Simple Veridical State Equations for Thermofluid Simulation

As outlined in previous and concurrent papers, thermofluid modeling, simulation, dynamics and control will always entail the equilibrium properties of at least one pure substance. Moreover, in many applications, two-phase and mixture properties may be required, say to represent boiling processes or else the perturbing effects of a noncondensible gas. Furthermore the general nature of process constraints may require at various times and locations all four classical thermodynamic potentials (i.e. energy, enthalpy, [Helmholtz] free energy, [Gibbs] free enthalpy). This need has always posed an analytical obstacle. Just over a century ago Johannes Diderik Van der Waals made a giant step for mankind by providing his elegant simple state equations yielding a continuous analytic path between the liquid and vapor states of matter. Unfortunately, while the Van der Waals model is qualitatively realistic, so to yield a model for understanding, it is quantitatively invalid, so failing to yield accurate veridical models for prediction. Surely continuing this quest for simple yet accurate state equations for working fluids thus poses a real and worthy challenge for us all. This paper suggests a very simple improvement to the Van der Waals model which can serve at least temporarily as a posada (Spanish for "way-station") enroute to better solutions.