Universal Scaling Form of the Equation of State of a Critical Pure Fluid

Close to the liquid gas critical point, the linear treatment of the symmetrical one-component Φ4 model to observe the fluid-restricted universality of the subclass of pure fluids is reversed. The comparison with the fitting results obtained from the recent applications of the crossover description to CO2, CH4, C2H4, C2H6, R134a, SF6, and H2O confirms that the dimensionless characteristic two scale factors involved in this description are: (a) the critical compressibility factor and (b) the slope at the critical point of the reduced potential \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\frac{P}{T}\frac{{T_c }}{{P_c }}$$ \end{document} along the critical isochore. For the two-phase domain along the critical isochore, a precise formulation for the extension range of the fluid-restricted universality is given in terms of the reduced scaling size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$l^{* - } = \frac{{\xi ^ - }}{{a_c }}$$ \end{document} of the critical density fluctuations, expressed as a function of the dilated scaling field which measures the distance to the critical point below Tc. The explicit definition of the microscopic length scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$a_c = (\frac{{k_B T_c }}{{P_c }})^{\frac{1}{3}} $$ \end{document}, which characterizes the short-range of the microscopic interaction, gives a correlative estimation of the crossover domain when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\xi ^ - \sim a_c $$ \end{document}.