Development of a general equation of state for real molecules in arbitrary regimes of temperature and pressure: I. The hard-core reference system

Abstract

A general equation of state for the hard-body reference system of real fluid has been developed from first principles, statistical mechanical arguments using metric differential geometry to describe the "available volume," V0, and its determining surface, S0, of a hard-body fluid. The rigorous, exact results of scaled particle theory of Reiss et al., which themselves obtain from statistical geometry, have been applied following the extension of Boublik et al. for hard bodies of non-spherical shape. The geometric description of the hard-body system can be used with the Boublik equation of state at low and modest densities. At high densities, this geometric description specifies the procedure to specify V0 and S0, notwithstanding that both become multiply-connected.