In the book "An Introduction to Thermal Physics" by Daniel Schroder, I got the following expressions Helmholtz free energy : F = U - TS and Gibbs Free energy : G = H - TS = U + PV - TS
I found in different places (Chemistry StackExchange, Wikipedia etc.) that Gibbs free energy is the capacity to do non-expansion work and Helmholtz free energy is the capacity to do both expansion work (pressure-volume work) and non-expansion work. But in the definition of Gibbs free energy there is a pressure-volume term which Helmholtz free energy does not have. Therefore, my intuition is that it should be the other way around. What am I missing here? I would really appreciate if anyone could help me with this.