ideal-solution-vpss model with HKFT species thermo does not satisfy Maxwell relation

[speth]

Problem description

A phase using the ideal-solution-vpss thermo model (class IdealSolnGasVPSS) with the HKFT species thermo model does not satisfy the Maxwell relation based on the Gibbs free energy, that is ds/dP at constant T = - dv/dT at constant P. The discrepancies seem to grow as temperature increases.

Steps to reproduce

p = ct.Solution('test/data/pdss_hkft.yaml')
p.TPX = 360, 5*ct.one_atm, "H2O(L):0.6, Na+:0.2, Cl-:0.2"
s1 = p.entropy_mole
T1 = 360
P1 = 5*ct.one_atm
v1 = p.volume_mole
dP = 1e-6 * P1
dT = 1e-6 * T1
p.TP = T1 + dT, P1
v2 = p.volume_mole
p.TP = T1, P1 + dP
s2 = p.entropy_mole
print((s2-s1)/dP)
print(-(v2-v1)/dT)

Behavior

The output values differ by ~8% in this case.

6.083871037790048e-07
5.599036232721721e-07

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.