Debye equation of state for fluid helium-3

Abstract

An equation of state for 3He using the Helmholtz potential function has been developed. The lower limit of the equation of 0.01 K is safely above the superfluid transition at 0.0026 K. The upper limit of 60 K is approximately the upper limit of available 3He property measurements. The new state equation form is based on Debye function which goes smoothly to zero in the limit of zero temperature and reduces to the ideal gas in the limit of zero density and/or very high temperature. The equation combines (a) necessary temperature-independent compressibility terms at the lowest temperatures, (b) terms describing the linear specific heat of a Fermi fluid below 1 K, (c) terms describing the phonon excitations which begin above about 1 K, and (d) terms which attempt to fit the conventional critical point thermodynamics at 3.3157 K and 114 604 Pa. State properties, e.g., p-V-T relations, specific heats, thermal expansion, sound velocity, etc., are determined from the Helmholtz energy by standard thermodynamics. Transport properties, e.g., thermal conductivity and viscosity, are not obtained in this work.