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406 C.M. COLINA et al. There have been a number of potential models proposed for CO2, obtained from correlation of VLE properties [2,7 – 9], liquid properties [10], crystal structures and lattice properties [11], or from combinations of experimental data for non-bonded interactions and ab initio electrostatic potentials for charge distributions [12]. Several of these models have been used to study mixture properties [13 – 16], structural properties [17] and the pure component vapor–solid coexistence curve [18]. The average of a property X in this ensemble can be expressed as: VLE and the authors showed that good predictions for densities and enthalpies could be obtained using this potential in a temperature range between 230 and 570 K, and for pressures up to 400 MPa. Although the authors calculated thermodynamic derivatives such as the isothermal compressibility during the optimization process of the potential model, they did not present a comparison with experimental values. In an earlier publication [19], we used the 2CLJQ model of Mo ̈ller and Fischer [2] to calculate the Joule – Thomson inversion curve (JTIC) of CO2. The JTIC was calculated from different thermodynamic properties (thermal expansivity and compressibility factor) and showed good agreement with experi- mental values. In this work, we present a compre- hensive comparison between calculated values of several thermodynamic properties for CO2 against experimental values as well as against results from the 2CLJQ EOS. We present simulation results for the isobaric heat capacity, volume expansivity, isother- mal compressibility, and combinations of these quantities such as the speed of sound and the Joule–Thomson coefficient. THERMODYNAMIC PROPERTIES IN THE ISOBARIC–ISOTHERMAL ENSEMBLE The isobaric – isothermal ensemble partition func- tion, D, of a molecular system with N particles at pressure P and temperature T is given in Ref. [20]: DðN; P; TÞ 1⁄4 XXexpð2bUÞ expð2bPVÞ VðN; V; UÞ ð1Þ UV where V is the microcanonical partition function, b 1⁄4 1=ðkBTÞ; kB is Boltzmann’s constant, V is the system volume and U is the system energy. P Cconf 1⁄4 1⁄4 ›kUl ›kVl þP 2NkB P PPXVðN; V; UÞ exp1⁄22bðU þ PVÞ UV UV 1⁄4 PPexp1⁄22bðU þ PVÞ ð2Þ kXl 1⁄4 Temperature and pressure derivatives of X in the isobaric – isothermal ensemble can be expressed in terms of fluctuations [21,22]: The 2CLJQ model for CO2 offers an excellent balance between simplicity and accuracy for the description of pressure – volume – temperature (PVT) properties. The interaction parameters presented by ›kXl Mo ̈ller and Fischer [2] were optimized to describe ›kXl ›X 1⁄4 ›b PP where H is the system enthalpy. From the above equations, it is possible to derive expressions for the volume expansivity, bP, the isothermal compressi- bility, k, and the configurational isobaric heat capacity, Cconf : 1⁄4 2 kVl ›b PP k1⁄42 1 ›kVl 1⁄42 b ðkVl22kV2lÞ ð6Þ kVl ›P b kVl ›b 1⁄4 ðkXlkHl 2 kXHlÞ ð3Þ 1⁄4 bðkXlkVl 2 kXVlÞ ð4Þ *›X + ›Pb ›Pb 1 ›kVl kBb2 ›kVl bP 1⁄4 kVl ›T kBb2 1⁄4 2 kVl ðkVlkHl 2 kVHlÞ ð5Þ ›kHl P ›TP ›TP ›TP 2NkB ›kUl ›b P ›kVl ›b P 1⁄4 2kBb2 Cconf 1⁄4 2kBb21⁄2kUlkHl 2 kUHl 2kBb2P 2 kBb2P1⁄2kVlkHl 2 kVHl 2 NkB ð7Þ where U is the configurational energy. The molar configurational isobaric heat capacity can be obtained as cconf 1⁄4 CconfðNA=NÞ; where NA is Avogadro’s PP number. To obtain the total isobaric heat capacity it is necessary to add to the above expression the ideal gas heat capacity, Cideal : P CP 1⁄4 Cideal þ Cconf ð8Þ PP The ideal gas heat capacity was calculated from the correlation given in Ref. [6] which represents a data set that consider first order corrections to the rigid rotator, harmonic-oscillator model, with devi- ations less than ^0.02%. From these properties, it is possible to derive other thermodynamic properties of interest, such as the isochoric heat capacity, the Joule – Thomson coeffi- cient and the speed of sound.PDF Image | Thermal Properties of Supercritical Carbon Dioxide
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