1. The following equation gives the analytic expression for entropy of an ideal gas, 5 S=KB = KN [In ( + ( 9) ") + 1/ 3/2 V (4mmU N3Nh 2 Where KB, and h are, respectively, Boltzmann's and Plank's constants (a) Invert this equation to obtain U(S,V,N),. Derive the expression for T, P, and. Verify the ideal gas law PV=NKB T. (b) Obtain F(T,V,N) and recompute S from F(T,V,N). (c) Obtain G(T,P,N) and compare it with un (d) Compute the heat capacity at constant volume Cv, the heat capacity at constant pressure Cp, isothermal compressibility kr, the coefficient of volumetric expansion B, and the isentropic compressibility ks. (e) Verify that, Cp- Cv = B V T/KT