Specific Heat and Helmholtz Free Energy?

["pi"mp]

I'm wondering if there's a simple relation between the specific heat capacity (at constant chemical potential) and the Helmholtz Free Energy? I can't seem to find a relation in the literature between these three quantities, specifically.

 

[ExXxEr]

There shouldn't be one...
Since $dF = -S\, dT - p\, dV$ or $dF = -S\, dT - p\, dV + \mu \, dN$, F can only be identified with work in isothermal process: $\Delta F = \Delta W$, and not with heat.