Equation of state of a³He-⁴He mixture near its liquid-vapor critical point

Abstract

Measurements of the pressure coefficient (∂P/∂T)_ρ,x are reported for a³He-⁴He mixture with a mole fractionX=0.805 of³He in the neighborhood of the liquid-vapor critical point. These include data on 16 isochores taken over the density interval−0.5≤Δρ≤0.5 and over the temperature range−0.1 ≤t≤0.1, where Δρ=(ρ−ρ _c )/ρ _c andt=(T-T _c )/T _c ,with ρ _c andT _c ,respectively, the critical density and temperature of the mixture. From the discontinuity of (∂P/∂T)_ρ,x at the boundary between the two-phase and the one-phase regions we determine the dew-bubble curve nearT _c with better precision than was done in recentPVT experiments. From the extrapolation of data not approachingT _c closer than1 mK, (∂P/∂T)_ρ,x along the critical isochore appears to be discontinuous atT _c ,while for the isochore ρ/ρ _c ≃0.92, (∂P/∂T)_ρ,x is continuous across the dew curve. It is found that this latter isochore cuts the dew curve at its highest temperature. These observations are discussed in terms of general thermodynamic arguments and theoretical predictions of the asymptotic behavior. We calculate (∂P/∂T)_ρ,x from the scaling equation of state proposed by Leung and Griffiths for³He-⁴He mixtures, using their numerical parameters. In spite of some systematic deviations, especially in the two-phase region, there is in general good agreement with experimental results. In particular, the shape of the measured dew-bubble curve and the apparent discontinuity of (∂P/∂T)_ρ,x along the critical isochore show excellent agreement with theory.