Scaling equation of state in real variables for fluids with accounting of asymmetry
Abstract
Modification of the nonparametric scale equation of state, considering asymmetry of real fluids is proposed. The asymmetric equation in reduced form for variables of density (ρ - ρc)/ρc and temperature (T - Tc)/Tc adequately describes Р-ρ-Т data and a thermal capacity near to critical points of fluids. The equation is received on the basis of a proposed method used previously for a derivation of the symmetric nonparametric equation of state, with use of scaling fields mixing (Pokrovski transformations). Approximation of Р-ρ-Т data on4Не, SF6 and isobutane in critical area with using of new equation of state shows what quite enough to consider the asymmetry on density in terms of the equation. Calculation of asymmetry of boundary curves with using constants of the asymmetric equation of state corresponds to a course of «the law of rectilinear diameter» for saturation curves in the given liquids not only in asymptotic area, but also in enough far on density from a critical point (|(ρ - ρc)/ρc| < 0.5). The proposed asymmetric equation of state describes Р-ρ-Т data in critical area with the same error or it is better, than with using of the symmetric equation of state, however number fitting constants for the asymmetric equation is more on two constants of Pokrovski transformation than for the symmetric equation. The new equation keeps advantages of simplicity of application to describe Р-ρ-Т data unlike the parametrical equations of state on the basis of Schofield linear model.
About the Authors
P. P. Bezverkhy
Институт неорганической химии СО РАН
Russian Federation
Russian Federation
V. G. Martynets
Институт неорганической химии СО РАН
Russian Federation
Russian Federation
E. V. Matizen
Институт неорганической химии СО РАН
Russian Federation
Russian Federation
References
1. Agayan V.A., Anisimov M.A., Sengers J.V. Crossover parametric equation of state for Ising-like systems // Phys. Rev. E, 2001. V. 64, 026125-1-19.
2. Kiselev S.B., Friend D.G. Cubic crossover equation of state for mixtures // Fluid Phase Equilibr. 1999. Vol.162. P. 51 - 82.
3. Безверхий П.П., Мартынец В.Г., Матизен Э.В., Кукарин В.Ф. Масштабное уравнение реальной жидкости // ТВТ, 1988. Т. 26. № 4. С. 700 - 706.
4. Schofield P. Parametric representation of the equation of state near a critical point // Phys. Rev. Lett., 1969, V. 22. № 12. P. 606 - 608.
5. Безверхий П.П., Мартынец В.Г., Матизен Э.В. Непараметрическое масштабное уравнение состояния для описания критического поведения жидкости // ТВТ. 2007. Т.45. № 4. С.510 - 517.
6. Безверхий П.П., Мартынец В.Г., Матизен Э.В. Непараметрическое масштабное уравнение состояния для описания термодинамических свойств 4Не в критической области // ЖЭТФ. 2007. Т. 132. № 1(7). С. 162 - 165.
7. Bezverkhy P.P., Martynets V. G., Matizen E. V. A scaling equation of state near the critical point and the stability boundary of a liquid // J. of Engin. Thermoph. 2007. Vol. 16. № 3. P. 164 - 168.
8. Безверхий П.П., Мартынец В.Г., Матизен Э.В. Непараметрическое масштабное уравнение состояния для жидкостей // ЖФХ. 2007. Т. 81. № 6. С. 978 - 984.
9. Паташинский А.З., Покровский В.Л. Флуктуационная теория фазовых переходов. М: Наука, 1982. 382 c.
10. Ландау Л.Д., Лифшиц Е.М.. Статистическая физика. 3-е изд., М: Наука, 1976. 584 c.
11. Безверхий П.П., Мартынец В.Г., Матизен Э.В. Непараметрическое масштабное уравнение состояния и аппроксимация P-ρ-T-данных вблизи критической точки парообразования жидкостей // ЖЭТФ. 2004. Т. 126. вып. 5. С. 1146 - 1152.
12. Кукарин В.Ф., Мартынец В.Г., Матизен Э.В., Сартаков А.Г. Экспериментальное изучение P-ρ-T зависимостей 4He вблизи критической точки парообразования // ФНТ. 1980. Т. 6. № 5. С. 549-559.
13. Funke M., Kleinrahm R., Wagner W. Measurement and correlation of the (P, ρ, T) relation of sulphur hexafluoride (SF6). The homogeneous gas and liqud region in the temperature range from 225 K to 340 K at pressures up to 12 MPa // J. Chem. Thermodynamics. 2002. V.34. P.717 - 734.
14. Roach P.R. Pressure - density - temperature surface of 4He near its critical point // Phys. Rev., 1968. V. 170. № 1. P. 213-223.
15. Funke M., Kleinrahm R., Wagner W. Measurement and correlation of the (p,ρ,T) relation of sulphur hexafluoride (SF6). II. Saturated-liquid and saturated-vapour densities and vapour pressures along the entire coexistence curve // J. Chem. Thermodynamics. 2001. V. 34. P. 735-754.
16. Masui G., Honda Y., Uematsu M. Critical parameters for isobutane determined by image analysis// J. Chem. Thermodynamics. 2006. V.38. P.1711-1716.
17. Miyamoto H., Koshi T, Uematsu M. Measurements of saturated-liquid densities for isobutane at T=(280 to 407) K // J. Chem. Thermodynamics. 2008. V.40. P. 1222-1225.
18. Kayukawa Y., Hasumoto M., Kano Y., Watanabe K. Liquid-phase thermodynamic properties for propane (1), n-butane (2), and isobutane (3) // J. Chem. Eng. Data. 2005. V.50(2). P. 556-564.
19. Miyamoto H., Uematsy M. Measurements of (p,ρ,T) properties for isobutаne in the temperature range from 280 K to 440 K at pressures up to 200 Mpa // J. Chem. Thermodynamics. 2006. V.38. P. 360-366.
20. Beattie J.A., Edwards D.G., Marple S. The vapor pressure, orthobaric liquid density, and critical constants of isobutane // J.Chem.Phys. 1949. V.17. № 6. P. 576.
21. Beattie J.A., Marple S., Edwards D.G. Compressibility of, and equation of state for gaseous isobutane // J.Chem.Phys. 1950. V.18. № 1. P. 127 - 128.
22. Waxman M., Gallagher J. S. Thermodynamic properties of isobutane for temperatures from 250 to 600 K and pressures from 0.1 to 40 MPa // J. Chem. Eng. Data. 1983. V.28(2), P. 224-241.
23. Bucker D. and Wagner W. Reference equations of state for the thermodynamic properties of fluid phase n-butane and isobutane // J. Phys. Chem. Ref. Data. 2006. V.35. № 2. P. 929 - 1019.
24. Кукарин В.Ф., Мартынец В.Г., Матизен Э.В., Сартаков А.Г. Аппроксимация p-g-T данных вблизи критической точки 4Не новым уравнением состояния.// ФНТ. 1981. Т. 7. № 12. С. 1501 - 1508.
25. Levelt Sengers J.M.H., Kamgar-Parsi B., Sengers J.V. Thermodynamic properties of isobutane in the critical region // J. Chem. Eng. Data. 1983. V.28(4). P. 354 - 362.
26. Glos S., Kleinrahm R., Wagner W. Measurement of the (p,ρ,T) relation of propane, propylene, n-butane, and isobutane in the temperature range from (95 to 340) K at pressures up to 12 MPa using an accurate two-sinker densimeter // J. Chem. Therm. 2004. V.36. P. 1037-1059.
27. Higashi Y. Critical parameters for 2-methylpropane (R600a) // J. Chem. Eng. Data. 2006. V.51. P. 406-408.
28. Goodwin R., Haynes W. Thermophysical properties of isobutane from 114 to 700 K at pressures to 70 MPa. NBS Tech. Note. № 1051. Boulder, 1982.
29. Безверхий П.П., Мартынец В.Г., Матизен Э.В. Объединённое уравнение состояния флюидов, включающее регулярную и скейлинговскую части // СФТП. 2008. Т.3. № 3. С.13 - 29.
30. Shin M.S., Lee Y., Kim H. A crossover lattice fluid equation of state for pure fluids// J. Chem. Thermodynamics. 2008. V.40. P. 174 - 179.
Review
For citations:
Bezverkhy P.P., Martynets V.G., Matizen E.V. Scaling equation of state in real variables for fluids with accounting of asymmetry. The Herald of the Siberian State University of Telecommunications and Information Science. 2009;(3):105-116. (In Russ.)
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