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