Expression for the internal energy for a real gas that obeys Van der Waals equation of state is given by the following equation:

$U=(\frac{3}{2})nRT-\frac{n^{2}a}{V},$

where $R$ is the gas constant, $8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}\text{K}},T$ is the temperature, $n$ is the number of moles, $a$ is the constant in the Van der Waals equation of state for the corresponding gas, and $V$ is the volume.

Prove that $dU$ is an exact differential.