Low-Temperature Limiting Behavior of Gas Imperfections Due to Gas—Solid Interactions

Abstract

An asymptotic form for the low temperature limiting behavior of the gas imperfection due to gas—solid interaction is derived. When $$\ln {\mathrm{\{T}}^{-\frac{1}{2}}\lim {\displaystyle {lim}_{\text{P→0}}}\mathrm{[(NkT/P)-V]\}}$$ is plotted against 1/T it is shown that the plot must approach linearity at low T, and expressions for calculating the deviations of the plot from its limiting tangent at higher temperatures are presented. The slope of the limiting tangent depends only on the depth of the minimum in a plot of potential energy for gas—solid interaction against distance (and not on the shape of the potential energy curve). The intercept (at 1/T=0) of the limiting tangent depends principally on the surface area of the solid and the curvature of the potential energy plot at its minimum; neither of these quantities can be inferred from the intercept unless the other is known. The inference of potential energy forms from gas imperfection data is briefly discussed in the light of the asymptotic form developed.