Specific Heat of He³ and He⁴ in the Neighborhood of their Critical Points

Abstract

Recently Bagatskil, Voronel’, and Gusak¹ showed that the specific heat at constant volume of argon exhibited what appears to be a logarithmic singularity at the critical temperature (T_c) for measurements taken at a density near the critical density. This singular behavior is in sharp contrast to the predictions of the traditional view of this phase transition by Landau and Lifshitz.² However, the behavior is precisely that to be expected for the so- called “lattice-gas” model for the liquid-gas transition. Lee and Yang³ have shown that the partition function of a classical gas of particles moving on a discrete lattice with a repulsive force preventing double occupancy of any site and a nearest-neighbor attraction can be mapped precisely onto the partition function of an Ising model of a spin system in an external magnetic field. The specific heat for this Ising model in zero field exhibits a logarithmic singularity at the Curie point. The specific heat for the corresponding lattice gas on the critical isochore exhibits a logarithmic singularity at the critical point. The measurements on argon then indicate that for a real gas the specific heat behaves in a manner similar to that of a lattice gas. We have investigated this point further by studying the specific heat at constant volume (C_v) of both He³ and He⁴ at densities close to the critical density. We have done this for two main reasons. Firstly, to see whether the behavior observed for argon is also observed for helium, for which quantum effects should be important, and secondly, to investigate the detailed nature of the sin gularity in the pressure-density plane, not only on the critical isochore but also in its immediate neighborhood. Yang and Yang⁴ have conjectured that the quantum effects would reduce the magnitude of the singular contribution to the specific heat in helium. Our results confirm this view.