Compressibility equation

In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid. It reads:

${\displaystyle kT\left({\frac {\partial \rho }{\partial p}}\right)=1+\rho \int _{V}\mathrm {d} \mathbf {r} [g(r)-1]}$

where ${\displaystyle \rho }$ is the number density, g(r) is the radial distribution function and ${\displaystyle kT\left({\frac {\partial \rho }{\partial p}}\right)}$ is the isothermal compressibility.

...
Wikipedia