Abstract. This paper deals with a fundamental equation of state (FEOS) for substances. We have suggested a new method. It allows constructing FEOS that is based on the scaling theory of critical phenomena and describes thermodynamic properties related to liquid and gas phases of a substance in a wide range of the pressures and temperatures. In the framework of the methodological approach, we have provided: (i) a transition of FEOS in a virial equation of state in the low density region; (ii) a transition of FEOS in a Widom equation of state in the critical region. The method has been tested on the example of FEOS of R218. The area of applicability of FEOS is 0 < ρ/ρc < 3.2 in the density and 133 < T < 440 K in the temperature.We have compared FEOS with some equations of state and discussed the results.
IntroductionThe problem of constructing a fundamental equation of state (FEOS) has attracted attention of researchers considered a substance behavior in the critical region [1][2][3][4][5][6][7][8][9][10][11][12]. Especially this problem is investigated concerning some metals, which are characterized by the critical point locating at high temperatures and pressures [13][14][15][16][17]. We have analyzed main approaches those let us get successful results. Articles [1-3] represent a crossover equation of state written in a parametric form. There is a transition of the crossover equation to Scofield-Litster-Ho model (LM) [18] in an asymptotic vicinity of the critical point.Our analysis [19] has shown that the crossover equation [1][2][3][4][5] has an area of applicability: 0.4 ω 1.3 and 0.97 t 1.3, here ω = ρ/ρ c and t = T /T c . Thus, an equation of state [5] represents: