  The thermodynamic stability of the hard-sphere gas has been examined, using
the formalism of scaled particle theory [SPT], and by applying explicitly the
conditions of stability required by both the second and third laws of
thermodynamics. The temperature and volume limits to the validity of SPT have
also been examined. It is demonstrated that scaled particle theory predicts
absolute limits to the stability of the fluid phase of the hard-sphere system,
at all temperatures within its range of validity. Because scaled particle
theory describes fluids equally well as dilute gases or dense liquids, the
limits set upon the system stability by SPT must represent limits for the
existence of the fluid phase and transition to the solid. The reduced density
at the stability limits determined by SPT is shown to agree exactly with those
of that estimated for the Alder-Wainwright, supercritical, high-density
gas-solid phase transition in a hard-sphere system, at a specific temperature,
and closely over a range of more than 1,000K. The temperature dependence of the
gas-solid phase stability limits has been examined over the range
0.01K-10,000K. It is further shown that SPT describes correctly the variation
of the entropy of a hard-core fluid at low temperatures, requiring its entropy
to vanish as T goes to zero by undergoing a gas-solid phase transition at
finite temperature and all pressures.
