Le Chatelier's principle: Difference between revisions
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'''Le Chatelier's principle''' describes the stability of a system in thermodynamic equilibrium<ref>[http://gallica.bnf.fr/ark:/12148/bpt6k3055h.image.r=Comptes+rendus+1884+Chatelier.f786.langFR H. L. Le Chatelier, "Sur un énoncé général des lois des équilibres chimiques", Comptes rendus '''99''' pp. 786-789 (1884)]</ref><ref>H. L. Le Chatelier, Annales des Mines '''13''' pp. 157- (1888)</ref>: | |||
:''In response to small deviations away from equilibrium, the system will change in a manner that restores equilibrium.'' | |||
This translates to conditions on the second derivatives of thermodynamic potentials such as [[entropy]], <math>S(U,\ldots)</math>. For instance, the entropy is a concave function of its arguments such as [[internal energy]]. Thus, one has | |||
:<math>\frac{\partial^2 S}{\partial U^2} \geq0\ .</math> | |||
Similarly, [[heat capacity |specific heats]] can be shown to be positive definite. | |||
==References== | |||
Similarly, specific heats can be shown to be positive definite. | <references/> | ||
'''Related reading''' | |||
*[http://dx.doi.org/10.1103/PhysRevE.63.051105 Denis J. Evans, Debra J. Searles, and Emil Mittag "Fluctuation theorem for Hamiltonian Systems: Le Chatelier’s principle", Physical Review E '''63''' 051105 (2001)] | |||
*[http://dx.doi.org/10.1063/1.3261849 Pouria Dasmeh, Debra J. Searles, Davood Ajloo, Denis J. Evans, and Stephen R. Williams "On violations of Le Chatelier's principle for a temperature change in small systems observed for short times", Journal of Chemical Physics '''131''' 214503 (2009)] | |||
[[category: classical thermodynamics]] | |||
Latest revision as of 13:31, 3 December 2009
Le Chatelier's principle describes the stability of a system in thermodynamic equilibrium[1][2]:
- In response to small deviations away from equilibrium, the system will change in a manner that restores equilibrium.
This translates to conditions on the second derivatives of thermodynamic potentials such as entropy, . For instance, the entropy is a concave function of its arguments such as internal energy. Thus, one has
Similarly, specific heats can be shown to be positive definite.
References[edit]
- ↑ H. L. Le Chatelier, "Sur un énoncé général des lois des équilibres chimiques", Comptes rendus 99 pp. 786-789 (1884)
- ↑ H. L. Le Chatelier, Annales des Mines 13 pp. 157- (1888)
Related reading
- Denis J. Evans, Debra J. Searles, and Emil Mittag "Fluctuation theorem for Hamiltonian Systems: Le Chatelier’s principle", Physical Review E 63 051105 (2001)
- Pouria Dasmeh, Debra J. Searles, Davood Ajloo, Denis J. Evans, and Stephen R. Williams "On violations of Le Chatelier's principle for a temperature change in small systems observed for short times", Journal of Chemical Physics 131 214503 (2009)