The Intramolecular Field and the Dielectric Constant

Abstract

A statistical calculation of the average internal field in a dielectric is carried out. The following relation is obtained between the dielectric constant, $\epsilon$, and the molecular polarizability, $p_0$: $\frac{\epsilon -1\mathrm{}}{\epsilon +2\mathrm{}}V=\frac{4\pi N{p}_0}{3}\frac{1}{1-{\lambda }_{0\rho }}$ where $V$ is the molal volume, $\rho$ is the density and ${\lambda }_0=\frac{32{\pi }^2{N}^2{P_0}^2}{45B}\left(1+\frac{1}{3}\frac{A}{\mathrm{BRT}}\right).$ Here $A$ and $B$ are the constants of a van der Waal type equation of state. This expression becomes identical with the familiar Clausius-Mosotti relation in the limit of zero density. The formula is applied to dielectric constant measurements on several gases.