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12.8.2 亥姆霍兹能量状态方程的混合属性 Lemmon,86 Lemmon and Jacobsen,87 Tillner-Roth et al.88 and Lemmon and Tillner-Roth89 已经定义了一种广义的混合模型来解释不同物质之间的相互作用,这种模型是以有了新性质的混合物中某一纯流体的状态方程为基础。 Lemmon and Jacobsen90的文章记载着目前描述二氟甲烷(R-32)、乙烷(R-125)、1,112-四氟乙烷 (R134a)、 1,1,1-三氟乙烷(R-143a)和1,1-乙烷(R-152a)的混合物性质的方程。Kunz et al扩展了之前Lemmon报道的方法,包括为减少参数和状态方程还有为混合物提供修正系数而附加的系数,包括甲烷和丁烷或氮气、二氧化碳的混合物的系数,适合更高的摩尔质量的混合物的新系数和以代表达21种成分的天然气体系(包括氢气、氦气和气态水)的热力学性质为目的系数。这个公式也可以被用来计算湿空气的性质。混合物的亥姆霍兹能量可以用这个式子计算: 其中理想混合物的亥姆霍兹能量方程:等式中,C是混合物的组分数,是组分i的理想气体亥姆霍兹能量,是在低温低压下计算的组分i的纯流体剩余亥姆霍兹能量。因混合而增加的超额亥姆霍兹能量是: 这些系数和指数是从很多的实验数据中按非线性回归得到的。参数Fij用来概括从一个二元混合物到另一个二元混合物而新增性质的联系。对于这个参数,相同的一组混合物系数也适用于一些二元混合物。有几种二元混合物不使用广义参数,它们有针对二元混合物特有的新功能而设的参数和指数,这些混合物包括如下:(甲烷和氮气),(甲烷的二氧化氮),(甲烷和乙烷),(甲烷和丙烷),(甲烷和氢气),(氮气和二氧化碳),(氮气和乙烷)。对这些二元混合物来说,有足够的实验数据来适用于特定的方程。所有的单项热力学性质都能在12.5秒内从亥姆霍兹能量中计算出来,所用公式如下:和其中和T是混合物的密度和温度,r(x)和Tr(x)是减少量,通过下式计算:参数和分别用来定义减少的温度和密度线的形状。这些减少的参数和混合物的临界参数不同,它是通过对混合模型的其他参数的实验数据的非线性拟合而确定的。12.9 计算热力学性质的软件有各种各样的软件包能运行文章中提到的状态方程,其中有两个程序,一是REFPROP, 可以从NIST (/srd/nist23.htm)获得;二是ThermoFluids(www.FirstGmbH.de),由Wagner和他的同事在德国的鲁尔大学开发。即可以用程序应用状态方程来计算热力学性质又可以用动态衔接库(DLL)在定义用户应用中来计算性质,例如Microsoft Excel.例如,这个程序也能算出影响焓值的压力大小,它是基于iso-property线用户提供的输入而产生的。尽管在大多数情况下推荐使用易于编程的算法,但是它也能导致新的问题。在档案文献里从程序获得的价值常常被成为数据源。因为被用来为某种流体产生数据的状态方程可能在之后的程序版本中不断更新,这样的一个参考是模糊的也可能导致得不到科学结果。即使使用有效的商用软件,引用用来计算性能数据和相关参数的状态方程也是非常重要的。因此软件开发商必须为用户提供原始参考资料。References1. 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Bender, Equations of State Exactly Representing the Phase Behaviourof Pure Substances, Proc. 5th Symp. Thermophys. Prop., 1970, 5, 227235.428 Chapter 128. R. D. McCarty, Provisional Thermodynamic Functions for Helium 4 forTemperatures from 2 to 1500K with Pressures to 100MN/m2 (1000Atmospheres), NBS Report 9762, 1970.9. J. Ahrendts and H. D. Baehr, Int. Chem. Eng., 1981, 21, 557571.10. J. Ahrendts and H. D. Baehr, Int. Chem. Eng., 1981, 21, 572579.11. R. Schmidt and W. Wagner, Fluid Phase Equilib., 1985, 19, 175200.12. R. T Jacobsen, R. B. Stewart, M. Jahangiri and S. G. Penoncello, Adv.Cryo. Eng., 1986, 31, 11611168.13. U. Setzmann and W. Wagner, J. Phys. Chem. Ref. Data, 1991, 20,10611155.14. R. Span and W. Wagner, J. Phys. Chem. Ref. Data, 1996, 25, 15091596.15. W. Wagner, Eine Mathematische-Statistische Methode zum AufstellenThermodynamischer Gleichungen-Gezeigt am Beispiel der DampfdruckkurveReiner Fluider Stoffe, Fortschr. -Ber. VDI, Dusseldorf, VDI-Verlag,1974.16. K. M. de Reuck and B. Armstrong, Cryogenics, 1979, 19, 505512.17. J. Ewers and W. Wagner, A Method for Optimizing the Structure ofEquations of State and its Application to an Equation of State for Oxygen,Proc. 8th Symp. Thermophys. Prop., New York, 1981.18. U. Setzmann and W. Wagner, Int. J. Thermophys., 1989, 10, 11031126.19. Ch. Tegeler, R. Span and W. Wagner, A New Fundamental Equation forArgon Covering the Fluid Region for Temperatures from the Melting Line to700K and Pressures to 1000 MPa, Fortschritt-Berichte, VDI, 1997.20. E. W. Lemmon and R. T Jacobsen, J. Phys. Chem. Ref. Data, 2005, 34,69108.21. M. Benedict, G. B. Webb and L. C. Rubin, J. Chem. Phys., 1940, 8,334345.22. M. Benedict, G. B. Webb and L. C. Rubin, Chem. Eng. Prog., 1951, 47,419422.23. T. R. Strobridge, The Thermodynamic Properties of Nitrogen from 64 to300K Between 0.1 and 200 Atmospheres, NBS Technical Note 129, 1962.24. K. E. 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Ihmels, Fluid Phase Equilibria, 2005, 228229C,173187.58. S. G. Penoncello, A. R. H. Goodwin and R. T Jacobsen, Int. J. Thermophys.,1995, 16, 519531.430 Chapter 1259. R. D. McCarty, Correlations for the Thermophysical Properties of Deuterium,National Institute of Standards and Technology, Boulder, CO,1989.60. E. C. Ihmels and E. W. Lemmon, Fluid Phase Equilib., 2007, 260, 3648.61. E. W. Lemmon and M. L. Huber, Energy and Fuels, 2004, 18, 960967.62. H. E. Dillon and S. G. Penoncello, Int. J. Thermophys., 2004, 25, 321335.63. K. M. de Reuck, International Thermodynamic Tables of the Fluid State-11Fluorine, International Union of Pure and Applied Chemistry, PergamonPress, Oxford, 1990.64. P. G. Hill, R. D. C. MacMillan and V. Lee, J. Phys. Chem. Ref. Data, 1982,11, 114.65. R. D. McCarty and V. D. Arp, Adv. Cryo. Eng., 1990, 35, 14651475.66. J. W. Leachman, R. T Jacobsen, S. G. Penoncello and E. W. Lemmon,J. Phys. Chem. Ref. Data, 2009, 38, 721748.67. K. M. de Reuck and R. J. B. 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Maurer, Thermophysical Properties of Refrigerants,Springer-Verlag Berlin Heidelberg, Germany, 1990.74. B. de Vries, R. Tillner-Roth, and H. D. Baehr, Thermodynamic Propertiesof HCFC 124, 19th International Congress of Refrigeration, The Hague,The Netherlands, International Institute of Refrigeration, IVa:582-589,1995.75. J. W. Magee, S. L. Outcalt and J. F. Ely, Int. J. Thermophys., 2000, 21,10971121.76. R. Tillner-Roth and H. D. Baehr, J. Phys. Chem. Ref. Data, 1994, 23,657729.77. E. W. Lemmon and R. T Jacobsen, J. Phys. Chem. Ref. Data, 2000, 29,521552.78. A. Kamei, S. W. Beyerlein and R. T Jacobsen, Int. J. Thermophys., 1995,16, 11551164.79. S. G. Penoncello, E. W. Lemmon, R. T Jacobsen and Z. Shan, J. Phys.Chem. Ref. Data, 2003, 32, 14731499.Multi-parameter Equations of State for Pure Fluids and Mixtures 43180. S. L. Outcalt and M. O. McLinden, An Equation of State for the ThermodynamicProperties of R236fa, NIST report to sponsor (U. S. Navy, DavidTaylor Model Basin) under contract N61533-94-F-0152, 1995.81. R. Tillner-Roth and A. Yokozeki, J. Phys. Chem. Ref. Data, 1997, 26,12731328.82. C. Guder and W. Wagner, J. Phys. Chem. Ref. Data, 2009, 38, 3394.83. E. W. Lemmon, M. L. Huber, and M. O. McLinden, NIST StandardReference Database 23: Reference Fluid Thermodynamic and TransportProperties-REFPROP, Version 8.0, National Institute of Standards andTechnology, Standard Reference Data Program, Gaithersburg, 2007.84. J. W. Leach, Molecular Structure Corrections for Application of the Theoryof Corresponding States to Non-Spherical Pure Fluids and Mixtures, Ph. D.Dissertation, Rice University, Houston, Texas, 1967.85. J. F. Ely, Adv. Cryog. Eng., 1990, 35, 15111520.86. E. W. Lemmon, A Generalized Model for the Prediction of the ThermodynamicProperties of Mixtures Including Vapour-Liquid Equilibrium, Ph.D. Dissertation, University of Idaho, Moscow, 1996.87. E. W. Lemmon and R. T Jacobsen, Int. J. Thermophys., 1999, 20, 825835.88. R. Tillner-Roth, J. Li, A. Yokozeki, H. Sato, and K. Watanabe, ThermodynamicProperties of Pure and Blended Hydrofluorocarbon (HFC)Refrigerants, Japan Society of Refrigerating and Air Conditioning Engineers,Tokyo, 1998.89. E. W. Lemmon and R. Tillner-Roth, Fluid Phase Equilib., 1999, 165, 121.90. E. W. Lemmon and R. T Jacobsen, J. Phys. Chem. Ref. Data, 2004, 33,593620.91. O. Kunz, R. Klimeck, W. Wagner, and M. Jaeschke, The GERG-2004Wide-Range Equation of State for Natural Gases and Other Mixtures,GERG TM15, Fortschritt-Berichte VDI, Volume 6, Number 557, 2007.13章 化学反应体系的状态方程SELVA PEREDA, ESTEBAN BRIGNOLE 和SUSANA BOTTINIPlanta Piloto de Ingeniera Qumica (PLAPIQUI) CONICET, Universidad Nacional del Sur, Camino La Carrindanga Km 7 C.C: 717, Argentina13.1 简介相平衡和化学平衡的计算对涉及到化学反应的过程设计是必要的。即便是在不能达到化学平衡的反应中,这个问题的解决也能提供一些关于问题的可能性和潜在的热力学极限。有很多情况下是同时计算化学反应和相转移。例如反应精馏中相分离用来推动化学平衡的转移。还有,在高介电常数的液体中气体和固体的溶解度的计算同时需要溶于液相中得不同物质间的化学平衡的解析度。文献中已提出了几种解决复杂的非线性问题的算法。而适当的热力学模型的选择还没有得到太多的关注。近年来,用超临界溶剂来提高可控制反应的速率和选择性已成为一项重要的技术。接近混合物的临界点的相特性对操作条件和混合组成是非常敏感的。开发过程潜能的适当的相条件的选择和设计需要这种热力学模型,它能处理涉及惰性气体、超临界溶剂和非挥发性物质的高度不对称混合物。这一章提出了一种相平衡的工程方法来分析化学反应中的相平衡。对体系中状态方程的基团贡献的运用进行了讨论。这些模型的主要优点是他们对化合物有预测能力。对反应混合物的相平衡数据的缺乏是十分普遍的;由此,基团贡献法允许设计者获得相平衡改变的信息作为反应所得。13.2 化学平衡问题平衡条件的一般标准是在给定的温度和压力下一个体系的吉布斯自由能达到体系的最小值。对于一个单相的反应体系,这种条件能以化学势i方便的表达出来,物质i的化学计量数计算公式:其中i对生成物来说取正对反应物取负。在一个非理想溶液中化学势与相应的化合物的活性i有关
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