def get_SoR(self, T, P=c.P0('bar')):
"""Calculates the dimensionless entropy
:math:`\\frac{S^{trans}}{R}=1+\\frac{n_{degrees}}{2}+\\log\\bigg(\\big(
\\frac{2\\pi mk_bT}{h^2})^\\frac{n_{degrees}}{2}\\frac{RT}{PN_a}\\bigg)`
Parameters
----------
T : float
Temperature in K
P : float, optional
Pressure (bar) or pressure-like quantity.
Default is atmospheric pressure
Returns
-------
SoR_trans : float
Translational dimensionless entropy
"""
V = self.get_V(T=T, P=P)
unit_mass = self.molecular_weight *\
c.convert_unit(from_='g', to='kg')/c.Na
return 1. + float(self.n_degrees)/2. \
+ np.log((2.*np.pi*unit_mass*c.kb('J/K')*T/c.h('J s')**2)
** (float(self.n_degrees)/2.)*V/c.Na)
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 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_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_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_GoRT(self, T, P=c.P0('bar')):
"""Calculates the dimensionless Gibbs energy
:math:`\\frac{G^{trans}}{RT}=\\frac{H^{trans}}{RT}-\\frac{S^{trans}}{R}`
Parameters
----------
T : float
Temperature in K
P : float, optional
Pressure (bar) or pressure-like quantity.
Default is atmospheric pressure
Returns
-------
GoR_trans : float
Translational dimensionless Gibbs energy
"""
return self.get_HoRT() - self.get_SoR(T=T, P=P)
def setUp(self):
unittest.TestCase.setUp(self)
# Testing Ideal Gas Model
CO2 = molecule('CO2')
CO2_PyMuTT_parameters = {
'trans_model':
trans.IdealTrans,
'n_degrees':
3,
'molecular_weight':
get_molecular_weight('CO2'),
'rot_model':
rot.RigidRotor,
'rot_temperatures':
rot.get_rot_temperatures_from_atoms(CO2, geometry='linear'),
'geometry':
'linear',
'symmetrynumber':
2,
'elec_model':
elec.IdealElec,
'potentialenergy':
-22.994202,
'spin':
0.,
'vib_model':
vib.HarmonicVib,
'vib_wavenumbers': [3360., 954., 954., 1890.],
}
CO2_ase_parameters = {
'atoms': CO2,
'potentialenergy': -22.994202,
'vib_energies': [c.wavenumber_to_energy(x) \
for x in CO2_PyMuTT_parameters['vib_wavenumbers']],
'geometry':'linear',
'symmetrynumber': 2,
'spin': 0.
}
self.CO2_PyMuTT = StatMech(**CO2_PyMuTT_parameters)
self.CO2_ASE = IdealGasThermo(**CO2_ase_parameters)
self.T0 = c.T0('K') # K
self.P0 = c.P0('Pa')
self.V0 = c.V0('m3')
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 get_n(self, V=c.V0('m3'), P=c.P0('bar'), T=c.T0('K'), gas_phase=True):
"""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
T : float, optional
Temperature in K. Default is standard temperature
gas_phase : bool, optional
Relevant if system is in vapor-liquid equilibrium. If True,
return the smaller moles (gas phase). If False, returns the
larger moles (liquid phase).
Returns
-------
n : float
Number of moles in mol
"""
return V / self.get_Vm(T=T, P=P, gas_phase=gas_phase)
def get_V(self, T=c.T0('K'), P=c.P0('bar'), n=1., gas_phase=True):
"""Calculates the 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
n : float, optional
Number of moles (in mol). Default is 1 mol
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
-------
V : float
Volume in m3
"""
return self.get_Vm(T=T, P=P, gas_phase=gas_phase) * n
def get_q(self, T, P=c.P0('bar')):
"""Calculates the partition function
:math:`q_{trans} = \\bigg(\\frac{2\\pi \\sum_{i}^{atoms}m_ikT}{h^2}
\\bigg)^\\frac {n_{degrees}} {2}V`
Parameters
----------
T : float
Temperature in K
P : float, optional
Pressure (bar) or pressure-like quantity.
Default is atmospheric pressure
Returns
-------
q_trans : float
Translational partition function
"""
V = self.get_V(T=T, P=P)
unit_mass = self.molecular_weight *\
c.convert_unit(from_='g', to='kg')/c.Na
return V*(2*np.pi*c.kb('J/K')*T*unit_mass/c.h('J s')**2) \
** (float(self.n_degrees)/2.)
def test_get_n(self):
self.assertAlmostEqual(
self.ideal_gas.get_n(T=c.T0('K'), V=c.V0('m3'), P=c.P0('bar')), 1.)
def test_get_P(self):
self.assertAlmostEqual(
self.ideal_gas.get_P(T=c.T0('K'), V=c.V0('m3'), n=1.), c.P0('bar'))
def test_P0(self):
self.assertEqual(c.P0('atm'), 1.)
with self.assertRaises(KeyError):
c.P0('arbitrary unit')