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