Pressure--density--temperature relations of 3He--4He mixtures near the liquid--vapor critical point

Measurements of the density ρ versus pressure P along isotherms for six He³-He⁴ solutions (X₃=0.960, 0.886, 0.800, 0.600, 0.400, and 0.200) near their liquid-vapor critical point are presented. For a given mole fraction X₃, it was found that the boiling and dew curves in the ρ-P plane could be represented by a relation similar to that for the coexistence curve of a pure fluid. Here the point at the extremity of the two-phase region, which we call the symmetry point with the parameters P_s, ρ_s, and T_s, takes the place of the critical point for a pure fluid. The dew curve is given by $({\rho }_s-\rho )\propto {(P_s-P)}^{{\beta }^{{}^{\prime }}}$ with β′=0.375±0.02, independent of X₃. The determination of the line of critical points in the P-T plane from the dew and boiling curves at various mole fractions is described. The pressure, density, and temperature for the critical and the symmetry points are presented and discussed. From the dew and boiling curves, the true coexistence curves were constructed in the ρ-P plane at constant T and in the ρ-T plane at constant P and could be described approximately by $({\rho }_L-{\rho }_G)\propto {(P_c-P)}^{\beta }T$ and $({\rho }_L-{\rho }_G)\propto {(T-T_c)}^{\beta }P$ with an average value for the various isotherms and isobars considered of β_T=0.42±0.06 and ${\beta }_P=0.39\pm 0.05$. Here ρ_L and ${\rho }_G$ are the densities along the coexistence curve on the liquid and the gas side, respectively. The measurements of the compressibility $k_{T,X}$ along the critical isochore in the one-phase region seem to exclude a "strong" divergence with (T-T_c), but do not extend close enough to T_c to either support or disprove the "weak" divergence as predicted by Griffiths and Wheeler. These measurements are compared with those of the normalized compressibility ${\left(\frac{\rho }{{\rho }_s}\right)}^2{k}_{T,X}$ along the dew and boiling curves. Comparisons are also made with the behavior of the compressibility for a pure fluid along the coexistence curve and above T_c. A brief addendum to the analysis for k_T in pure He³ is presented.