Le Chatelier's principle: Difference between revisions

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This principle describes the stability of a system in thermodynamic equilibrium.
'''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.''


'''Le Chatelier's principle:''' ''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


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>


<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)]
[[category: classical thermodynamics]]

Revision as of 11:27, 16 November 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

Related reading