(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove

(∂V/∂T)_s/(∂V/∂T)_p = 1/1-(gamma) (gamma = Cp/Cv)

2. Relevant equations

(∂V/∂T)_s = -C_v (kappa)/(beta)T (where beta = 1/V(∂V/∂T)_p, kappa = -1/V(∂V/∂P)_T

C_v= - T(∂P/∂T)_v(∂V/∂T)_s

3. The attempt at a solution

As part(a) ask me to find C_v, I do it similar for C_p

(∂S/∂T)_p=1/T(∂U/∂T)_p

C_p=T(∂S/∂T)_p=-T(∂P/∂T)_s/(∂P/∂S)_T=-T(∂P/∂T)_s(∂V/∂T)_p

(∂V/∂T)_s/(∂V/∂T)_p = -C_v/T(∂P/∂T)_v /C_p/-T(∂P/∂T)_s=C_v(∂P/∂T)_s/ C _p(∂P/∂T)_v

Then, i cannot figure out the remaining calculation out....

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# Homework Help: Proving Thermodynamics equations using partial derivatives

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