Pressure-Density-Temperature Relations ofHe3-He4Mixtures near the Liquid-Vapor Critical Point

Abstract

Measurements of the density $\ensuremath{\rho}$ versus pressure $P$ along isotherms for six ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ solutions (${X}_{3}=0.960, 0.886, 0.800, 0.600, 0.400, \mathrm{and} 0.200$) near their liquid-vapor critical point are presented. For a given mole fraction ${X}_{3}$, it was found that the boiling and dew curves in the $\ensuremath{\rho}\ensuremath{-}P$ 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 ${P}_{s}$, ${\ensuremath{\rho}}_{s}$, and ${T}_{s}$, takes the place of the critical point for a pure fluid. The dew curve is given by $({\ensuremath{\rho}}_{s}\ensuremath{-}\ensuremath{\rho}) \ensuremath{\propto}{({P}_{s}\ensuremath{-}P)}^{{\ensuremath{\beta}}^{\ensuremath{'}}}$ with ${\ensuremath{\beta}}^{\ensuremath{'}}=0.375\ifmmode\pm\else\textpm\fi{}0.02$, independent of ${X}_{3}$. The determination of the line of critical points in the $P\ensuremath{-}T$ 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 $\ensuremath{\rho}\ensuremath{-}P$ plane at constant $T$ and in the $\ensuremath{\rho}\ensuremath{-}T$ plane at constant $P$ and could be described approximately by $({\ensuremath{\rho}}_{L}\ensuremath{-}{\ensuremath{\rho}}_{G})\ensuremath{\propto}{({P}_{c}\ensuremath{-}P)}^{\ensuremath{\beta}}T$ and $({\ensuremath{\rho}}_{L}\ensuremath{-}{\ensuremath{\rho}}_{G})\ensuremath{\propto}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{\beta}}P$ with an average value for the various isotherms and isobars considered of ${\ensuremath{\beta}}_{T}=0.42\ifmmode\pm\else\textpm\fi{}0.06$ and ${\ensuremath{\beta}}_{P}=0.39\ifmmode\pm\else\textpm\fi{}0.05$. Here ${\ensuremath{\rho}}_{L}$ and ${\ensuremath{\rho}}_{G}$ 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 ($T\ensuremath{-}{T}_{c}$), 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 ${(\frac{\ensuremath{\rho}}{{\ensuremath{\rho}}_{s}})}^{2}{k}_{T,X}$ 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 ${\mathrm{He}}^{3}$ is presented.