An Investigation of the Nature of the Specific Heat in the Neighborhood of the Critical Point of 4He

Abstract

Recently, Bagatskii, Voronel’, and Gusak1 showed that the specific heat at constant volume of argon exhibited a logarithmic singularity at the critical temperature, T c , for measurements taken at the critical density. This singular behavior is in sharp contrast to the predictions of the accepted theory of phase transition of 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 for a classical gas of particles moving on a discrete lattice with a repulsive force preventing double occupancy of any site and a near neighbor attraction, the partition function can be mapped precisely onto that of an Ising model in an external magnetic field. The specific heat for this Ising model in zero field exhibits a logarithmic singularity at the Curie point. The critical point of the lattice gas corresponds to the Curie point of the corresponding Ising model. The measurements on argon then indicate that for a real gas the specific heat behaves in a similar manner to that of a lattice gas. We have investigated this point further by studying the specific heat at constant volume, C v , of 4He at densities close to the critical density.