Empirical Determination of the Pressure-Volume-Temperature-Entropy Equation of State of Polyethylene in Isothermal, Isobaric and Isochoric Ensembles: V. The Internal Energy, Enthalpy, Helmholtz Free Energy and Gibbs Free Energy for the Various Ensembles

The internal energy, U, enthalpy, H, Helmholtz free energy, A, and Gibbs free energy, G, for the isothermal, isobaric, isochoric and isoentropic ensembles for polyethylene (PE) have been determined over a range of temperature, including the zero Kelvin, using the intrinsic equation of states based on the pressure-volume-temperature-entropy equations of state, P-V-T-S Eos determined in our previous reports. Each energy function was separated into its two parts; the energy = (the energy- the energy (0 K)) and the energy (0 K) where the energy (0 K) is the energy at the zero Kelvin. The energy (0 K) was much larger than the former, (the energy- the energy (0 K)), for the internal energy in the isobaric ensemble, the enthalpy in the isothermal, isochoric and isoentropic ensembles and the Gibbs free energy in the isothermal, isochoric and isoentropic ensembles, while the energy (0 K) was negligibly small for the internal energy in the isothermal ensemble and the Helmholtz free energy in the isothermal and isoentropic ensembles. The energy derivatives intrinsic to each ensemble, such as (∂U∂T)P,(∂H∂T)V,(∂A∂V)S,(∂G∂P)S, were evaluated where the subscripts, P, V, S, mean the isobaric, the isochoric and the isoentropic ensembles, respectively.