I need help with this problem. I want to see detailed steps.

2. Let A = A(T, V) and G = G (T, p) be thermodynamic state functions with total differentials dA = SdT pdV and d0 = SdT + Vdp, where 39, V, T, and S are, respectively, pressure, volume, temperature and entropy. a) Use CM and suitable relationships between partial derivatives to show that CV 05 d8 _ ?dT + (;)dV (2) where o: = %(%)p, a = %(%)T and 0V = T(%S)V. b) Use dG and suitable relationships between partial derivatives to show that d8 = %dT anp (3) where 0,, = T(gg) P c) Use (2) and (3) and suitable relationships between partial derivatives to show that 012 d) For a particular material, the values of 0p, 0:, and a as a function of tempera- ture and pressure are readily available. A mole of this material is subjected to an expansion process from V1 to V2 during which the temperature is observed to change from T1 to T2 in a manner that depends with volume as T = a + (JV ((1 and b are constants to be determined). Use (2) and (4) to nd an integral expression for the change in entropy for this process, A8142 = 3(T2, V2) 8(T1, V1), in terms of the experimentally accessible quantities Up, or, and a