Maxwell's relations
From SklogWiki
\[\left. \frac{\partial S}{\partial V} \right\vert_T = \left. \frac{\partial p}{\partial T} \right\vert_V \]
\[\left. \frac{\partial T}{\partial p} \right\vert_S = \left. \frac{\partial V}{\partial S} \right\vert_p \]
\[\left. \frac{\partial S}{\partial p} \right\vert_T = - \left. \frac{\partial V}{\partial T} \right\vert_p \]
\[\left. \frac{\partial T}{\partial V} \right\vert_S = - \left. \frac{\partial p}{\partial S} \right\vert_V \]
where \(S\) is the entropy, \(V\) is the volume, \(T\) is the temperature, \(p\) is the pressure
