On the equivalence between the energy and virial routes to the equation   of state of hard-sphere fluids
  The 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. 
Andres Santos