Problem 2.13. Compute the entropy, enthalpy, Helmholtz free energy, and Gibbs free energy of a paramagnetic substance and write them explicitly in terms of their natural variables when possible. Assume that the mechanical equation of state is m = (DH/T) and that the molar heat capacity at constant magnetization is cm =

c, where m is the molar magnetization, H is the magnetic field, D is a constant, c is a constant, and T is the temperature.