### Partition function, chemical potential, entropy, and free energy

Derive equations: S = -(∂F/∂T)_V, N = Nk [ln (V/N_vQ) + 5/2] - ∂F_int/∂T and μ = (∂F/∂N)_T, V = -kT ln (VZ_int/N_vQ) for the entropy and chemical potential of an ideal gas.