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Entropy maximization in the free expansion process

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Publication Date
2005-07
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Velasco Maíllo, Santiago
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IOP Publishing Ltd.
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The entropy maximum principle is applied to obtain the final equilibrium state in the free expansion of a perfect gas. This provides an example where the entropy of an isolated system at equilibrium has an absolute maximum which is not a local maximum.
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© 2005 IOP Publishing Ltd. SV thanks financial support by Comisión Interministerial de Ciencia y Tecnología (CICYT) of Spain under grants BFM 2002-01225 FEDER and BFM 2003-07106 FEDER, and by Junta de CyL-FSE of Spain under grants SA080/04 and SA092/04.
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[1] Kestin J 1979 A Course in Thermodynamics vol II (New York: Hemisphere) p 2 [2] Callen H B 1985 Thermodynamics and an Introduction to Thermostatistics 2nd edn (New York: Wiley) pp 25–6 [3] Gibbs J W 1961 The Scientific Papers of J W Gibbs. Thermodynamics vol I (New York: Dover) p 57 [4] Tisza L 1966 Generalized Thermodynamics (Cambridge, MA: MIT Press) p 43 [5] For a general mathematical study of these topics see, for example, Marsden J E and Tromba A J 1988 Vector Calculus 3rd edn (New York: Freeman) chapter 4 [6] Haase R 1969 Thermodynamics of Irreversible Processes (Reading, MA: Addison-Wesley) p 50 [7] Münster A 1970 Classical Thermodynamics (London: Wiley-Interscience) pp 56–8 [8] Sanfeld A 1971 Equilibrium, stability and displacements Physical Chemistry. An Advanced Treatise. Vol. I. Thermodynamics ed W Jost (New York: Academic) chapter 2A (see section X, Stability of Chemical Systems) [9] Haase R 1956 Thermodynamik der Mischphasen (Berlin: Springer) p 105 (See, also, [7]) [10] Fernández-Pineda C and Velasco S 2001 Application of thermodynamic extremum principles Am. J. Phys. 69 1160–5 [11] Velasco S and Fernández-Pineda C 2002 A simple example illustrating the application of thermodynamic extremum principles Eur. J. Phys. 23 501–11
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