Empirical Determination of the Pressure-Volume-Temperature-Entropy Equation of State of Polyethylene in Isothermal, Isobaric and Isochoric Ensembles: III. Correlation Between the Three Dimensional Plane Plot and the Three Dimensional List Point Plot in the Various Ensembles

Abstract

The pressure-volume-temperature-entropy equations of state, P-V-T-S Eos, of polyethylene (PE) for its isothermal, isobaric, isochoric and isoentropic ensembles and the correlation between the P-V-T-S Eos in the various ensembles were reported in our previous reports. The three dimensional plane plot, 3D plane plot, for the various ensembles, such as the 3D (PV -V-SV ) isochoric plane plot, and the three dimensional list point plot, 3D list point plot, for the ensemble, such as the 3D (PT , VT , ST ) isothermal list point plot, were determined based on the P-V-T-S Eos of PE where the subscripts, T, P, V, and S meaning for the isothermal, isobaric, isochoric and isoentropic ensembles, respectively. In this paper a projection of the 3D list point plot on the 3D plane plot for an appropriate pair of the planes gave a new 3D plot where the list points in the 3D list point plot were found on the surface of the 3D plane plot.