Pressure equation

The pressure equation, also known as the virial equation is given by

$P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r$

where $\Phi(r)$ is a central potential and ${\rm g}(r)$ is the pair distribution function.