We describe a new form of a fluid state equation, based on a conceptual extrapolation from the Debye equation for the specific heat of solid materials. The Debye characteristic temperature, theta, which is nominally a constant for solids, becomes a function of the fluid density d. Further assuming theta = c1*d^(2/3)(1 + c2*d + c3*d^2 + ...) yields the conventional fluid virial equation in the high T and low d limit for a monatomic fluid. Additional terms must be added to describe (a) 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 has been useful in the state equation for 3He, continuous from 0.005 K to above room temperature. The mathematical form of conventional fluid state equations precludes their use below about 1/2 of the critical temperature, or 2 K for 3He, though they might be more accurate than the Debye equations above that temperature.
, Huang, Y.
, Radebaugh, R.
and Chen, G.
THE DEBYE FLUID STATE EQUATION, International Journal of Thermophysics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50420
(Accessed June 4, 2023)