Density Equation for Saturated 3He

Abstract

A density equation for saturated vapor and liquid 3 He is presented based on 205 experimental measurements for temperatures greater than 0.2 K collected after a careful survey of the literature. The average deviation of the densities predicted by the equation against the experimental values is 0.39%. There are only 16 points with deviations larger than 1%. This equation is valid for both liquid and vapor densities of 3 He up to the critical temperature of 3.3157 K. The form of the equation satisfies known scaling laws approaching the critical point, with β = 0.3653. In the low-density limit, the vapor curve of our equation matches smoothly to the published virial equation density at a temperature of 1.62 K and at the saturation pressure. The rectilinear density deviates from the critical density by less than 0.28% down to 0.48 K.

The history of the rectilinear diameter law

“…Although the rectilinear diameter rule has recently satisfactorily verified for some specific substances, 67 it is generally nowadays considered incorrect for the full group of elements and compounds, and non-analytic contributions determine the behaviour when approaching the critical point. 68 The relative importance of the various non-analytic terms determining the asymptotic behaviour is difficult to assess and remains an actual topic of experimental and theoretical investigations.…”

Study on Surface Tension of Fluid Helium Three

“…However, the big difference between 3 He and 4 He quantum statistics should not be neglected. 4 He obeys Bose-Einstein (BE) statistics and transitions to superfluid below 2.172 K through BE condensation. But 3 He obeys Fermi-Dirac statistics and becomes superfluid only below 2.6 mK through a condensation similar to the BCS mechanism of a superconductor.…”

“…The temperature dependence of the surface tension should be quite different between 3 He and 4 He, since the ripplons on the latter might be damped, at least at very low temperatures, because of the substance's large bulk viscosity. The internal excitations in 3 He should also be different from 4 He. An experiment by Guo et al [14] on 3 He floating on bulk liquid 4 He has shown a quadratic temperature dependence of the surface tension.…”

“…[2], the densities for the liquid and vapor (ρ l and ρ g ) are from Ref. [4] (in kg · m −3 ), and the temperature (in K) is denoted by T . Based on the data analysis and filter of the measurements in Table 1, high weight was given to the high accuracy data from Iino et al [10,11].…”

“…theoretical studies have been carried out internationally on the properties of this special fluid, especially at temperatures lower than 1 K. However, no compiled reference data for 3 He has been announced in a wide range of temperature and pressure, until the recent work by Chen and Huang [1][2][3][4][5] on raw data mining and equation-of-state development. Recently, the transport properties of 3 He are being studied, and encouraging progress has been achieved for thermal conductivity, viscosity, and surface tension.…”