Homework Help: Thermodynamics - Maxwell Relations

1. Jun 26, 2015

Lucas Mayr

1. The problem statement, all variables and given/known data

2. The attempt at a solution
I've tried using the relation Cp = T(dS/dT), isolating "T" for T = Cv2(dT/dS) and using the maxwell relations to reduce the derivatives, reaching, T = Cv2/D (dV/dS), but i don't think this is the right way to do solve this problem, i couldn't find a similar example on the chapter either.

2. Jun 26, 2015

TSny

$T$ is a state variable that can be thought of as a function of $v$ and $P$: $\;T(v,P)$.

Consider $dT$ which will be something times $dv$ plus something times $dP$. Can you express the coefficients of $dv$ and $dP$ in terms of $\alpha$ and $\kappa_T$?

3. Jun 28, 2015

Lucas Mayr

Ok, so i've tried looking at dT as a function of both P and v and reached dT = (∂T/∂P)v dP + (∂T/∂v)P dv
And after reducing the derivatives, dT = KT/α dP + 1/vα dv , and using the problem's KT and α.
dT = 1/D dv + Ev2/D dP
dT = 1/D dv + EPava2/(PbD) dP
Tb = Ta + (vb - va)/D + EPava2 Ln(Pb/Pa)/D

which is close but still different from the answer given on the question and i can't find a reason why, what did i miss?

Last edited: Jun 28, 2015
4. Jun 28, 2015

TSny

Check the sign of the first term on the right. Otherwise, that looks good.

Can you express $\ln(P_b/P_a)$ in terms of $v_a$ and $v_b$?

Last edited: Jun 28, 2015