Internal energy

The internal energy is given by

$U=-T^{2}\left.{\frac {\partial (A/T)}{\partial T}}\right\vert _{N,V}=k_{B}T^{2}\left.{\frac {\partial \log Z(T)}{\partial T}}\right\vert _{N,V}$

where $A$ is the Helmholtz energy function and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Z} is the partition function.