The Thermodynamics of Liquid Helium on the Basis of the Two-Fluid Theory

Abstract

The thermodynamics of liquid helium is developed in the light of the two-fluid theory, which says that below the $\lambda$-point liquid helium consists of two "phases," one a superfluid phase and one a phase of normal fluid; and the thermodynamic consequences of assuming these phases to be in equilibrium with each other are worked out. It is pointed out that there is some evidence that these phases are separated not only in momentum space, as in London's theory based on the Bose-Einstein gas, but also in ordinary space. The specific heat just above the $\lambda$-point is considered on the assumption that in this region superfluid is beginning to appear in the form of small globules; it is estimated that these globules contain around 60 to 80 helium atoms. The thermodynamic properties below the $\lambda$-point are used to estimate the entropy of mixing of the two fluids in this region. The results suggest that in this region the superfluid forms a "partially condensed system," having possibly a fibroid structure. The nature of the second-order transition at the $\lambda$-point is considered in the light of this picture. A new relation is derived for the change of the $\lambda$-point with pressure, and the change with concentration of ${\mathrm{He}}^3$ is also considered. The thermodynamic results, though discussed in the light of the hypothesis that the two phases separate in ordinary space as well as momentum space, depend for the most part only on pure thermodynamics and the mere existence of two phases.