Additivity of thermodynamic potentials?

[heyhey281]

Homework Statement

Two ideal gases, e.g. helium and argon with NA and NB atoms, are mixed, NA + NB = 1 mol. Determine the helmholtz energy of the entire system.

Relevant Equations

F = E - TS

My professor said that F is not additive, meaning F ≠ F1 + F2, where F1 is the helmholtz energy of system 1 and F2 is the helmholtz energy of system 2. So my question is, how can I decide wether a thermodynamic potential (F, H, G) is additive or not?

 

[Demystifier]

If the two systems have the same temperature and have a negligible interaction energy, then F additive.