Helmholtz Free Energy Equation of State for 3He–4He Mixtures at Temperatures Above 2.17 K

Changzhao Pan,Bo Gao,Gérard Rouillé,Laurent Pitre,Haiyang Zhang

doi:10.1063/5.0056087

Abstract

The work presents the first wide-range equation of state (EOS) for 3He–4He mixtures based on the reduced Helmholtz free energy multi-fluid approximation model. It covers the temperature range from 2.17 to 300 K and the pressure from the vapor pressure up to 3 MPa for any given mixture 3He mole fraction. In this model, the 4He and 3He reduced Helmholtz free energy equations and departure functions from the literature are employed and only five unknown mixture parameters are needed for each given departure function. The parameters and the best model for the concerned binary mixture were determined by the Levenberg–Marquardt optimization method. With the best developed model, the liquid, gaseous, and saturated thermophysical properties of the mixture can be mostly described with an accuracy better than 5%. Furthermore, a database for the thermophysical properties of 3He–4He mixtures is generated and provided for interpolation in temperature, pressure, and 3He mole fraction. The current EOS and database can be applied to the design and optimization of ultra-low temperature refrigerators.

Highlights

IntroductionSince the first liquefaction of 4He in 19081 and the discovery of the superfluidity of pure 3He in 1971,2 the fascination for understanding the properties of 3He–4He quantum fluids at ultra-low temperatures has not ended
The work presents the first wide-range equation of state (EOS) for 3He–4He mixtures based on the reduced Helmholtz free energy multi-fluid approximation model
The present work developed the first wide-range EOS for 3He–4He mixtures based on the Helmholtz free energy, which is reliable for temperatures from 2.17 K to room temperature and pressures from the vapor pressure to higher than 3 MPa

Summary

Introduction

Since the first liquefaction of 4He in 19081 and the discovery of the superfluidity of pure 3He in 1971,2 the fascination for understanding the properties of 3He–4He quantum fluids at ultra-low temperatures has not ended. The ideal Fermi gas model of 3He–4He solutions was first proposed by Landau and Pomeranchuk and improved by Bardeen et al., Radebaugh, and Kuerten et al.. The ideal Fermi gas model of 3He–4He solutions was first proposed by Landau and Pomeranchuk and improved by Bardeen et al., Radebaugh, and Kuerten et al.6 Those calculations were restricted to zero pressure, 3He mole fractions below 8%, and temperatures below 250 mK. Extending these efforts, Chaudhry et al. published the thermodynamic properties of liquid 3He–4He mixtures over the entire composition range between 0.15 and 1.5 K and up to 10 bars. There is still no unified EOS for 3He–4He mixtures covering a wide range of temperature, pressure, and composition

Objectives

Results

Conclusion