Equation of state of³He near its liquid-vapor critical point

Abstract

We report high-resolution measurements of the pressure coefficient (∂P/∂T)_ρ for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals−0.1≤t≤+0.1 and−0.2≤Δρ≤+0.2, wheret=(T−T _c )/T _c and Δρ=(ρ−ρ _c )/ρ _c . We have determined the discontinuity Δ(∂P/∂T)_ρ of (∂P/∂T)ρ between the one-phase and the two-phase regions along the coexistence curve as a function of Δρ. The asymptotic behavior of (1/ρ) Δ(∂P/∂T)ρ versus Δρ near the critical point gives a power law with an exponent (γ+β−1)β⁻¹=1.39±0.02 for0.01≦Δρ≤0.2 or−1×10 ⁻²≤t≤−10 ⁻⁶, from which we deduce γ=1.14±0.01, using β=0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity Δ(∂P/∂T)_ρ with a correction-to-scaling term gives γ=1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (∂μ/∂T)ρ _c as a function oft. In the two-phase region the slope (∂²μ/∂T ²)_ρc is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores Δρ≠0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of μ−μ (ρ _c ,t) as a function of Δγ on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the range‖t‖≤0.1. A fit of our data to the “linear model” approximation is obtained for‖Δρ‖≤0.10 andt≤0.02, giving a value of γ=1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (∂P/∂T)_ρ data analysis for⁴He by Kierstead. A power law plot of (1/ρ) Δ∂P/∂T)_ρ versus Δρ belowT _c leads to γ=1.13±0.10. An analysis with a correction-to-scaling term gives γ=1.06±0.02. In contrast to³He, the slopes (∂²μ/∂T ²)_ρc above and belowT _c are only marginally different.