To prove that (∂u/∂T)_P=c_P – Pβv where _P =>P constant;β=>co-eff. of vol exp. I proved it for ideal gases. Write d'Q=dh-vdP Now expand d'Q with 1st law and du(in 1st law) in terms of dP and dT.Since du is a total differential. Expand dh as total differential in dP and dT. Now I used the property of ideal gases: (∂u/∂v)_T=(∂h/∂P)_T=0 The rest is a bit manipulation. Can anyone say how to prove this in general? The book does not mention specifically that "use ideal behaviour" or so. There must be some way to get it. Please help.
