Equation of state and size distribution of particles in the Gibbs system

Within the framework of the Gibbs statistical theory, the issue of the size distribution of particles forming a statistical system and the moments of this distribution are considered. The size distribution of particles and the moments of this distribution are determined from probabilistic considerations. The particle size depends on the interactions in the system, the compressibility factor, the number of interacting particles, and the volume of the system. The relations for the average particle size are substituted into expressions for the intrinsic volume of particles in the equations of state written using excluded volume theory for various expressions for the exclusion factor. The equations of state obtained in this way can be considered as a refinement of the equation of state for dense systems, that is, as a transition to a higher level of description.