# Water vapor P-ρ-T properties calculation in the temperature range from 773 K to 1673 K

R.A. Magomedov, E.N. Akhmedov

^{} The Joint Institute for High Temperatures of the Russian Academy of Sciences

**DOI:** 10.26456/pcascnn/2022.14.298

* Original article*

**Abstract: ** The paper presents the calculation of isotherms of the equation of state of water vapor in the temperature range from T = 773 K to T = 1673 K. The calculation was made using a specially developed software module “Fract EOS”. An approach that improves the accuracy of calculations of the previously described method is proposed. If there are tabular data of the P-V-T (P-ρ-T) ratio for several temperatures and the pressure dependences of the fractional derivative exponent α(ρ) (which is fitting parameter for the proposed model) obtained from them, then it is possible to obtain the dependence α(ρ) for any temperature within the range. After that, the equation of state can be calculated at a given temperature with high accuracy, without fitting α by experimental values. The results obtained are in good agreement with experimental data. It is shown that proposed method is suitable for calculating isotherms in the temperature ranges not presented in tabulated reference data.

*Keywords: equation of state, integral-differentiation of fractional order, Maxwell relations, Helmholtz potential, partition function, water vapor, isotherm, thermophysical properties *

- Ramazan A. Magomedov – Senior Researcher, Institute for Geothermal Researches and Renewable Energy, The Joint Institute for High Temperatures of the Russian Academy of Sciences
- Enver N. Akhmedov – Junior Researcher, Institute for Geothermal Researches and Renewable Energy, The Joint Institute for High Temperatures of the Russian Academy of Sciences

**Reference: **

**Magomedov, R.A. ** Water vapor P-ρ-T properties calculation in the temperature range from 773 K to 1673 K /
R.A. Magomedov, E.N. Akhmedov //
Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials. — 2022. — I. 14. — P. 298-306. DOI: 10.26456/pcascnn/2022.14.298. (In Russian).

**Full article (in Russian): **
download PDF file

**References: **

1. Russo J., Akahane K., Tanaka H. Water-like anomalies as a function of tetrahedrality, Proceedings of the National Academy of Sciences, 2018, vol. 115, issue 15, pp. E3333-E3341. DOI: 10.1073/pnas.1722339115.

2. Galkin A.A., Lunin V.V. Subcritical and supercritical water: a universal medium for chemical reactions, Russian Chemical Reviews, 2005, V. 74, no. 1, pp. 21-35. DOI: 10.1070/RC2005v074n01ABEH001167.

3. Bushman A.V., Fortov V.E. Model equations of state, Soviet Physics Uspekhi, 1983, V. 26, no. 6, pp. 465-496. DOI: 10.1070/PU1983v026n06ABEH004419.

4. Reid R.C., Prausnitz J.M., Sherwood T.K. The properties of gases and liquids, 3rd ed. New York: McGraw-Hill, 1977, 669 p.

5. Kaplun A.B., Meshalkin A.B. A low-parametric state equation for calculating the thermodynamic properties of substances in liquid and gaseous state, Russian Journal of Physical Chemistry A, 2013, vol. 87, no. 8, pp. 1284-1290. DOI: 10.1134/S003602441308013X.

6. Petrik G.G. Uravnenie sostoyaniya Van-der-Vaal'sa i ego modifikatsii v modeli vzaimodejstvuyushchikh tochechnykh tsentrov [Van der Waals equation of state and its modifications in the model of interacting point centers], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2012, Issue 4, pp. 235-247. (In Russian).

7. Meilanov R.P., Magomedov R.A. Thermodynamics in fractional calculus, Journal of Engineering Physics and Thermophysics, 2014, vol. 87, issue 6, pp. 1521-1531. DOI: 10.1007/s10891-014-1158-2.

8. Magomedov R.A., Meilanov R.R., Meilanov R.P. et al. Generalization of thermodynamics in of fractional-order derivatives and calculation of heat-transfer properties of noble gases, Journal of Thermal Analysis and Calorimetry, 2018, vol. 133, issue 2, pp. 1189-1194. DOI: 10.1007/s10973-018-7024-2.

9. Akhmedov E.N., Magomedov R.A., Aliverdiev A.A. Fract EOS. Certificate RF, no 2021661219, 2021. (In Russian).

10. Kilbas A.A., Samko S.G. Integraly i proizvodnie drobnogo poryadka i nekotorie ikh prilozheniya [Fractional integrals and derivatives and some of their applications]. Minsk, Nauka i tekhnika Publ., 1987, 688 p. (In Russian)

11. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations. North-Holland, Amsterdam, Elsevier, 2006, 540 р.

12. Landau L.D., Lifshitz E.M. Teoreticheskaya fizika. Tom 5, Chast’ 1: Statisticheskaya fizika [Theoretical physics. Vol. 5, Part 1: Statistical physics]. Moscow: Fizmatlit Publ., 2002, 616 p.

13. Sivukhin D.V. Obschiy kurs fiziki. Tom 2: Termodinamika i molekulyarnaya fizika [General course of physics. Vol. 2: Thermodynamics and molecular physics]. Moscow: Fizmatlit Publ., 2005, 544 p. (In Russian).

14. Magomedov R.A., Akhmedov E.N., Meilanov R.R. et al. K raschetu teplofizicheskikh kharakteristik ksenona [To the calculation of the thermophysical characteristics of xenon], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur I nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2018, issue 10, pp. 446-452. DOI: 10.26456/pcascnn/2018.10.446. (In Russian).

15. Dobbins R.A., Mohammed K., Sullivan D.A. Pressure and density series equations of state for steam as derived from the Haar–Gallagher–Kell formulation, Journal of Physical and Chemical Reference Data, 1988, vol. 17, issue 1, pp. 1-8. DOI: 10.1063/1.555819.

16. Glushko V.P., Gurvich L.V. Termodinamicheskie svoistva individual’nikh veschestv: spravochnoe izdanie. Part 1. Elementy O, H(D,T), F, Cl, Br, I, He, Ne, Ar, Kr, Xe, Rn, S, N, P i ikh soedineniya [Thermodynamic properties of individual substances: a reference book. Part 1. Elements O, H(D,T), F, Cl, Br, I, He, Ne, Ar, Kr, Xe, Rn, S, N, P and their compounds]. Nauka Publ., 1978, 496 p. (In Russian).

17. Fizicheskie velichiny: Spravochnik [Physical Quantities: Handbook], ed. by I.S. Grigoriev, E.Z. Meilikhov. Moscow: Energoatomizdat Publ., 1991, 1232 p. (In Russian).

18. Frolov S.M., Kuznetsov N.M., Krueger C. Real-gas properties of n-alkanes, O2, N2, H2O, CO, CO2, and H2 for Diesel engine operation conditions, Russian Journal of Physical Chemistry B, 2009, vol. 3, issue 8, pp. 1191-1252. DOI: 10.1134/S1990793109080090.

19. Aleksandrov A.A., Grigor’ev B.A. Tablitsi teplofizicheskikh svoistv vody I vodyanogo para: Spravochnik. [Tables of thermophysical properties of water and water vapor: a Handbook]. Moscow: MEI publ., 1999, 168 p. (In Russian).