Maxwell Relationship

Maxwell关系式是四个热力学势的二阶导数的等式

$$\begin{array}{c}\begin{array}{rl}{\left(\frac{\partial T}{\partial V}\right)}_S& =-{\left(\frac{\partial p}{\partial S}\right)}_V\end{array}=\frac{{\partial }^{2}U}{\partial S\partial V}\\ {\left(\frac{\partial T}{\partial p}\right)}_S=+{\left(\frac{\partial V}{\partial S}\right)}_p=\frac{{\partial }^{2}H}{\partial S\partial p}\\ {\left(\frac{\partial S}{\partial V}\right)}_T=+{\left(\frac{\partial p}{\partial T}\right)}_V=-\frac{{\partial }^{2}A}{\partial T\partial V}\\ -{\left(\frac{\partial S}{\partial p}\right)}_T={\left(\frac{\partial V}{\partial T}\right)}_p=\frac{{\partial }^{2}G}{\partial T\partial p}\end{array}$$

其中$U$为内能, $H$为焓, $A$为Helmholtz自由能, $G$为Gibbs自由能