证明纯想气体,(∂T/∂p)s=v/Cp

Question

证明纯想气体,(∂T/∂p)s=v/Cp

Answer 1

有热力学基本方程有：dU = TdS-PdV,H = U+PV
因此,dH = TdS+VdP.
然后,V = (∂H/∂P)s = [(∂H/∂T) * (∂T/∂P)]s ,
根据定义有 Cp = (∂H/∂T) ,
所以,V = Cp * (∂T/∂P)s
即 (∂T/∂p)s = V/Cp