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In the framework of Gibbs statistical theory, the issue of the distributionof particle sizes forming the statistical system and the moments of thisdistribution are considered. This task is relevant for a wide variety ofapplications. The distribution for particle sizes and moments of this quantityare determined from probabilistic considerations. Particle size depends oninteractions in the system, on the compressibility factor, on the number ofinteracting particles, on the volume of the system. The expressions for theintrinsic volume of particles are substituted into the equations of statewritten using the theory of excluded volume for various expressions of theexclusion factor. The equations of state thus obtained can be considered as arefinement of the equation of state, a transition to a higher level ofdescription.

Equation of state and distribution of particle sizes in Gibbs system