The critical compressibility factor of fluids from the global isomorphism approach

Abstract

The relation between the critical compressibility factors Zc of the Lennard-Jones fluid and the Lattice Gas (Ising model) is derived within the global isomorphism approach. On this basis, we obtain the alternative form for the value of the critical compressibility factor which is different from widely used phenomenological Timmermans relation. The estimates for the critical pressure Pc and Zc of the Lennard-Jones fluid are obtained in case of two and three dimensions. The extension of the formalism is proposed to include the Pitzer's acentric factor into consideration.

Global Isomorphism Approach: Main Results and Perspectives

“…This also clarifies the nature of the difference between value of Z c for simple fluids and that of classical vdW EoS. The possibility to include the Pitzer's acentric factor into consideration was considered in [20,22]. The estimate for the value of critical pressure is: The value of the critical pressure of the 2D LJ fluid is: The estimates for critical density and temperature are consistent with known results for two dimensional LJ fluid [38].…”

“…noble gases Ar, Kr, Xe, have Z c ranged between 0:28 and 0:3. Using (3.23) and the results about the loci of the CP the relation between the critical compressibility factors of the LJ-fluid and the lattice gas can be derived [22]. With this (3.24) allows to derive the relation between the critical compressibility factors Z c of a fluid and the corresponding lattice model.…”

“…On this basis we obtain the relation between the entropies of these systems and show that this relation is consistent with the basic thermodynamic Clausius-Clapeyron relation. Also we present recent results on the critical compressibility factor values of molecular fluids [22] and discuss routes for further research. The structure of the paper is as follows.…”

“…According to (3.8) it is possible to calculate the state the LJ fluids based on the information about the lattice model [17,22,37] (see Fig. 3.2).…”

The van der Waals idea of pseudo associations and the critical compressibility factor

“…This problem is a subject of permanent interest. A number of recent papers are devoted to this problem (see [5,7,8] and references quoted). Considerations reported here show that the van der Waals conjecture on the role of pseudo associates is reasonable.…”