Hi, how can i derive this fundamental identity "without using entropy"?(adsbygoogle = window.adsbygoogle || []).push({});

[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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# University thermodynamics fundamental equation/identity derivation.

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