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Monte Carlo simulation for a gas of hard spheres in d-dimensional space: Equilibrium structure and state equations

In this work, we emphasize that it is possible using a personal computer to perform a MonteCarlo simulations in a reasonable computing time, and find the equilibrium structure of a hardsphere gas for a Euclidean multi-dimensional spaces. We study the properties of equilibrium and determine the equation of state of gas of hard spheres in Euclidean spaces from two to seven dimensions. The results show that the pressure is in agreement with different theoretical models based on virial expansion in spaces from two to five dimensions, also our results are extended for seven dimensions. As expected, it was found that the system of hard spheres loses its structure and the pressure of the system decreases when the dimension of the space increases.