  The internal energy of hard spheres (HS) is the same as that of an ideal gas,
so that the energy route to thermodynamics becomes useless. This problem can be
avoided by taking an interaction potential that reduces to the HS one in
certain limits. In this paper the square-shoulder (SS) potential characterized
by a hard-core diameter $\sigma'$, a soft-core diameter $\sigma>\sigma'$ and a
shoulder height $\epsilon$ is considered. The SS potential becomes the HS one
if (i) $\epsilon\to 0$, or (ii) $\epsilon\to\infty$, or (iii)
$\sigma'\to\sigma$ or (iv) $\sigma'\to 0$ and $\epsilon\to\infty$. The
energy-route equation of state for the HS fluid is obtained in terms of the
radial distribution function for the SS fluid by taking the limits (i) and
(ii). This equation of state is shown to exhibit, in general, an artificial
dependence on the diameter ratio $\sigma'/\sigma$. If furthermore the limit
$\sigma'/\sigma\to 1$ is taken, the resulting equation of state for HS
coincides with that obtained through the virial route. The necessary and
sufficient condition to get thermodynamic consistency between both routes for
arbitrary $\sigma'/\sigma$ is derived.
