I need help with the problems. Want to see detailed steps.

Following the steps below, derive the heat capacity relation, OH ap Cp - CV = ( V (1) ap T . aT V for a general equation of state where Cp, Cv, V, H, T, and P are heat capacity at constant pressure, heat capacity at constant volume, volume, enthalpy, temperature, and pressure respectively. (a) [8 pts] Compute the total differentials dH(P, T), dH(V, T), and dP(V, T) for H = H(P, T), H = H(V, T), and P = P(V, T) respectively. Hint. Recall that if f = f(x, y) its total differential is aj af ( x, y ) = dx + dy ax ay ) y x Draw a box around your three final equations.(b) [6 pts] Using your results from (a) determine the righthand side of equations OH OH av aT Hint. Plug dP into dH(P, T) and compare the result with dH(V, T). Draw a box around your two final equations. (c) [6pts] Given that internal energy is related to enthalpy by H = U + PV and heat capacities Cv and Cp are defined as CV = ne aT Cp = OH aT use your results from (b) to complete the derivation resulting in Eq. 1. Hint: Do this by substituting H in (OH/aT)v