申論題

13. (20 pts) A system of n mole ideal gas is characterized by (a) U = nCT where U is the internal energy, T the absolute temperature, and C a constant, (b) PV = nRT where R is the gas constant, (c) μ = RTI(n/V) + CT I(n/U) where μ is the chemical potential.

(b) (4 pts) Suppose that a slightly different gas system satisfies (a') U= nCT^δ but not (a), where the constant δ  ≠1. Show that the conditions (a')(b)(C) imply that the entropy change dS is not an exact differential.