[OrionZodiac]

Show (∂H/∂T)V = (1 - (αµ)/Kt)Cp. Where µ=(∂T/∂p)H , α=1/V(∂V/∂T)p , KT = - 1/V(∂V/∂p)T

I have no clue how to do this. Please help. I believe that you are supposed to use Euler Chain relations to show this.

[Hunt]

Here's an overview.

start from : dH = C_pdT + (dH/dP)_TdP

Then : (dH/dT)_V = C_p + (dP/dT)_V(dH/dP)_T

Use the chain rule for H,P,T and substitute for (dH/dP)_T to get :

(dH/dT)_V = C_p [ 1 - (dT/dP)_H(dP/dT)_V ]

Again use the chain rule for P,T,V to substitute (dP/dT)_V and get :

(dH/dT)_V = C_p [ 1 + (dT/dP)_H(dP/dV)_T(dV/dT)_V ]

Manipulate the differential part - by multiplying and dividing by V -  and plug in the factors given.