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 ${\displaystyle n=1}$