Regarding the Universality of Some Consequences of the van der Waals Equation in the Supercritical Domain

Abstract

We show that some of the thermodynamic regularities, following from the van der Waals (VDW) equation, are valid for the real substances and models described by completely different equations of state. These regularities relate to lines of ideal enthalpy, enthalpy minima, and isothermal compressibility maxima. The first one appears to be the straight line on the density-temperature plane, while for the two others there are universal relations, which are the same for various substances and models (argon and Lennard-Jones system as examples). The model systems were studied by Monte Carlo simulations (NVT MC), while experimental data were analyzed for the real substances. Our numerical calculations and the analysis of experimental data have shown that for the considered systems these curves are similar to the VDW ones.

Simple liquids’ quasiuniversality and the hard-sphere paradigm

“…These involve, e.g. the liquid-vapor coexistence region [115,116], the so-called Zeno line [117], the behavior of supercritical fluids [118], and the existence of generalized corresp onding-states equations [116,119].…”

The generalized scaling laws based on some deductions from the van der Waals equation

“…Hence, one can see that the condition of the enthalpy "ideality," the parameters of which are denoted by the subscript H, is achieved on the same straight line: (6) This line, by analogy with the Z-line, is called the H-line [17]. Its parameters for the WE exactly correlate with the Boyle parameter as T H = 2T B and n H = n B .…”

“…Let us consider an ideal enthalpy line H that also appears to be straight for the WE. The enthalpy of an ideal monoatomic gas is H id = 5NT/2, while the enthalpy for the WE is written in the form [17] (5)…”

“…However, the new scaling laws are not necessarily related to the WE, like, for example, the law of the rectilinear diameter of a binodal [3]. They may concern various characteristics of a substance at the critical point and along the phase transition lines [3][4][5][6][7][8][9] or can be related to the universal behavior of some geometric lines on the phase plane [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Some combinations are also possible [21].…”

Global Isomorphism Approach: Main Results and Perspectives

“…Additionally, it is known that the Zeno line is tangent to the extension of the binodal into the low temperature region so that the binodal appears to be inscribed into the triangle formed by the T-axis and the Zeno line [2,10]. Apfelbaum and Vorob'ev also revealed a number of correlations between the critical point parameters T c ; n c and those of Zeno line T B ; n B [11][12][13].…”