4. Given the exact differential expression for dH : dH=TdS+Vdp (i) and knowing that the total derivative of S(p,T) can be expressed in terms of changes in p and T as: dS=(TS)pdT+(pS)Tdp Substitute (ii) into (i) and derive expressions (iii) and (iv): (TS)p=TCp(pS)T=T1[(pH)TV] Hint: you will also need to express the total derivative of H(p,T) in terms of its partial derivatives. Hint: how is Cp defined with respect to enthalpy