2. A system is described by the fundamental equation
$$(S - S_0)^4 = AVU^2$$
where A, $S_0$ are constants. U, S and V are the internal energy, entropy and the volume.
(a) Use the representation U(S, V) with its partial derivative equations to write U(T,P) (U as a function of temperature T and pressure P).
(b) Write Helmholtz energy F(T, P) (F as a function of T and P).
(c) Write the Gibbs energy G(T, P) (G as a function of T and P).