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.
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Polak LS. Variational principles of mechanics: their development and application to physics. Moscow: LIBROKOM; 2010 (in Russian).
Kaganovich BM, Filippov SP, Antsiferov EG. Efficiency of energy technologies: thermodynamics, economics, forecasts. Novosibirsk: Nauka; 1989 (in Russian).
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.
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.
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.
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.
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.
Kaganovich BM. Equilibrium thermodynamics. Problems and perspectives. Saarbrücken: LAP Lambert Academic Publishing; 2015 (in Russian).
Lagrange J. Analytical Mechanics. Dordrecht: Kluwer; 1997.
Bellman RE. Dynamic programming. Princeton: Princeton Univ. Press; 1957.
Caratheodory C. Untersuchungen uber die grundlagen der thermodynamik. Math Ann. 1909;61:355–90.
Born M. Kritische Betrachtungen zur traditionellen Darstellung der Thermodynamik. Physic Zeitschr. 1920; 22: 218–24, 249–54, 282–6.
Kirchhoff GR. Ueber den Durchgang eines elektrischen Stromes durch Ebene, insbesondere durch eine kreisformige. Ann Phys. 1845;64:497–514.
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.
Maxwell JCA. Treatise on electricity and magnetism. London: The Clarendon Press; 1891.
Viktor Yakovlevich Khasilev: Memoirs of Life and Work. Scientific Legacy. Novosibirsk: Academic Publishing House “Geo”; 2012. (in Russian).
Merenkov AP, Khasilev VY. Theory of hydraulic circuits. Moscow: Nauka; 1985 (in Russian).
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.
Kantorovich LV. On the translocation of masses. J Math Sci. 2006;4:1381–2.
Gorban AN. Equilibrium encircling: equations of chemical kinetics and their thermodynamic analysis. Novosibirsk: Nauka; 1984 (in Russian).
Gorban AN. Thermodynamic tree: the space of admissible paths. SIAM J Appl Dyn Syst. 2013;12(1):246–78.
Kaganovich BM, Merenkov AP, Balyshev OA. Elements of the Theory of Heterogeneous Hydraulic Circuits. Novosibirsk: Nauka; 1997. p. 120 (in Russian).
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Kaganovich, B.M., Zarodnyuk, M.S. & Yakshin, S.V. Construction of trajectories of irreversible processes on the basis of equilibrium thermodynamic propositions. J Therm Anal Calorim 133, 1225–1232 (2018). https://doi.org/10.1007/s10973-018-7368-7
- Extreme trajectory
- Irreversible process
- Step-by-step equilibrium modeling
- Circuit modeling
- Thermodynamic space
- One-dimensional potential space