Debye Fluid State Equation

A new form of a fluid state equation, based on a conceptual extrapolation from the Debye equation for the specific heat of solid materials is described. The Debye characteristic temperature, Θ, which is nominally a constant for solids, becomes a function of the fluid density ρ. Further assuming \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta = c_{1}\rho^{2/3}(1 + c_{2} \rho + c_{3} \rho ^{2} + {\cdots})}$$\end{document} yields the conventional fluid virial equation in the high-T and low-ρ limits for a monatomic fluid. Additional terms must be added to describe (a) the compressibility of the dense subcooled fluid and (b) properties in the near-critical range. Discussion of the Gruneisen parameter and other factors is included. This Debye fluid theory was used as a state equation for 3He, continuous from 0.005 K to above room temperature.