Probability distribution of hard-disk and hard-sphere gases over finite subvolumes

The probability distribution of a gas consisting of No hard disks (hard spheres) over finite subvolumes is modeled by the hypergeometric distribution. The effects of mutual exclusion between particles are incorporated by a density dependent effective volume per particle. This effective volume is related to the fluctuation in particle number. The behavior of the computed effective volume is compared with analytical expressions calculated from well-known equations of state. Corrections for this effective volume due to the considered finite-size effects are proposed.