Equation of State Beyond the Radius of Convergence of the Virial Expansion

Abstract

The well-known problem of the virial expansion low-density limitation is considered within Mayer's cluster expansion method. The expression for the configuration integral and the corresponding equation of state are presented based on this approach but not limited by the convergence radius of the series for density and activity. When taking into account any number of irreducible integrals at the thermodynamic limit, this equation of state demonstrates the exact coincidence with the virial one inside the domain of its convergence but specifies the condensation process directly outside that domain. Thus, the assumption of some researchers that the condensation should appear in the domain where the proof of the virial expansion is limited may now be regarded as confirmed, exclusively using the classical Gibbs statistics.

Communication: Ab initio Joule–Thomson inversion data for argon

“…In principle (i.e., the limiting case m → ∞), the virial EOS can be expected to apply up to the liquid-vapor coexistence line. 28 However, since the attractive component of the argon interaction potential gives rise to B n (T) values of different signs (including zero) for varying n and given T, 22, 29 a term of order m + 1 does not necessarily improve over the mth-order EOS in all regimes. It is therefore difficult to speculate how many more terms would have to be included to cover a given P-T range.…”

Quark-gluon plasma phase transition using cluster expansion method

“…Ushcats [5] made EoS for the finite number of particles that showed significant differences in comparison with the virial 1 expansion at high densities. The Equation of state not limited by condition equation (1),…”

“…The volume is varied keeping temperature fixed and the corresponding 12 pressure is calculated. The same can be done by changing the density ρ, as done by Ushcats [5,6] using the Lennard-Jones 13 potential. 14 2.…”

“…So the phenomena of phase transition cannot be proved using classical statistical mechanics. Ushcats, using analytical 4 complex calculation, [5,6] shows that it is possible to neglect the forbidden region in Mayer's equation of state where the 5 equation of state cannot be defined. The equation as derived by Ushcats clearly demonstrates the process of condensation 6 at high density region.…”

High-density equation of state for a lattice gas

“…At higher density, this equation must include the virial coefficients of higher orders, but the computation of corresponding irreducible integrals involves great technical difficulties even for the simplest models of molecular interaction. Moreover, recent studies [4][5][6][7] have proved a strong theoretical limitation,…”