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.

(a) (8 pts) Integrate the first and the second laws Tds = dU + PdV - μdn, together with the above conditions (a)(b)(c), to obtain the entropy formula S(U, V,n), which is a function of U,V and n (and T, P, μ are all eliminated).