Thermodynamic consistency of the multi-scale Gibbs-Helmholtz constrained equation of state

In this article it is shown that mathematical representation of isothermal molecular internal energies of departure as a staircase function in pressure leads directly to thermodynamic consistency of the multi-scale GHC equation. Experimentally validated numerical results for density for pure components and mixtures, two- and three-phase equilibrium, comparisons with other cubic EOS, and geometric illustrations are presented to illustrate key ideas and to show that the GHC equation provides both accurate and thermodynamically consistent numerical results.