Statistical mechanics with molecular distance as a parameter

This article proposes a new statistical mechanics framework based on intermolecular distance parameters. The study first constructed statistical probability distribution functions for one-dimensional and three-dimensional spaces, namely W=A * exp (- β u - λ r) and W=A * r2exp (- β u - λ r), respectively. The theoretical results of the one-dimensional model have been validated through molecular dynamics simulations. On this basis, the state equation of the hard sphere model gas was derived using this three-dimensional statistical method, and the pressure formula P=RT/(V-b) was obtained. Furthermore, the pressure and internal energy of the rarefied three-dimensional square potential well gas were calculated. Research has shown that as gas density increases, its pressure and internal energy exhibit characteristics including density fractional powers. In addition, this method has been successfully applied to calculate the thermodynamic properties of low-temperature liquids near the triple point, and the specific heat at constant pressure of single atom liquids and diatomic liquids were obtained to be 5.5R and 6.5R, respectively.