Derive the general relation that between the heat capacity at constant volume (Cᵥ) and the heat capacity at constant pressure (Cₚ​) :
Cₚ​ − Cᵥ​ = TVα²/κ

where κ is the isothermal compressibility, and α is the coefficient of thermal expansion (at constant pressure). Start by considering T and p as independent variables so that the entropy S=S(T,p).