Testing intermolecular potential functions using transport property data. Part 2.—Thermal conductivities of mixtures of helium with the hydrogen isotopes

Abstract

The thermal conductivities of mixtures of helium with three hydrogen isotopes are reported at 77.6 and 283.2 K. Each system exhibits a negative “excess” thermal conductivity, which, with the single exception of helium + hydrogen deuteride at 283.2 K, can be predicted from the Hirschfelder–Eucken equation in conjunction with a realistic helium–hydrogen potential function. As has been asserted previously, the minima in the plots of thermal conductivity against composition for helium + hydrogen deuteride at 283.2 K, and helium + hydrogen at both temperatures, are not the product of any special cross-relaxation effects: they are due simply to the closeness of the pure component conductivities.

Taken together with viscosities and second virial coefficients from the literature, the results are used to test four He/H₂ intermolecular potentials: (1) a Lennard–Jones (12 : 6) function derived from the Lorentz–Berthelot combining rules; (2) a Lennard–Jones (12 : 6) function derived from the Smith and Kong combining rules; (3) a function derived from molecular beam scattering studies; (4) an ab initio theoretical function. The theoretical potential (4) is the most successful in reproducing the bulk property measurements; the Lennard–Jones (12 : 6) Lorentz–Berthelot potential (1), the least. While there is little to choose between potentials (2) and (3) at 283.2 K, the molecular beam function is better at the lower temperature.