Help With Thermodynamic Proof

  • Thread starter thekenw
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  • #1
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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
 

Answers and Replies

  • #2
Mapes
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Hi thekenw, welcome to PF. The partial derivative identity

[tex]\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[/tex]

might come in handy here.
 

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