.g. J/mol). If not specified, dimensionless units used.
S_units (str) – Units to plot entropy. See R() for accepted units. If not specified, dimensionless units used.
G_units (str) – Units to plot Gibbs free energy. See R() for accepted units but omit the ‘/K’ (e.g. J/mol). If not specified, dimensionless units used.

Returns:

figure (matplotlib.figure.Figure) – Figure
axes (tuple of matplotlib.axes.Axes.axis) – Axes of the plots. 0. Cp 1. H 2. S 3. G

to_cti()

Writes the object in Cantera’s CTI format.

Returns:: CTI_str – Object represented as a CTI string.
Return type:: str

to_dict()

Represents object as dictionary with JSON-accepted datatypes

Returns:: obj_dict
Return type:: dict

to_omkm_yaml()

Returns a dictionary compatible with Cantera’s YAML format

Returns:: yaml_dict – Dictionary compatible with Cantera’s YAML format
Return type:: dict

property units