An explicit thermodynamic equation of state is proposed for the region near the line of liquid-vapor critical points in mixtures of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$. The equation (of the scaling form) embodies nonclassical exponents and uses chemical potentials or activities as independent variables in place of composition and volume. The properties of the mixtures are shown to result, in the main, from an interpolation between the critical properties of the pure components, in a suitable set of variables. Failure of experiments to reveal a weak divergence in the isothermal compressibility (at fixed composition), in contrast to previous phenomenological theories, is explained through the small size of the region near the critical line where one might expect to see the "true" asymptotic behavior.

• Received 4 April 1973

DOI:https://doi.org/10.1103/PhysRevA.8.2670