Coomber's relationship

Coomber's relationship can be used to describe how the internal pressure and dielectric constant of a non-polar liquid are related.

As ${\displaystyle p_{i}=\left({\frac {\partial E}{\partial V}}\right)_{T}\,}$, which defines the internal pressure of a liquid, it can be found that:

${\displaystyle p_{i}=n\cdot {I}\cdot {b(T)}{\frac {N^{2}\alpha ^{2}}{V^{n+1}}}\,}$

where ${\displaystyle N\,}$ is equal to the number of molecules

${\displaystyle I\,}$ is the ionization potential of the liquid

${\displaystyle b(T)\,}$ is a temperature dependent relation based on numerical constants of the pair summation from inter-particle geometry

${\displaystyle \alpha \,}$ is the polarizability

${\displaystyle V\,}$ is the volume of the liquid

where for most non-polar liquids ${\displaystyle n=1\,}$