THE CANONICAL EQUATION OF STATE OF TECHNICAL GASES FOR THE OPTIMIZING PROGRAMS

Abstract

On the base of the analysis of the real gas surface of state it has been shown that thermodynamic surface can be formed through the movement of rectilinear in coordinates Т,r and DF,r (T — temperature, r — density, DF — configuration part of the Helmgolts free energy) beam around the point with coordinates Т=0 and r = r₀ . The linear surface coincides with the surface of state within the interval of densities up to r =1,5 r_cr (r_cr — critical density). The following equation of state gases for the interval of densities 0–1,5 rcr in canonical form — Helmgolts free energy depending on the temperature and density is proposed with the use of the virial equation. Equation can be presented in the form: DF / r = RT₀B, where Т₀ — parametric temperature equals , r₀ — density of point with coordinates Т = 0 and r=r₀ , В — second virial coefficient related to parametric temperature Т₀ . It has been shown that equation of state can be represented as Van der Waals equation . As compared to the classical equation of state of the Van der Waals the value r₀ = 1/b for DF is twice as much than for the compressibility coefficient Z = PV / RT . Hence method for obtaining of equation of state in canonical form: on the base of P, v, T-data are determined В(Т₀) and r₀ , and then r0 redoubles. Results of comparison, of experimental and calculated values DF and Z for model system Lennard-Jones (12–6) have been reported. It has been shown that equation of state describes «experimental»data with the experiment error.