Equations of state of a system of hard spheres in a reduced form

The equations of state are investigated for a system of hard spheres in the general quantum-mechanical case. The equations are presented in the reduced form. A comparison is made between the classical approximation, the semiclassical approximation with allowance for the first correction, and the cell-cluster expansion with allowance for three-particle clusters, inclusive. The cell-cluster expansion, as calculations show, is more efficient than the semiclassical approximation at high densities. It is shown that the density dependence in the caloric equation of state is significant, which is also preserved at high temperatures. In the general case, Joule's law does not hold for a system of hard spheres.