The pressure-volume-temperature relationship is the most familiar of the equations of state (EOS) and is obtained by partial differentiation of the AVT function. It is the only model in this collection that contains measurable variables only and is thus the physical entry point for the development of fundamental equations. Since the Peng-Robinson EOS provides much of the property basis for the entire collection, this drawing is simply a plot of the P-R equation:

where b is calculated from critical properties and a is determined both from critical data and also from an empirically determined function of temperature and the Pitzer acentric factor .

All equation-of-state forms have a geometrical shape referred to as a "cusp catastrophe.” The green and red crosses are located differently on the EOS drawings – they appear on the red-yellow boundaries (as minimum or maximum points) that denote the stability limits. The red cross always represents the higher-density liquid state.

Iowa State University