Related Experiment Video
Updated: May 11, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Adequacy of the virial equation of state and cluster expansion
1National University of Shipbuilding Geroyev Stalingrada avenue 9, Mykolayiv 54025, Ukraine.
Abstract:
The limits for the accuracy of the virial expansion and the problem of its divergence have been investigated using the exact cluster expansion of the configuration integral. In the subcritical temperature regimes the virial equation of state is applicable up to the singularity point of the isothermal compressibility, i.e., to the possible beginning of the condensation process. At supercritical temperatures this equation should be applicable within the region where the cluster expansion is adequate. The problem of the virial series divergence has been found to be irrelevant to the actual behavior of the cluster expansion. Considering the Lennard-Jones fluid as well as the system of hard spheres, the inadequate behavior of the cluster expansion has been discovered in the high density regime. The major reason for this inadequacy should be the basic simplification of the cluster expansion: the integration of irreducible diagrams over the infinite limits.
Related Concept Videos
Van der Waals Equation
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
The Van der Waals Equation
Equation of State
Variables and Equations of State
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
Deviation from Ideal Behaviour

