- #1
kntsy
- 82
- 0
Hi, how can i derive this fundamental identity "without using entropy"?
[tex]\left(\frac {\partial U}{\partial V}\right)_T = T\left(\frac {\partial P}{\partial T}\right)_V - P[/tex]
I believe the above equation is purely thermal and has nothing to do with entropy and statistical mechanics but unfortunately the below identity is the key to this derivation:
[tex]\left(\frac {\partial P}{\partial T}\right)_V = \left(\frac {\partial S}{\partial V}\right)_T[/tex]
of course:
[tex]dU=TdS-PdV[/tex]
[tex]\left(\frac {\partial U}{\partial V}\right)_T = T\left(\frac {\partial P}{\partial T}\right)_V - P[/tex]
I believe the above equation is purely thermal and has nothing to do with entropy and statistical mechanics but unfortunately the below identity is the key to this derivation:
[tex]\left(\frac {\partial P}{\partial T}\right)_V = \left(\frac {\partial S}{\partial V}\right)_T[/tex]
of course:
[tex]dU=TdS-PdV[/tex]
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