EDN: KTGWUL
Authors & Affiliations
Kazantsev A.A., Chernova P.D.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
Kazantsev A.A. – Leading Researcher, Cand. Csi. (Tech.), Associate Professor. Contacts: 1, pl. Bondarenko, Obninsk, Kaluga region, Russia, 249033. Tel.: +7 (484) 399-70-00 (add. 51-97); e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..
Chernova P.D. – Researcher.
Abstract
Sodium alkali metal vapor is a mixture of monomers (Na atoms) and polymers: dimers, trimers, and tetramers. Expressions for calculating the thermodynamic properties of sodium in the pressure-temperature-density-activity variables are obtained analytically in this paper. The method uses a thermodynamic state equation based on the cluster expansion theory and the source atom method. The basics of the method were developed by a group of researchers from the Moscow National Research University (MPEI) and the Joint Institute of High Temperatures of the Russian Academy of Sciences (JIHT RAS). In this article, the semi-empirical equation of state for alkali metal vapors is presented as a thermodynamic system that performs an additional type of polymerization work in addition to compression work. This method requires the use of a state equation with an additional degree of freedom necessary to describe the parameters of a real gas. The activity of metal vapor monomers is used as an additional parameter. The decomposition of vapor density in terms of activity coefficients turns out to be a compact, rapidly converging representation that is convenient for describing the properties of alkali metal vapors, particularly sodium. Due to polymerization reactions, the specific isobaric heat capacity exhibits the strongest deviation from the ideal gas The real gas equation of state with a small uncertainty describes the thermodynamic properties of sodium vapor, such as density, specific enthalpy, and thermal coefficients. The presented method reproduced the reference tables for seven properties of sodium vapor well in the temperature range of 700–2500 K and in the pressure range from 1 kPa up to 3 MPa.
Keywords
thermodynamic equation of state (EOS), sodium vapor, real gas, caloric equation of state, cluster expansion theory, source atom method, polymerization reactions, monomer activity, thermal coefficients, properties of sodium on the saturation line
Article Text (PDF, in Russian)
References
- Semenov A.M. K teorii gruppovykh razlozheniy dlya smesey real'nykh gazov. Gruppovyye integraly [On the cluster expansion theory for a real gas mixtures. Cluster integrals]. DAN USSR, 1981, vol. 256, issue 4, pp. 841–844. Available at: https://www.mathnet.ru/rus/dan/v256/i4/p841 (accessed 11.03.2026).
- Reva T.D., Semenov A.M. Raschet termodinamicheskikh svoystv parov natriya i kaliya na osnove poluempiricheskogo uravneniya sostoyaniya. Uravneniye sostoyaniya [Calculation of the thermodynamic properties of sodium-and potassium vapors based on semi-empirical equation of state. Equation of state]. Teplofizika vysokikh temperatur – High Temperature, 1984, vol. 22, pp. 372–380. Available at: https://www.mathnet.ru/rus/tvt/v22/i3/p463 (accessed 11.03.2026).
- Reva T.D., Semenov A.M. Raschet termodinamicheskikh svoystv parov natriya i kaliya na osnove poluempiricheskogo uravneniya sostoyaniya. Gruppovyye integraly i virial'nyye koeffitsiyenty [Thermodynamic properties of sodium and potassium vapors on the basis of a semiempirical equation of state – group integrals and viral coefficients]. Teplofizika vysokikh temperatur – High Temperature, 1984, vol. 22, issue 4, pp. 556–561. Available at: https://www.mathnet.ru/rus/tvt/v22/i4/p692 (accessed 11.03.2026).
- Reva T.D., Semenov A.M. Raschet termodinamicheskikh svoystv parov natriya i kaliya na osnove poluempiricheskogo uravneniya sostoyaniya. Termodinamicheskiye svoystva [Calculation of thermodynamic properties of sodium and potassium vapors based on semiempirical equation of state. Thermodynamic properties]. Teplofizika vysokikh temperatur – High Temperature, 1984, vol. 22, issue 5, pp. 680–688. Available at: https://www.mathnet.ru/rus/tvt/v22/i5/p874 (accessed 11.03.2026).
- Kuznetsova O.D., Semenov A.M. Uravneniye sostoyaniya para natriya. Teplofizika vysokikh temperatur [Equation of state for sodium vapor]. Teplofizika vysokikh temperatur – High Temperature, 1999, vol. 37, issue 6, pp. 841–845. Available at: https://www.mathnet.ru/rus/tvt/v37/i6/p871 (accessed 11.03.2026).
- Kuznetsova O.D., Semenov A.M. New reference data on the thermodynamic properties of sodium vapor. High Temp, 2000, vol. 38, issue 1, pp. 26–32. DOI: https://doi.org/10.1007/BF02755562.
- Lunin V.Yu., Semenov A.M. Raschet termodinamicheskikh svoystv para natriya metodom iskhodnykh atomov na osnove potentsialov mezhatomnogo vzaimodeystviya [Calculating the thermodynamic properties of sodium vapor by the initial-atom method on the basic of atomic-interaction potentials]. Teplofizika vysokikh temperatur – High Temperature, 1985, vol. 23, issue 3, pp. 364–371. Available at: >https://www.mathnet.ru/rus/tvt/v23/i3/p456 (accessed 11.03.2026).
- Semenov A.M. Kharakter skhodimosti gruppovykh i virial'nykh razlozheniy dlya neideal'nykh dissotsiiruyushchikh gazov [Convergence of group and virial expansions for non-ideal dissociating gases]. Teplofizika vysokikh temperatur – High Temperature, 1974, vol. 12, issue 6, pp. 1167–1176. Available at: https://www.mathnet.ru/rus/tvt/v12/i6/p1167 (accessed 11.03.2026).
- Semenov A.M. Metod iskhodnykh atomov v statisticheskoy termodinamike neideal'nykh khimicheski reagiruyushchikh gazov [The method of initial atoms in the statistical thermodynamics of non-ideal chemically reacting gases] V sb.: Matematicheskiye metody khimicheskoy termodinamiki [In: Mathematical Methods of Chemical Thermodynamics]. Novosibirsk, Nauka, Sib. otd. Publ., 1982. Pp. 88–99.
- Fink J.K., Leibowitz L. Thermodynamic and transport properties of sodium liquid and vapor. Report ANL/RE–95–2. Reactor Engineering Division. Argonne National Laboratory, 1995. 238 p. Available at: https://inis.iaea.org/records/1ga2v-1dw87 (accessed 11.03.2026).
- Kudryasheva N.S. Kurs lektsiy po fizicheskoy khimii: uchebnoye posobiye [A course of lectures on physical chemistry: A textbook]. Krasnoyarsk, Krasnoyar. gos. un-t Publ., 2007. 189 p.
- Barkovsky E.V., Khrustalev V.V., Tkachev S.V., Bolbas O.P., Buinitskaya E.Yu., Kontyava O.V., Yuzefovich O.N. Khimicheskaya termodinamika i kinetika dlya provizorov: uchebno-metodicheskoye posobiye [Chemical Thermodynamics and Kinetics for Pharmacists. Tutorial]. Minsk, BMGU Publ., 2018. 274 p. ISBN 978-985-21-0111-0.
- Zuev A.Yu., Tsvetkov D.S. Khimicheskaya termodinamika: uchebnoye posobiye [Chemical Thermodynamics: Textbook]. Yekaterinburg, Izdatel'stvo Ural'skogo universiteta Publ., 2020. 183 p. ISBN 978-5-7996-3029-4.
- Sychev V.V. Slozhnyye termodinamicheskiye sistemy. 4-ye izd. [Complex Thermodynamic Systems. 4th edition]. Moscow, Energoatomizdat Publ., 1986, 208 p.
- Forsythe G.E., Malcolm M.A., Moler C.B. Computer Methods for Mathematical Computations. Englewood Cliffs, New Jersey, Prentice Hall Inc., 1977. 270 p. ISBN 9780131653320.
- Termodinamicheskiye svoystva individual'nykh veshchestv. T. 4, kn. 2. Pod red. Glushko V.P. [Thermodynamic Properties of Individual Substances. Vol. 4, Book 2. Ed. V. P. Glushko]. Moscow, Nauka Publ., 1982. 560 p.
UDC 621.039.52.034.6:536.423
Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2026, no. 2, 2:20
