[7] a) Derive the following expression starting from the differential of U in terms of its canonical variables: (VU)N,T=T(TP)N,VP b) Evaluate (U/V)T,N for: i) an ideal gas and ii) for a gas with the following equation of state: P=VbRT where b is a constant. c) Explain your (U/V)T,N result for the two equations of state