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.

摘要

基于PVT和1 atm的等压热容的实验数据，确定了聚乙烯（PE）的经验压力（P）-体积（V）-温度（T）-熵（S）状态方程（PVTS Eos ）对于PE。P、V、T和S的热力学量分为等温 ( T = const)、等压 ( P = const) 和等容 ( V = const)三个系综，每个系综都有一个固有的PVTS Eos。的热力学导数${\left(\frac{\partial 伏}{\partial 吨}\right)}_{磷}$ 和 ${\left(\frac{\partial 秒}{\partial 吨}\right)}_{磷}$在等压系综的等压PVTS Eos 中，${\left(\frac{\partial 磷}{\partial 吨}\right)}_{伏}\mathrm{ }$ 和 ${\left(\frac{\partial 秒}{\partial 吨}\right)}_{伏}$在等容集合中的等容PVTS Eos 和${\left(\frac{\partial 秒}{\partial 伏}\right)}_{吨}\mathrm{ }\mathit{和}\mathrm{ }{\left(\frac{\partial 秒}{\partial 磷}\right)}_{吨}$在等温集合中的等温PVTS Eos 中，已经在 293-343 K 的温度范围内和高达 1.0 GPa 的压力对 PE 进行了评估。本工作中的PVTS Eos 由麦克斯韦方程组检验，如${\left(\frac{\partial 秒}{\partial 伏}\right)}_{吨} =\mathrm{ }{\left(\frac{\partial 磷}{\partial 吨}\right)}_{伏},$ 和热力学关系表示为 ${\left(\frac{\partial C_{伏}}{\partial 伏}\right)}_{吨}$ = $吨{\left(\frac{{\partial }^2磷}{\partial {吨}^2}\right)}_{伏}$ 和 ${\left(\frac{\partial C_{磷}}{\partial 磷}\right)}_{吨}=-吨{\left(\frac{{\partial }^2伏}{\partial {吨}^2}\right)}_{磷}$. 讨论了PVTS Eos的热力学意义以及PVTS Eos 相对于PVT Eos的优势。