Pressure-Density-Temperature Surface ofHe4near the Critical Point

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Abstract
The density ρ of He4 as a function of temperature and pressure has been measured along several different paths in the vicinity of the critical point. The results of the measurements are interpreted in terms of power-law descriptions near the critical point: For the coexistence curve, |ρ−ρc|∝(Tc−T)β; for the critical isotherm, |P−Pc|∝|ρ−ρc|δ; for the critical isobar, |T−Tc|∝|ρ−ρc|π; for the isothermal compressibility along the coexistence curve, (1ρ)(∂ρ∂P)T∝|T−Tc|−γ′T; and for the thermal expansion coefficient along the coexistence curve, (1ρ)(∂ρ∂T)P∝|P−Pc|−γ′P. The subscript c identifies the value of a quantity at the critical point. It is shown why simple power-law descriptions might be inadequate to describe all the behavior at the critical point and how this problem can be partly solved by the use of additional, non-singular factors. The values of the exponents are found to be β=0.354±0.010, 3.8≤δ≤4.1, 3.8≤π≤4.2, γ′T=1.1±0.1, and γ′P=1.5±0.2. Combined with Moldover's specific-heat measurements, which give for the exponent α′ of the expression CV∝|T−Tc|−α′ a value of α′=0.017±0.008, we can test various inequalities proposed for the exponents. For Rushbrooke's and Fisher's inequality, γ′T+2β+α′≥2, we obtain 2.0 for the maximum value of the left side; for Griffiths's inequality,