[UPSC CSE 2007] Thermodynamics (Q124, 25M)

Establish the relation C_p - C_v = \left[ P + \left(\frac{\partial U}{\partial V}\right)_T \right] \left(\frac{\partial V}{\partial T}\right)_P Use it to find out an expression for C_p of one mole of a gas whose internal energy is given by U = cT - \frac{a}{V} and which satisfies the equation of state \left[ P + \frac{a}{V^2} \right](V - b) = RT. Here a, b and c are constants.