Answer to Question #215601 in Physical Chemistry for RAJA

Question

Prove

(

∂T

∂P)

v

=

γ

γ − 1

[μJT +

v

Cp

]

Answer 1

dU = T dS − P dV

dH = T dS + V dP

dA = −P dV − S dT

dG = V dP − S dT

∂U∂S V= T

and

∂U∂V S = −P

∂G∂T P

= −S

and

∂G∂P T= V

Furthermore,

α (T, P) ≡1V∂V∂T P

and

κ (T, P) ≡ −1V∂V∂P T

(∂T∂P)v=γγ − 1[μJT +vCp]

hence proven