mcdonkdik
Oct5-11, 06:22 AM
I have the answer to this question but I'm finding it hard making sense of it...
Q5) Dervive a relationship relating Cp-Cv to the isothermal compressibility (∂p/∂V)T and the coefficient of thermal expansion (∂V/∂T)p. Hint: consider the intensive entropy S as a function of T and V.
So I've started with S(T, V):
dS = (∂S/∂T)dT + (∂S/∂V)dV
Apparently we take the partial derivative wrt T while holding p(pressure) constant.. then we use a Maxwell relation to remove the partial derivative containing S. Then we use the triple product rule for something.
We end up with:
Cp - Cv = -T(∂p/∂V)T(∂V/∂T)2p
I'd really appreciate it if someone could give me a thorough explanation of how to do this.
Many thanks!
Q5) Dervive a relationship relating Cp-Cv to the isothermal compressibility (∂p/∂V)T and the coefficient of thermal expansion (∂V/∂T)p. Hint: consider the intensive entropy S as a function of T and V.
So I've started with S(T, V):
dS = (∂S/∂T)dT + (∂S/∂V)dV
Apparently we take the partial derivative wrt T while holding p(pressure) constant.. then we use a Maxwell relation to remove the partial derivative containing S. Then we use the triple product rule for something.
We end up with:
Cp - Cv = -T(∂p/∂V)T(∂V/∂T)2p
I'd really appreciate it if someone could give me a thorough explanation of how to do this.
Many thanks!