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Received October 1, 2004
Accepted November 15, 2004
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Ambiguity and Non-uniqueness in Nonequilibrium Thermodynamics
Department of Chemical and Materials Engineering, University of Cincinnati, Cincinnati, OH 45221-0012, Korea
shwang@alpha.che.cu.edu
Korean Journal of Chemical Engineering, January 2005, 22(1), 133-141(9), 10.1007/BF02701475
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Abstract
The ambiguity and non-uniqueness of splitting fluxes and forces from the entropy generation equation raise confusion in nonequilibrium thermodynamics and misunderstanding of the Onsager reciprocal relationships. However, they provide an opportunity to select different sets of fluxes and forces that represent a given nonequilibrium process. By symmetrization of the phenomenological coefficient matrix, one can always find a proper set of fluxes and forces. This paper shows how the implementation of the transformation theory can produce several different sets of fluxes and forces through many engineering examples such as ideal gas permeation through a membrane, reverse osmosis, nanofiltration, ultrafiltration, and simultaneous heat and mass transfer. Also, guidance is presented on how to study nonequilibrium thermodynamics for a given irreversible process together with a short summary of the principles of nonequilibrium thermodynamics. These contain the entropy generation equation, linear relations of fluxes and all generalized forces including the Curie theorem, and the Onsager reciprocal relationships.
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References
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DeGroot SR, Mazur P, Non-Equilibrium Thermodynamics, John Wiley & Sons, New York, 20, 27 (1962)
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Katchalsky A, Curran PF, Nonequilibrium Thermodynamics, Harvard University Press, Cambridge, MA, 113 (1975)
Kedem O, J. Membr. Sci., 47, 277 (1989)
Kondepudi D, Prigogine I, Modern Thermodynamics, John Wiley & Sons, New York, 344 (1998)
Narebska A, Koter S, J. Membr. Sci., 30, 141 (1987)
Narebska A, Koter S, Pol. J. Chem., 71, 1643 (1997)
Narebska A, Koter S, Kujawski W, J. Membr. Sci., 25, 153 (1985)
Narebska A, Koter S, Warszawski A, Le TT, J. Membr. Sci., 106(1-2), 39 (1995)
Narebska A, Warszawski A, J. Membr. Sci., 88(2-3), 167 (1994)
Narebska A, Kujawski W, Koter S, J. Membr. Sci., 30, 125 (1987)
Narebska A, Warszawski A, Koter S, Le TT, J. Membr. Sci., 106(1-2), 25 (1995)
Onsager L, Phys. Rev., 37, 405 (1931)
Onsager L, Phys. Rev., 38, 2265 (1931)
Prigogine I, Etude Thermodynamique des Prosseus Irreversible, Desoer, Liege (1947)
Prigogine I, Introduction to Thermodynamics of Irreversible Processes, John Wiley & Sons, New York, 40 (1967)
Rizvi SA, Zaidi SB, J. Membr. Sci., 29, 259 (1986)
Whitaker S, Introduction to Fluid Mechanics, Prentice-Hall, New Jersey, 133 (1968)
