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

A new variant of a scaling hypothesis and a fundamental equation of state based on it

“…Thirdly, we have revealed that Landau's function, φ 0 (ρ, T ) is used as a crossover function in [7]. The function can cause the generation remarkable errors connected with properties (p, F , s, i, w, C v , C p ), and we have shown this in our calculations.…”

“…The 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].…”

“…The authors [7] proposed to solve the problem of FEOS constructing with the use of a combined equation of state in an empirical form: • a local virial equation of state p r (ρ, T ) related to a gas phase,…”

“…The authors of [7] used φ 0 (ρ, T ) in the form of Landau's function [21]. FEOS (1) considered in [7,8] has a number of disadvantages.…”

“…Secondly, there are non-trivial formulas which significantly complicate calculations of thermodynamic properties (the Helmholtz free energy F , the entropy s, the enthalpy i, the sound speed w, the isochoric heat capacity C v , the isobaric heat capacity C p ) on the base of FEOS (1) [7,8]. These mathematical difficulties are connected with some differential binomials included in the formulas of properties (p, F , s, i, w, C v , C p ).…”