Thermodynamic Properties of Liquid 3He-4He Mixtures Between 0.15 K and 1.8 K

Abstract

Thermodynamic property relations for liquid [3][4] He mixtures between temperatures of 0.15 K and 1.8 K are determined. The relations are valid over the entire concentration range. Thermodynamic properties are first calculated at saturated pressure (which is more or less equal to zero pressure) in the two-phase region, and then extended to the single-phase He-II (up to 1.8 K) and He-I (up to 1.5 K) regions. The calculations at saturated pressure are based on available specific heat data and previously determined sub-0.15 K properties. The property relations are then extended to higher pressures (up to 10 bar) between 0.15 K and 1.5 K, using available molar volume data. The results are largely in good agreement with some other 3 He-4 He mixture property data, though the scarcity of experimental data in large parts of the region of interest precludes a more thorough comparison. Applications of the derived properties to components of sub-Kelvin refrigerators, specifically He-II mixture heat exchangers and He-II mixture throttles, are also discussed.

THERMODYNAMIC PROPERTIES OF LIQUID [sup 3]He-[sup 4]He MIXTURES BETWEEN 0.15 K AND 1.5 K

“…As in the two-phase region, the Gibbs free energy can be used to get µ 4 , which can then be used with h to get h os in the He-II region. The calculated values are generally in good agreement [4,5] with other data (for example, Refs. 1,10,16,17), although the data available for comparison is admittedly sparse.…”

“…However, what data there are (molar volumes for 6%- 3 He mixtures at 1.2 K [20] and osmotic pressures for mixtures at low values of x and T [17]) are in good agreement [4,6] with the model results. Reviewing the model, it is expected that the quantities that depend strongly on v alone (and not its derivatives), such as g and h, should be reasonable everywhere, since the volume deviation term is quite small in comparison to the pure 3 He and 4 He molar volumes.…”

“…The specific heats obtained from the fit [4,5] can be integrated to get h and s in the single-phase region. As in the two-phase region, the Gibbs free energy can be used to get µ 4 , which can then be used with h to get h os in the He-II region.…”

“…There are several regions in the x-T-p space where there is no data -specifically, in the He-I region at high pressure (and low temperature), and at all concentrations at high pressure and high temperature. The lack of low-temperature He-I data is mitigated by estimating the molar volumes along the concentrated-phase surface using the thermodynamic relation [4,6]:…”

3He-3He Scattering in 3He-HeII Mixtures at Low Temperatures

“…A renewed interest has risen in the calculation of cross sections of 3 He-HeII mixtures, due to their importance in the cooling down to the mK-range (Chaudhry and Brisson, 2009). These cross sections provide useful information about the interactions experienced by the colliding atoms.…”