HMW Electrolyte has discrepancies in specific heat, activity coefficients

[speth]

Problem description

The HMWSoln class (YAML phase name HMW-electrolyte displays some small discrepancies in calculations involving specific heats and entropy derivatives. There are also some major discrepancies in the molarity-based activity coefficients.

Steps to reproduce

import cantera as ct
p = ct.Solution('test/data/HMW_NaCl.yaml')
s = ct.SolutionArray(p, 3)
T = 330
P = 10 * ct.one_atm
dT = T * 1e-6
dP = P * 1e-6
s.TPX = [T, T+dT, T], [P, P, P+dP], [55, 5.0, 4.8, 1e-7, 0.2]

print('cp_mole:', s.cp_mole[0])
print('cp from h:', (s.enthalpy_mole[1] - s.enthalpy_mole[0])/dT)
print('cp from s:', (s.entropy_mole[1] - s.entropy_mole[0])/dT * T)

print('ds/dP|T:', (s.entropy_mole[2] - s.entropy_mole[0])/dP)
print('-dv/dT|P:', -(s.volume_mole[1] - s.volume_mole[0])/dT)
print('activities', p.activities)
print('X * gamma ', p.X * p.activity_coefficients)

Behavior

Output:

cp_mole: 60099.47245958206
cp from h: 59694.77052038366
cp from s: 59695.02446532715

ds/dP|T: -9.795058221764663e-06
-dv/dT|P: -9.923389540644756e-06

activities [7.43182302e-01 1.03517736e+01 1.10237209e+01 1.23344100e-07 3.43606673e-02]
X * gamma  [7.43182302e-01 1.86487202e-01 1.98592331e-01 2.22204396e-09 6.19007422e-04]

System information

• Cantera version: 2.6.0 or main at 1ab81ac

Additional context

This was discovered as part of #1299, which implements Cantera/enhancements#114.