maxwell relation hard

Question

One Maxwell relation from fundamental thermodynamic potential U(S,V) is:

RankGuru · Accepted Answer

Maxwell relations are derived from the fact that thermodynamic potentials (like $U$) are state functions with exact differentials.
- From the first law: $dU = T \, dS - P \, dV$.
- Since $dU$ is an exact differential, the mixed partial derivatives must be equal:
$\left( \frac{\partial T}{\partial V} \right)_S = \left( \frac{\partial (-P)}{\partial S} \right)_V = -\left( \frac{\partial P}{\partial S} \right)_V$
This identifies a deep connection between the temperature-volume relationship and the pressure-entropy relationship.

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maxwell relation hard

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