Energy equation

The energy equation is given by

${\frac {U^{\rm {ex}}}{N}}={\frac {\rho }{2}}\int _{0}^{\infty }\Phi (r)~{\rm {g}}(r)~4\pi r^{2}~{\rm {d}}r$

where $\Phi (r)$ is a central potential, $U^{\rm {ex}}$ is the excess internal energy per particle, and ${\rm {g}}(r)$ is the pair distribution function.