Advertisement

Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 2, pp 1225–1232 | Cite as

Construction of trajectories of irreversible processes on the basis of equilibrium thermodynamic propositions

  • Boris M. Kaganovich
  • Maxim S. Zarodnyuk
  • Sergey V. Yakshin
Article
  • 25 Downloads

Abstract

The paper is concerned with the problem of macroscopic (unrelated with probability theory) construction of trajectories of irreversible physicochemical processes. The research involves simple and universal principles of conservation, equilibrium and extremality of classical mechanics and thermodynamics. The capabilities of their implementation increase greatly with development of computer engineering and information technologies. Two methods for construction are suggested: (1) a step-by-step method and (2) a method based on statement of the problem solved in one-dimensional graphical circuit variable space. For the implementation of the first method, the steps are chosen so small that the assumptions about the stationarity of motion and the observance of conservative system behavior regularities are made permissible. For intrastep simulation, we use the model of extreme intermediate states developed at the Melentiev Energy Systems Institute. To increase the optimal results of calculations when transitioning from one step to another, the dynamic programming method is applied. The properties of reversible processes in the case of constructing trajectories by the second method are always observed by the potentiality of one-dimensional motion. The need for the use and applicability of the proposed methodical approach is explained by examples.

Keywords

Extreme trajectory Irreversible process Step-by-step equilibrium modeling Circuit modeling Thermodynamic space One-dimensional potential space 

References

  1. 1.
    Polak LS. Variational principles of mechanics: their development and application to physics. Moscow: LIBROKOM; 2010 (in Russian).Google Scholar
  2. 2.
    Kaganovich BM, Filippov SP, Antsiferov EG. Efficiency of energy technologies: thermodynamics, economics, forecasts. Novosibirsk: Nauka; 1989 (in Russian).Google Scholar
  3. 3.
    Gorban AN, Kaganovich BM, Filippov SP, Keiko AV, Shamansky VA, Shirkalin IA. Thermodynamic equilibria and extrema analysis of attainability regions and partial equilibria. Berlin: Springer; 2006.Google Scholar
  4. 4.
    Kozlov A, Svishchev D, Donskoy I, Keiko AV. Thermal analysis in numerical thermodynamic modeling of solid fuel conversion. J Therm Anal Calorim. 2012;109:1311–7.CrossRefGoogle Scholar
  5. 5.
    Muvhiiwa RF, Lu X, Hildebrandt D, Glasser D, Matambo T. Applying thermodynamics to digestion/gasification processes: the attainable region approach. J Therm Anal Calorim. 2018;131:25–36.CrossRefGoogle Scholar
  6. 6.
    Kaganovich BM, Keiko AV, Shamansky VA. Equilibrium thermodynamic modeling of dissipative macroscopic systems. In: West DH, Yablonsky G, editors. Advances in chemical engineering. Vol. 39. Thermodynamics and kinetics of complex systems. Elsevier; 2010. pp. 1–74.Google Scholar
  7. 7.
    Kaganovich BM, Keiko AV, Shamansky VA, Zarodnyuk MS. On the interrelations between kinetics and thermodynamics as the theories of trajectories and states. In: Patel V, editor. Chemical kinetics. Rijeka: Intech; 2012. pp. 31–60.Google Scholar
  8. 8.
    Kaganovich BM. Equilibrium thermodynamics. Problems and perspectives. Saarbrücken: LAP Lambert Academic Publishing; 2015 (in Russian).Google Scholar
  9. 9.
    Lagrange J. Analytical Mechanics. Dordrecht: Kluwer; 1997.CrossRefGoogle Scholar
  10. 10.
    Bellman RE. Dynamic programming. Princeton: Princeton Univ. Press; 1957.Google Scholar
  11. 11.
    Caratheodory C. Untersuchungen uber die grundlagen der thermodynamik. Math Ann. 1909;61:355–90.CrossRefGoogle Scholar
  12. 12.
    Born M. Kritische Betrachtungen zur traditionellen Darstellung der Thermodynamik. Physic Zeitschr. 1920; 22: 218–24, 249–54, 282–6.Google Scholar
  13. 13.
    Kirchhoff GR. Ueber den Durchgang eines elektrischen Stromes durch Ebene, insbesondere durch eine kreisformige. Ann Phys. 1845;64:497–514.CrossRefGoogle Scholar
  14. 14.
    Kirchhoff GR. Ueber die Anwendbarkeit der Formeln fur die Intensitaten der galvanischen Strome in einem Systeme linearer Leiter auf Systeme, die zum Theil aus nicht linearen Leitern bestehen. Ges. Abhandl. Leipzig: Johann Ambrosius Barth; 1882. pp. 33–49.Google Scholar
  15. 15.
    Maxwell JCA. Treatise on electricity and magnetism. London: The Clarendon Press; 1891.Google Scholar
  16. 16.
    Viktor Yakovlevich Khasilev: Memoirs of Life and Work. Scientific Legacy. Novosibirsk: Academic Publishing House “Geo”; 2012. (in Russian).Google Scholar
  17. 17.
    Merenkov AP, Khasilev VY. Theory of hydraulic circuits. Moscow: Nauka; 1985 (in Russian).Google Scholar
  18. 18.
    Einstein A. Contributions to quantum theory. In: The collected papers of Albert Einstein, Vol. 6. The Berlin years: writings, 1914–1917. Princeton: Princeton University Press; 1997. pp. 20–27.Google Scholar
  19. 19.
    Kantorovich LV. On the translocation of masses. J Math Sci. 2006;4:1381–2.CrossRefGoogle Scholar
  20. 20.
    Gorban AN. Equilibrium encircling: equations of chemical kinetics and their thermodynamic analysis. Novosibirsk: Nauka; 1984 (in Russian).Google Scholar
  21. 21.
    Gorban AN. Thermodynamic tree: the space of admissible paths. SIAM J Appl Dyn Syst. 2013;12(1):246–78.CrossRefGoogle Scholar
  22. 22.
    Kaganovich BM, Merenkov AP, Balyshev OA. Elements of the Theory of Heterogeneous Hydraulic Circuits. Novosibirsk: Nauka; 1997. p. 120 (in Russian).Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Boris M. Kaganovich
    • 1
  • Maxim S. Zarodnyuk
    • 1
  • Sergey V. Yakshin
    • 1
  1. 1.Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of ScienceIrkutskRussia

Personalised recommendations