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

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.