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

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

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

$\alpha\,$ is the polarizability

$V\,$ is the volume of the liquid

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

References

• Meeten, G.H., "Theoretical Basis for Coomber's Relationship", Nature Vol. 223, August 23, 1969