Computer visualization enables us to view the structures of fundamental equations -- particularly those for the fluid phases, where properties may be predicted from analytic state equations. Using a high-performance workstation and solid-modeling software we have produced images of various fundamental forms and their first derivatives. We have used the Peng-Robinson equation for the fluid properties of pure, binary, and ternary systems, and we have focused on the near critical regions to show how stability considerations underlie phase-splitting. Below we show the Peng-Robinson PVT function based on the properties of ethylene. Blue represents stable states (readily prepared), yellow represents metastable states (possible to prepare but usually short-lived), and red represents unstable states (impossible to prepare because of violation of the Second Law).
Three white isotherms cross the PVT surface -- one at a temperature above critical and two below. The subcritical isotherms show the minima and maxima marking the onset of instability (the yellow-red boundary), and the lower curve has those points marked with red and green crosses.