My professor did this in lecture, and I can't figure out his logic. Can someone fill in the gaps?(adsbygoogle = window.adsbygoogle || []).push({});

He went from:

[tex]

dS = \left( \frac{\partial S}{\partial P} \right)_T dP + \left( \frac{\partial S}{\partial T} \right)_P dT

[/tex]

(which I totally understand; it just follows from the fact that [itex]S[/itex] is an exact differential) to the following:

[tex]

\left( \frac{\partial S}{\partial T} \right)_V = \left( \frac{\partial S}{\partial P} \right)_T \left( \frac{\partial P}{\partial T}\right)_V + \left( \frac{\partial S}{\partial T} \right)_P

[/tex]

Where the heck does THAT come from? Anyone have any ideas?

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# Partial derivatives (Maxwell relations) in thermodynamics

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