Physics: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 [math]\displaystyle{ p_i=\left(\frac{\partial E}{\partial V}\right)_T\, }[/math], which defines the internal pressure of a liquid, it can be found that: [math]\displaystyle{ p_i = n \cdot I \cdot b(T) \frac{N^2\alpha^2}{V^{n+1}} }[/math] where

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

where for most non-polar liquids [math]\displaystyle{ n=1 }[/math]

References

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