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

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, ${\left(\frac{\partial C_V}{\partial V}\right)}_T=T{\left(\frac{{\partial }^{2}P}{\partial T^2}\right)}_V,$ was considered. The three dimensional plots (3D plot) indicating the interrelation, such as the 3D $(T_V,V,{\left(\frac{\partial C_V}{\partial V}\right)}_T)\mathrm{\text{and}} \mathrm{\text{the}} 3D(T_V,V,T{\left(\frac{{\partial }^{2}P}{\partial T^2}\right)}_V)$ 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.

Keywords:

• Intrinsic equation of state
• isobaric
• isochoric
• isoentropic
• isothermal
• thermodynamic derivatives

Disclosure statement

No potential conflict of interest was reported by the author.