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In our previous reports, two types of the internal energy for polyethylene ( PE ) were derived, which were based on the thermodynamic relation thatand based on the partition function, thatwhereC Vis the isochoric heat capacity,is the thermal pressure coefficient andis the Boltzmann factor. In this work, a revised internal energy based on the  U TH , U rev.TH, was derived by introducing a zero Kelvin internal energy. A revised internal energy based on the  U PF,  U rev.PF, was also derived by introducing the zero Kelvin internal energy. The zero Kelvin internal energy,  U ( V, T  = 0 K), was determined based on a zero Kelvin isotherm, which was determined from the  P-V-T  equation of state derived in our previous work. In this report, the three-dimensional ( 3D ) plot,  3D  plot, with the three axes,  x = T U , y = P U , z = V Uexpressed by the  3D  ( T U,  P U,  V U) and the  3D  ( T U , V U . S U) at constant  U  in  PE  were determined by the  U rev.THwhere the processes were characterized by decreasing of the volume and the entropy with increasing of the pressure, while the temperature in the iso-internal process had a maximum with increasing the pressure, which were different from those determined by the  U THin our previous work. The revised internal energy  U rev.PFwas expressed by the summation of the terms of  T2  and  T4 , the Boltzmann factorsand the  U ( V , T  = 0 K) where the temperature dependence of the  T4  term and the Boltzmann factorswith  i  = 6 and 3 were dominant in the  U rev.PFat  V  = 1.04 cm 3 /g, while at  V  = 0.85 cm 3 /g in the range of high pressure, the  U ( V , T  = 0 K) became a controlling factor. In the case of the  Urev,PF  at constant temperature  T  = 320 K, the volume dependence of the  T2  term and the  U ( V , T  = 0 K) were dominant factors.

journal of macromolecular science, part b

Empirical Determination of the Internal Energy of Polyethylene Based on the Pressure-Volume-Temperature-Entropy Equation of State. II. The Revised Internal Energy Based on the Zero Kelvin Isotherm