Abstract
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, ( ∂ C V ∂ V ) T = T ( ∂ 2 P ∂ T 2 ) V , was considered. The three dimensional plots (3D plot) indicating the interrelation, such as the 3D ( T V , V , ( ∂ C V ∂ V ) T ) and the 3 D ( T V , V , T ( ∂ 2 P ∂ T 2 ) 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 C V is the isochoric heat capacity and the subscripts T and V mean the isothermal and isochoric ensembles, respectively.
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