Equation of state for He4, including a regular and a scalar part

Abstract

A new unified equation of state is proposed which describes the P–ρ–T data of He4 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.