2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/26307The energy route to the equation of state of hard-sphere fluids is ill-defined since the internal energy is just that of an ideal gas and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a square-shoulder interaction and taking the limit of vanishing shoulder width. The resulting hard-sphere equation of state coincides exactly with the one obtained through the virial route. Therefore, the energy and virial routes to the equation of state of hard-sphere fluids can be considered as equivalent.2 pagesStatistical MechanicsSoft Condensed MatterChemical Physicstext