題組內容

4. 請証明
(提示: dE = TdS - PdV, dH = TdS + VdP, dA = -PdV - SdT, dG = VdP - SdT) 其中, E: Internal energy S: Entropy H: Enthalpy A: Helmholtz function G: Gibbs function R: Gas constant

(a) $C_p - C_v = (\frac{\partial V}{\partial T})_p \left[ P + (\frac{\partial E}{\partial V})_T \right]$。(5 分)