Equation of state for He 4 , including a regular and a scalar part

• Published in: Low temperature physics (Woodbury, N.Y.) N.Y.), 2009-10, Vol.35 (10), p.741-747
• Main Authors: Bezverkhy, P. P., Martynets, V. G., Matizen, E. V.
• Format: Article
• Language: English
• ISSN: 1063-777X; 1090-6517
• DOI: 10.1063/1.3253391

A new unified equation of state is proposed which describes the P – ρ – T data of He 4 with an error with respect to pressure P of about ± 1 % in the interval of reduced densities from − 1 to + 1 and reduced temperatures from − 0.3 to + 0.3 . The unified equation P ( ρ , T ) , which for the first time is written in explicit functions of density ρ and temperature T , includes a regular equation of state for approximating the data outside the critical region, a nonparametric scaling equation of state that adequately represents the P – ρ – T data near the critical point of vaporization, and a crossover function that joins the two different equations of state. The crossover function that is proposed is a classical damping function for the density and temperature fluctuations characteristic of the critical region. The regular part of the unified equation consists of a universal seven-constant Kaplun–Meshalkin equation of state and a new, five-constant cubic equation. The unified equation of state obeys the condition that the first and second derivatives of the pressure with respect to the density vanish at the critical point; there are a binodal and a spinodal.