Behringer, RP; Doiron, T; Meyer, H, *Equation of state of*^{3}He near its liquid-vapor critical point,
Journal of Low Temperature Physics, vol. 24 no. 3-4
(1976),
pp. 315-344 [doi] .
**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, where t=(T-Tc)/Tcand Δρ=(ρ-ρc)/ρc. 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 for 0.01≦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 from statistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (∂μ/∂T)ρc as a function of t. In the two-phase region the slope (∂2μ/∂T2)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 (ρc, 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 {norm of matrix}t{norm of matrix}≤0.1. A fit of our data to the "linear model" approximation is obtained for {norm of matrix}Δρ{norm of matrix}≤0.10 and t≤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 below Tcleads 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/∂T2)ρc above and below Tcare only marginally different. © 1976 Plenum Publishing Corporation.*