Quantitative Comparison of the Approximate Dielectric Polarization Theories with an Exact One at Low Densities

The total dielectric polarization of a polar gas is expanded in inverse powers of the molar volume and the first term representing deviations from ideal gas behavior evaluated for an assembly of point polarizable dipoles, using the method developed by Buckingham and Pople. The approximate dielectric polarization equations of Debye, Onsager, Kirkwood, and Harris and Alder are expanded similarly and the corresponding coefficients of the term proportional to the first power of the density compared with the exact one. There is no term proportional to the density in the equations of Debye and of Onsager; also, to this order Kirkwood's and Harris' and Alder's theories are equivalent, both somewhat underestimating the total polarization. The use of Onsager's relationship for the dipole moment of a molecule is shown to be inappropriate for an imperfect gas.