Empirical Determination of Pressure-Volume-Temperature-Entropy Equation of State of Polyethylene in Isothermal, Isobaric and Isochoric Ensembles

Abstract

An empirical pressure (P)-volume (V)-temperature (T)-entropy (S) equation of state (P-V-T-S Eos) of polyethylene (PE) has been determined based on the experimental data of P-V-T and isobaric heat capacity at 1 atm for PE. The thermodynamic quantities of P, V, T, and S fall into three ensembles which are an isothermal (T = const), isobaric (P = const), and isochoric (V = const) one and each ensemble has an intrinsic P-V-T-S Eos. Thermodynamic derivatives of ${\left(\frac{\partial V}{\partial T}\right)}_P$ and ${\left(\frac{\partial S}{\partial T}\right)}_P$ in the isobaric P-V-T-S Eos in the isobaric ensemble, the derivative of ${\left(\frac{\partial P}{\partial T}\right)}_V\mathrm{ }$ and ${\left(\frac{\partial S}{\partial T}\right)}_V$ in the isochoric P-V-T-S Eos in the isochoric ensemble and the ${\left(\frac{\partial S}{\partial V}\right)}_T\mathrm{ }\mathit{and}\mathrm{ }{\left(\frac{\partial S}{\partial P}\right)}_T$ in the isothermal P-V-T-S Eos in the isothermal ensemble have been evaluated over the temperature range of 293–343 K and pressure up to ∼1.0 GPa for PE. The P-V-T-S Eos in this work were checked by the Maxwell’s equations, such as ${\left(\frac{\partial S}{\partial V}\right)}_T =\mathrm{ }{\left(\frac{\partial P}{\partial T}\right)}_V,$ and thermodynamic relations expressed by ${\left(\frac{\partial C_V}{\partial V}\right)}_T$ = $T{\left(\frac{{\partial }^{2}P}{\partial T^2}\right)}_V$ and ${\left(\frac{\partial C_P}{\partial P}\right)}_T=-T{\left(\frac{{\partial }^{2}V}{\partial T^2}\right)}_P$ . The thermodynamic significance of the P-V-T-S Eos and the advantage of the P-V-T-S Eos over the P-V-T Eos are discussed.

Keywords:

• isobaric ensemble; isochoric ensemble; isothermal ensemble; Maxwell equation;
• polyethylene
• pressure-volume-temperature-entropy equation of state