Empirical Determination of the Pressure-Volume-Temperature-Entropy Equation of State of Polyethylene in Isothermal, Isobaric and Isochoric Ensembles: IV. The Modified Intrinsic Equation of State for the Various Ensembles

The intrinsic equations of state for the isothermal, isobaric, isochoric and isoentropic ensembles based on the pressure-volume-temperature-entropy equations of state, P-V-T-S Eos, of polyethylene (PE) reported in our previous works were modified by taking into account a thermodynamic condition at a zero Kelvin limit, such as the entropy and heat capacity are zero at 0 K. The thermodynamic interrelations between the derivatives in the various ensembles were derived from the intrinsic equation of state in the various ensembles, in which a typical interrelation, ( partial differential CV partial differential V)T=T( partial differential 2P partial differential T2)V, was considered. The three dimensional plots (3D plot) indicating the interrelation, such as the 3D (TV,V,( partial differential CV partial differential V)T) and the 3D(TV,V,T( partial differential 2P partial differential T2)V) plots, were determined based on the modified intrinsic equation of state and compared to examine the accuracy of the intrinsic equations of state where CV is the isochoric heat capacity and the subscripts T and V mean the isothermal and isochoric ensembles, respectively.