def get_SoR(self, Ts, P=1., verbose=False):
"""Calculate the dimensionless entropy.
Parameters:
Ts : float or (N,) `numpy.ndarray`_
Temperature(s) in K
P : float, optional
Pressure in atm. Default is 1 atm.
verbose : bool
Whether a table breaking down each contribution should be printed
Returns:
SoR : float or (N,) `numpy.ndarray`_
Dimensionless entropy (S/R) at the specified temperature and pressure
"""
try:
iter(Ts)
except TypeError:
SoR = self.model.get_entropy(
Ts,
pressure=P * c.convert_unit(from_='atm', to='Pa'),
verbose=verbose) / c.R('eV/K')
else:
SoR = np.zeros_like(Ts)
for i, T in enumerate(Ts):
SoR[i] = self.model.get_entropy(
T,
pressure=P * c.convert_unit(from_='atm', to='Pa'),
verbose=verbose) / c.R('eV/K')
return SoR
def get_Vm(self, T=c.T0('K'), P=c.P0('bar'), gas_phase=True):
"""Calculates the molar volume of a van der Waals gas
Parameters
----------
T : float, optional
Temperature in K. Default is standard temperature
P : float, optional
Pressure in bar. Default is standard pressure
gas_phase : bool, optional
Relevant if system is in vapor-liquid equilibrium. If True,
return the larger volume (gas phase). If False, returns the
smaller volume (liquid phase).
Returns
-------
Vm : float
Volume in m3
"""
P_SI = P * c.convert_unit(from_='bar', to='Pa')
Vm = np.roots([
P_SI, -(P_SI * self.b + c.R('J/mol/K') * T), self.a,
-self.a * self.b
])
real_Vm = np.real([Vm_i for Vm_i in Vm if np.isreal(Vm_i)])
if gas_phase:
return np.max(real_Vm)
else:
return np.min(real_Vm)
def from_critical(cls, Tc, Pc):
"""Creates the van der Waals object from critical temperature and
pressure
Parameters
----------
Tc : float
Critical temperature in K
Pc : float
Critical pressure in bar
Returns
-------
vanDerWaalsEOS : vanDerWaalsEOS object
"""
Pc_SI = Pc * c.convert_unit(from_='bar', to='Pa')
a = 27. / 64. * (c.R('J/mol/K') * Tc)**2 / Pc_SI
b = c.R('J/mol/K') * Tc / 8. / Pc_SI
return cls(a=a, b=b)
def get_SoR(self, Ts, verbose=False):
"""Calculate dimensionless entropy at a given temperature.
Args:
Ts (float or numpy array): Temperature(s) in K
verbose (bool): Flag to print each contribution to entropy
Returns:
SoR (float or numpy array): Dimensionless entropy (S/R)
"""
try:
iter(Ts)
except TypeError:
SoR = self.model.get_entropy(Ts, verbose) / c.R('eV/K')
else:
SoR = np.zeros_like(Ts)
for i, T in enumerate(Ts):
SoR[i] = self.model.get_entropy(T, verbose) / c.R('eV/K')
return SoR
def get_Tc(self):
"""Calculates the critical temperature
Returns
-------
Tc : float
Critcial temperature in K
"""
return 8. * self.a / 27. / self.b / c.R('J/mol/K')
def get_SoR(self, Ts, P=1., verbose=False):
"""Calculate the dimensionless entropy.
Parameters:
Ts : float or (N,) `numpy.ndarray`_
Temperature(s) in K
P : float
Pressure in atm. Default is 1 atm
verbose : bool
Whether a table breaking down each contribution should be printed
Returns:
SoR : float or (N,) `numpy.ndarray`_
Dimensionless entropy (S/R)
"""
try:
iter(Ts)
except TypeError:
SoR = self.model.get_entropy(Ts, verbose)/c.R('eV/K')
else:
SoR = np.zeros_like(Ts)
for i, T in enumerate(Ts):
SoR[i] = self.model.get_entropy(T, verbose)/c.R('eV/K')
return SoR
def setUp(self):
unittest.TestCase.setUp(self)
H2_thermo = BaseThermo(name='H2',
phase='G',
elements={'H': 2},
thermo_model=IdealGasThermo,
T_ref=c.T0('K'),
HoRT_ref=0.,
vib_energies=np.array([4306.1793]) *
c.c('cm/s') * c.h('eV s'),
potentialenergy=-6.7598,
geometry='linear',
symmetrynumber=2,
spin=0,
atoms=molecule('H2'))
H2O_thermo = BaseThermo(
name='H2O',
phase='G',
elements={
'H': 2,
'O': 1
},
thermo_model=IdealGasThermo,
T_ref=c.T0('K'),
HoRT_ref=-241.826 / (c.R('kJ/mol/K') * c.T0('K')),
vib_energies=np.array([3825.434, 3710.264, 1582.432]) *
c.c('cm/s') * c.h('eV s'),
potentialenergy=-14.2209,
geometry='nonlinear',
symmetrynumber=2,
spin=0,
atoms=molecule('H2O'))
O2_thermo = BaseThermo(name='H2O',
phase='G',
elements={'O': 2},
thermo_model=IdealGasThermo,
T_ref=c.T0('K'),
HoRT_ref=0.,
vib_energies=np.array([2205.]) * c.c('cm/s') *
c.h('eV s'),
potentialenergy=-9.86,
geometry='linear',
symmetrynumber=2,
spin=1,
atoms=molecule('O2'))
self.references = References(
references=[H2_thermo, H2O_thermo, O2_thermo])
def get_V(self, T=c.T0('K'), P=c.P0('bar'), n=1.):
"""Calculates the volume of an ideal gas
Parameters
----------
T : float, optional
Temperature in K. Default is standard temperature
P : float, optional
Pressure in bar. Default is standard pressure
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
V : float
Volume in m3
"""
return n * c.R('m3 bar/mol/K') * T / P
def get_T(self, V=c.V0('m3'), P=c.P0('bar'), n=1.):
"""Calculates the volume of an ideal gas
Parameters
----------
V : float, optional
Volume in m3. Default is standard volume
P : float, optional
Pressure in bar. Default is standard pressure
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
T : float
Temperature in K
"""
return P * V / c.R('m3 bar/mol/K') / n
def get_n(self, V=c.V0('m3'), P=c.P0('bar'), T=c.T0('K')):
"""Calculates the volume of an ideal gas
Parameters
----------
V : float, optional
Volume in m3. Default is standard volume
P : float, optional
Pressure in bar. Default is standard pressure
T : float, optional
Temperature in K. Default is standard temperature
Returns
-------
n : float
Number of moles in mol
"""
return P * V / c.R('m3 bar/mol/K') / T
def get_V(self, T, P):
"""Calculates the molar volume of an ideal gas at T and P
:math:`V_m=\\frac{RT}{P}`
Parameters
----------
T : float
Temperature in K
P : float
Pressure in bar
Returns
-------
V : float
Molar volume in m3
"""
return T * c.R('J/mol/K') / (P * c.convert_unit(from_='bar', to='Pa'))
def get_SoR(self, temperature, pressure=1.0, verbose=False):
"""Calculate the dimensionless entropy.
Parameters:
temperature (float): Temperature(s) in K
pressure (float, optional): Pressure in atm. Default is 1 atm.
verbose (bool): Print a table breaking down each contribution
"""
if self.specie_type == 'ideal gas':
entropy = self.model.get_entropy(
temperature,
pressure=pressure * c.convert_unit(from_='atm', to='Pa'),
verbose=verbose)
else:
entropy = self.model.get_entropy(temperature, verbose=verbose)
return entropy / c.R('eV/K')
def get_P(self, T=c.T0('K'), V=c.V0('m3'), n=1.):
"""Calculates the pressure of an ideal gas
Parameters
----------
T : float, optional
Temperature in K. Default is standard temperature
V : float, optional
Volume in m3. Default is standard volume
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
P : float
Pressure in bar
"""
return n * c.R('m3 bar/mol/K') * T / V
def get_P(self, T=c.T0('K'), V=c.V0('m3'), n=1.):
"""Calculates the pressure of a van der Waals gas
Parameters
----------
T : float, optional
Temperature in K. Default is standard temperature
V : float, optional
Volume in m3. Default is standard volume
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
P : float
Pressure in bar
"""
Vm = V / n
return (c.R('J/mol/K')*T/(Vm - self.b) - self.a*(1./Vm)**2) \
*c.convert_unit(from_='Pa', to='bar')
def get_T(self, V=c.V0('m3'), P=c.P0('bar'), n=1.):
"""Calculates the volume of a van der Waals gas
Parameters
----------
V : float, optional
Volume in m3. Default is standard volume
P : float, optional
Pressure in bar. Default is standard pressure
n : float, optional
Number of moles (in mol). Default is 1 mol
Returns
-------
T : float
Temperature in K
"""
Vm = V / n
return (P*c.convert_unit(from_='bar', to='Pa') + self.a/Vm**2) \
*(Vm - self.b)/c.R('J/mol/K')
def plot_statmech_and_empirical(self,
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 ``PyMuTT.constants.R`` for
accepted units. If not specified, dimensionless units used.
H_units : str
Units to plot enthalpy. See ``PyMuTT.constants.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 ``PyMuTT.constants.R`` for accepted
units. If not specified, dimensionless units used.
G_units : str
Units to plot Gibbs free energy. See ``PyMuTT.constants.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
.. _`matplotlib.figure.Figure`: https://matplotlib.org/api/_as_gen/matplotlib.figure.Figure.html
.. _`matplotlib.axes.Axes.axis`: https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.axis.html
"""
if T_low is None:
T_low = self.T_low
if T_high is None:
T_high = self.T_high
T = np.linspace(T_low, T_high)
f, ax = plt.subplots(4, sharex=True)
'''
Heat Capacity
'''
ax[0].set_title('Specie: {}'.format(self.name))
T, Cp_plot_statmech, Cp_plot_empirical = self.compare_CpoR(T=T)
if Cp_units is None:
ax[0].set_ylabel('Cp/R')
else:
ax[0].set_ylabel('Cp ({})'.format(Cp_units))
Cp_plot_statmech = Cp_plot_statmech * c.R(Cp_units)
Cp_plot_empirical = Cp_plot_empirical * c.R(Cp_units)
ax[0].plot(T, Cp_plot_statmech, 'r-', label='Stat Mech Model')
ax[0].plot(T, Cp_plot_empirical, 'b-', label='Empirical Model')
ax[0].legend()
'''
Enthalpy
'''
T, H_plot_statmech, H_plot_empirical = self.compare_HoRT(T=T)
if H_units is None:
ax[1].set_ylabel('H/RT')
else:
ax[1].set_ylabel('H ({})'.format(H_units))
H_plot_statmech = H_plot_statmech *\
c.R('{}/K'.format(H_units))*T
H_plot_empirical = H_plot_empirical *\
c.R('{}/K'.format(H_units))*T
ax[1].plot(T, H_plot_statmech, 'r-')
ax[1].plot(T, H_plot_empirical, 'b-')
'''
Entropy
'''
T, S_plot_statmech, S_plot_empirical = self.compare_SoR(T=T)
if S_units is None:
ax[2].set_ylabel('S/R')
else:
ax[2].set_ylabel('S ({})'.format(S_units))
S_plot_statmech = S_plot_statmech * c.R(S_units)
S_plot_empirical = S_plot_empirical * c.R(S_units)
ax[2].plot(T, S_plot_statmech, 'r-')
ax[2].plot(T, S_plot_empirical, 'b-')
'''
Gibbs energy
'''
ax[3].set_xlabel('Temperature (K)')
T, G_plot_statmech, G_plot_empirical = self.compare_GoRT(T=T)
if G_units is None:
ax[3].set_ylabel('G/RT')
else:
ax[3].set_ylabel('G ({})'.format(G_units))
G_plot_statmech = G_plot_statmech *\
c.R('{}/K'.format(G_units))*T
G_plot_empirical = G_plot_empirical *\
c.R('{}/K'.format(G_units))*T
ax[3].plot(T, G_plot_statmech, 'r-')
ax[3].plot(T, G_plot_empirical, 'b-')
return f, ax
def plot_empirical(self,
T_low=None,
T_high=None,
Cp_units=None,
H_units=None,
S_units=None,
G_units=None):
"""Plot 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 ``PyMuTT.constants.R`` for
accepted units. If not specified, dimensionless units used.
H_units : str
Units to plot enthalpy. See ``PyMuTT.constants.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 ``PyMuTT.constants.R`` for accepted
units. If not specified, dimensionless units used.
G_units : str
Units to plot Gibbs free energy. See ``PyMuTT.constants.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
"""
if T_low is None:
T_low = self.T_low
if T_high is None:
T_high = self.T_high
Ts = np.linspace(T_low, T_high)
f, ax = plt.subplots(4, sharex=True)
'''
Heat Capacity
'''
ax[0].set_title('Specie: {}'.format(self.name))
Cp_plot = np.array(map(self.get_CpoR, Ts))
if Cp_units is None:
ax[0].set_ylabel('Cp/R')
else:
ax[0].set_ylabel('Cp ({})'.format(Cp_units))
Cp_plot *= c.R(Cp_units)
ax[0].plot(Ts, Cp_plot, 'r-')
'''
Enthalpy
'''
H_plot = np.array(map(self.get_HoRT, Ts))
if H_units is None:
ax[1].set_ylabel('H/RT')
else:
ax[1].set_ylabel('H ({})'.format(H_units))
H_plot *= c.R('{}/K'.format(H_units)) * Ts
ax[1].plot(Ts, H_plot, 'g-')
'''
Entropy
'''
S_plot = np.array(map(self.get_SoR, Ts))
if S_units is None:
ax[2].set_ylabel('S/R')
else:
ax[2].set_ylabel('S ({})'.format(S_units))
S_plot *= c.R(S_units)
ax[2].plot(Ts, S_plot, 'b-')
'''
Gibbs energy
'''
ax[3].set_xlabel('Temperature (K)')
G_plot = np.array(map(self.get_GoRT, Ts))
if G_units is None:
ax[3].set_ylabel('G/RT')
else:
ax[3].set_ylabel('G ({})'.format(G_units))
G_plot *= c.R('{}/K'.format(G_units)) * Ts
ax[3].plot(Ts, G_plot, 'k-')
return f, ax
def test_R(self):
self.assertEqual(c.R('J/mol/K'), 8.3144598)
with self.assertRaises(KeyError):
c.R('arbitrary unit')
def test_get_GoRT(self):
expected_GoRT_CO2 = \
self.CO2_ASE.get_gibbs_energy(temperature=self.T0, pressure=self.P0,
verbose=False)/c.R('eV/K')/self.T0
calc_GoRT_CO2 = self.CO2_PyMuTT.get_GoRT(T=self.T0, V=self.V0)
self.assertTrue(np.isclose(expected_GoRT_CO2, calc_GoRT_CO2))
def test_get_SoR(self):
expected_SoR_CO2 = \
self.CO2_ASE.get_entropy(temperature=self.T0, pressure=self.P0,
verbose=False)/c.R('eV/K')
calc_SoR_CO2 = self.CO2_PyMuTT.get_SoR(T=self.T0, V=self.V0)
self.assertTrue(np.isclose(expected_SoR_CO2, calc_SoR_CO2))
def test_get_HoRT(self):
expected_HoRT_CO2 = \
self.CO2_ASE.get_enthalpy(temperature=self.T0, verbose=False) \
/c.R('eV/K')/self.T0
calc_HoRT_CO2 = self.CO2_PyMuTT.get_HoRT(T=self.T0)
self.assertTrue(np.isclose(expected_HoRT_CO2, calc_HoRT_CO2))
import numpy as np
import matplotlib.pyplot as plt
from PyMuTT import constants as c
from PyMuTT.models.empirical.nasa import Nasa
# Gas phase heat capacity data (in J/mol/K) for CH3OH from NIST
# https://webbook.nist.gov/cgi/cbook.cgi?ID=C67561&Units=SI&Mask=1#Thermo-Gas
Ts = np.array([50, 100, 150, 200, 273.15, 298.15, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1750, 2000, 2250, 2500, 2750, 3000])
Cp = np.array([34.00, 36.95, 38.64, 39.71, 42.59, 44.06, 44.17, 51.63, 59.7, 67.19, 73.86, 79.76, 84.95, 89.54, 93.57, 97.12, 100.24, 102.98, 105.4, 110.2, 113.8, 116.5, 118.6, 120, 121])
CpoR = Cp/c.R('J/mol/K')
#Enthalpy of Formation for CH3OH (in kJ/mol) from NIST
T_ref = c.T0('K')
H_ref = -205.
HoRT_ref = H_ref/c.R('kJ/mol/K')/T_ref
#Standard molar entropy (in J/mol/K) from Wikipedia, https://en.wikipedia.org/wiki/Methanol_(data_page)
S_ref = 239.9
SoR_ref = S_ref/c.R('J/mol/K')
#Units to plot the figure
Cp_units = 'J/mol/K'
H_units = 'kJ/mol'
S_units = 'J/mol/K'
G_units = 'kJ/mol'
#Input the experimental data and fitting to a NASA polynomial
CH3OH_nasa = Nasa(name ='CH3OH', Ts=Ts, CpoR=CpoR, T_ref=T_ref, HoRT_ref=HoRT_ref, SoR_ref=SoR_ref)
#Compare the Nasa polynomial to the input data
fig, axes = CH3OH_nasa.plot_empirical(Cp_units=Cp_units, H_units=H_units, S_units=S_units, G_units=G_units)
axes[0].plot(Ts, Cp, 'ko')
def setUp(self):
unittest.TestCase.setUp(self)
H2_thermo = Reference(name='H2',
phase='G',
elements={'H': 2},
T_ref=c.T0('K'),
HoRT_ref=0.,
statmech_model=StatMech,
trans_model=trans.IdealTrans,
n_degrees=3,
vib_model=vib.HarmonicVib,
elec_model=elec.IdealElec,
rot_model=rot.RigidRotor,
vib_wavenumbers=np.array([4306.1793]),
potentialenergy=-6.7598,
geometry='linear',
symmetrynumber=2,
spin=0,
atoms=molecule('H2'))
H2O_thermo = Reference(
name='H2O',
phase='G',
elements={
'H': 2,
'O': 1
},
T_ref=c.T0('K'),
HoRT_ref=-241.826 / (c.R('kJ/mol/K') * c.T0('K')),
statmech_model=StatMech,
trans_model=trans.IdealTrans,
n_degrees=3,
vib_model=vib.HarmonicVib,
elec_model=elec.IdealElec,
rot_model=rot.RigidRotor,
vib_wavenumbers=np.array([3825.434, 3710.264, 1582.432]),
potentialenergy=-14.2209,
geometry='nonlinear',
symmetrynumber=2,
spin=0,
atoms=molecule('H2O'))
O2_thermo = Reference(name='H2O',
phase='G',
elements={'O': 2},
T_ref=c.T0('K'),
HoRT_ref=0.,
statmech_model=StatMech,
trans_model=trans.IdealTrans,
n_degrees=3,
vib_model=vib.HarmonicVib,
elec_model=elec.IdealElec,
rot_model=rot.RigidRotor,
vib_wavenumbers=np.array([2205.]),
potentialenergy=-9.86,
geometry='linear',
symmetrynumber=2,
spin=1,
atoms=molecule('O2'))
self.references = References(
references=[H2_thermo, H2O_thermo, O2_thermo])
