: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 $p\_i=\backslash left(\backslash frac\{\backslash partial\; E\}\{\backslash partial\; V\}\backslash right)\_T\backslash ,$, which defines the internal pressure of a liquid, it can be found that:

$$p\_i\; =\; n\; \backslash cdot\; I\; \backslash cdot\; b(T)\; \backslash frac\{N^2\backslash alpha^2\}\{V^\{n+1\}\}$$

where

• $N$ is equal to the number of molecules
• $I$ is the ionization potential of the liquid
• $b(T)$ is a temperature dependent relation based on numerical constants of the pair summation from inter-particle geometry
• $\backslash alpha$ is the polarizability
• $V$ is the volume of the liquid

where for most non-polar liquids $n=1$