Maxwell Relation

\[ \begin{array}{l}\text { 表 I 均匀封闭系的普遍热力学关系 }\\\begin{array}{|c|c|c|c|}\hline \text { 热力学势 } & \text { 热力学基本方程 } & \text { 热力学偏导数 } & \text { 麦克斯韦关系 }\\\hline U & \mathrm{d} U=T \mathrm{d} S-p \mathrm{d} V & T=\left(\frac{\partial U}{\partial S}\right)_{V} \quad p=-\left(\frac{\partial U}{\partial V}\right)_{S} & \left(\frac{\partial T}{\partial V}\right)_{S}=-\left(\frac{\partial p}{\partial S}\right)_{V} \\\hline H \equiv U+pV& \mathrm{d} H=T \mathrm{d} S+V \mathrm{d} p & T=\left(\frac{\partial H}{\partial S}\right)_{p} \quad V=\left(\frac{\partial H}{\partial p}\right)_{S} & \left(\frac{\partial T}{\partial p}\right)_{S}=\left(\frac{\partial V}{\partial S}\right)_{p} \\\hline F \equiv U-T S & \mathrm{d} F=-S \mathrm{d} T-p \mathrm{d} V & S=-\left(\frac{\partial F}{\partial T}\right)_{V} \quad p=-\left(\frac{\partial F}{\partial V}\right)_{T} & \left(\frac{\partial p}{\partial T}\right)_{V}=\left(\frac{\partial S}{\partial V}\right)_{T} \\\hline G \equiv H-T S & \mathrm{d} G=-S \mathrm{d} T+V \mathrm{d} p & S=-\left(\frac{\partial G}{\partial T}\right)_{p} \quad V=\left(\frac{\partial G}{\partial p}\right)_{T} & \left(\frac{\partial V}{\partial T}\right)_{p}=-\left(\frac{\partial S}{\partial p}\right)_{T} \\\hline\end{array}\end{array} \]