Combined equation of liquid and gas states, including classical and scaling parts

Abstract

A new equation of state is proposed to describe the Р–ρ–Т data for Не 4 and SF 6 in the intervals of densities − 1 < Δ ρ < 1 (Δ ρ = ( ρ − ρ c)/ ρ c) and reduced temperatures − 0.3 < τ < 0.3 ( τ = ( T − T c)/ T c). A dimensionless combined equation of state is written in terms of the explicit functions of Δ ρ and τ, and includes a regular part for approximation of Р–ρ–Т data outside the critical region, and a nonparametric scaling equation of state which adequately describes the Р–ρ–Т data near the critical point of vaporization, and a crossover function combining smoothly these equations of state. A crossover function is proposed as a classical function, which damps the influence of density and temperature fluctuations as the distance from the critical point increases. Two different equations of state were taken as a regular part of the combined equation of state: 1) a new cubic equation with five system-dependent adjustable parameters three of which are related by equations in the critical point; 2) an equation with seven adjustable factors, three of which are also related to critical conditions to describe the data within the above limits, including the liquid states. Approximation of the most accurate data reported for Не 4 and SF 6 by the new equation indicates that the combined equation of state correctly describes the Р–ρ–Т data to within a pressure error of ± 0.5%. For the combined equation of state the ( ∂P/∂v) T = 0 and (∂ 2 P/∂v 2 ) T = 0 conditions are satisfied at the critical point and there are binodal and spinodal as in classical equations.