On Solutions ofHe3inHe4

Abstract

Elementary thermodynamics has been applied to recent data on the equilibrium concentrations of ${\mathrm{He}}^3$ in the liquid and vapor phases of ${\mathrm{He}}^4$. The differences between ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ as regards partial molar heat and entropy have been calculated and briefly discussed. Above the $\lambda$-point the energy of ${\mathrm{He}}^3$ in the liquid is greater than that of ${\mathrm{He}}^4$ by about 13 cal. ${\mathrm{mole}}^{-1\mathrm{}}$, an amount which can be accounted for theoretically by the difference in zero-point energy. But below the $\lambda$-point the energy and entropy of ${\mathrm{He}}^3$ are considerably lower than those of ${\mathrm{He}}^4$ in the same solution $\Delta {\overline{H}}_3-\Delta {\overline{H}}_4\approx -170\mathrm{}$ cal. ${\mathrm{mole}}^{-1\mathrm{}}$. The entropy decrease per ${\mathrm{He}}^3$ atom dissolved is equivalent to the entropy contents of about 50 ${\mathrm{He}}^4$ atoms in pure liquid helium II. An explanation of this strange result is suggested by Tisza's hypothesis that below the $\lambda$-point helium may be considered to be a mixture of a "normal" and a "superfluid" phase. The thermal data obtained lead to the conclusion that the $\lambda$-transition of pure ${\mathrm{He}}^4$ might become a transition of first order in dilute solutions of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$. On this basis, the effect of concentration of ${\mathrm{He}}^3$ on the $\lambda$-point has been considered.