Problem description

The implementations of getPartialMolarIntEnergies and getPartialMolarCp in the RedlichKwongMFTP class incorrectly return the standard state internal energies and heat capacities, respectively. This can be seen pretty clearly from their implementations

which are just scaling the values returned by functions which return the non-dimensional standard state values:

In reality, the calculation of the partial molar heat capacities should be significantly more involved. The correct implementation of the partial molar internal energies can be done fairly easily by using the identity h_k = u_k + P * v_k, where the complexity is in the already-implemented methods for the partial molar enthalpies and partial molar volumes.

Steps to reproduce

This can also be seen in by computing these values as (a) the total quantity directly, (b) the dot product of the partial molar quantities with the mole fractions and (c) the dot product of the standard state quantities with the mole fractions.

>>> gas = ct.Solution('nDodecane_Reitz.yaml')
>>> gas.TPY = 300, 100 * ct.one_atm, 'CO2: 1.0, CH4: 1.0'

>>> gas.int_energy_mole
-164146896.2111432
>>> sum(gas.partial_molar_int_energies * gas.X)
-162451424.60398442
>>> sum(gas.X * gas.standard_int_energies_RT * ct.gas_constant * gas.T)
-162451424.6039844

>>> gas.cp_mole
56325.864657238315
>>> sum(gas.partial_molar_cp * gas.X)
35800.6557848247
>>> sum(gas.X * gas.standard_cp_R * ct.gas_constant)
35800.655784824696

Behavior

(a) and (b) should give identical values, but instead, (b) and (c) give identical values:

System information

• Cantera version: 2.5.1 / main branch at bbb752a