Pressure equation

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

$p^{*}={\frac {\beta p}{\rho }}={\frac {pV}{Nk_{B}T}}=1-\beta {\frac {2}{3}}\pi \rho \int _{0}^{\infty }\left({\frac {{\rm {d}}\Phi (r)}{{\rm {d}}r}}~r\right)~{\rm {g}}(r)r^{3}~{\rm {d}}r$

where $\beta =1/k_{B}T$, $\Phi (r)$ is a central potential and ${\rm {g}}(r)$ is the pair distribution function.