# Help With Thermodynamic Proof

1. Nov 9, 2009

### thekenw

Can Anyone Show Me the Steps to solving for these equalities; the proofs for them as it were:

Prove that, (dT/dP)s=TV((alpha)p/Cp)

and, Cp/Cv=Kt/Ks=gamma

and, Cp(Kt-Ks)= TV((alpha)p)^2

(alpha)p = coefficiant of thermal expansion, Kt= isothermal compressibility, Ks= adiabatic compressibility. (dx/dy)z means that z is held constant, like s in the first equation (dT/dP)s

Im really lost here and would really appreciate it if anyone could show me the steps to prove any or all three of the above equalities. Thank You

2. Nov 9, 2009

### Mapes

Hi thekenw, welcome to PF. The partial derivative identity

$$\left(\frac{\partial x}{\partial y}\right)_z=-\left(\frac{\partial y}{\partial z}\right)^{-1}_x \left(\frac{\partial z}{\partial x}\right)^{-1}_y$$

might come in handy here.