Clausius theorem: Difference between revisions
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The '''Clausius theorem''' (also known as the [[Nicolas Léonard Sadi Carnot |Carnot]]-[[Rudolf Julius Emanuel Clausius |Clausius]] theorem) states that | The '''Clausius theorem''' <ref>[http://dx.doi.org/10.1002/andp.18501550306 R. Clausius "Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen", Annalen der Physik und Chemie '''79''' pp. 368-397 (1850)]</ref><ref>[http://dx.doi.org/10.1080/14786446208643322 R. Clausius "On the Application of the Theorem of the Equivalence of Transformations to the Internal Work of a Mass of Matter", Philosophical Magazine '''24''' series 4 pp. 81-97 (1862)]</ref> | ||
<ref>[http://dx.doi.org/10.1002/andp.18652010702 R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie '''125''' pp. 353-400 (1865)]</ref> | |||
<ref>[http://www.numdam.org/item?id=ASENS_1872_2_1__393_0 Nicolas Léonard Sadi Carnot "Reflexions sur la Puissance Motrice de Feu et sur les Machines Propres a Développer cette Puissance" (1824), printed in Annales scientifiques de l'École Normale Supérieure Sér. '''2''', 1 pp. 393-457 (1872)]</ref>(also known as the [[Nicolas Léonard Sadi Carnot |Carnot]]-[[Rudolf Julius Emanuel Clausius |Clausius]] theorem) states that | |||
:<math>\oint \frac{dQ}{T} \leq 0</math> | :<math>\oint \frac{dQ}{T} \leq 0</math> | ||
where ''Q'' is the [[heat]] and ''T'' is the [[temperature]]. This equation becomes an equality for a reversible cycle. | where ''Q'' is the [[heat]] and ''T'' is the [[temperature]]. This equation becomes an equality for a reversible cycle. This theroem has recently been derived without making use of the [[Second law of thermodynamics]] <ref>[http://dx.doi.org/10.1063/1.3592531 Denis J. Evans, Stephen R. Williams, and Debra J. Searles "A proof of Clausius’ theorem for time reversible deterministic microscopic dynamics", Journal of Chemical Physics '''134''' 204113 (2011)]</ref> by making use of the [[Evans-Searles transient fluctuation theorem]] and the [[Crooks fluctuation theorem]]. | ||
==See also== | ==See also== | ||
*[[Entropy]] | *[[Entropy]] | ||
*[[Second law of thermodynamics]] | *[[Second law of thermodynamics]] | ||
*[[Carnot cycle]] | |||
==References== | ==References== | ||
<references/> | |||
[[category: classical thermodynamics]] | [[category: classical thermodynamics]] | ||
Latest revision as of 11:21, 30 May 2011
The Clausius theorem [1][2] [3] [4](also known as the Carnot-Clausius theorem) states that
where Q is the heat and T is the temperature. This equation becomes an equality for a reversible cycle. This theroem has recently been derived without making use of the Second law of thermodynamics [5] by making use of the Evans-Searles transient fluctuation theorem and the Crooks fluctuation theorem.
See also[edit]
References[edit]
- ↑ R. Clausius "Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen", Annalen der Physik und Chemie 79 pp. 368-397 (1850)
- ↑ R. Clausius "On the Application of the Theorem of the Equivalence of Transformations to the Internal Work of a Mass of Matter", Philosophical Magazine 24 series 4 pp. 81-97 (1862)
- ↑ R. Clausius "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik und Chemie 125 pp. 353-400 (1865)
- ↑ Nicolas Léonard Sadi Carnot "Reflexions sur la Puissance Motrice de Feu et sur les Machines Propres a Développer cette Puissance" (1824), printed in Annales scientifiques de l'École Normale Supérieure Sér. 2, 1 pp. 393-457 (1872)
- ↑ Denis J. Evans, Stephen R. Williams, and Debra J. Searles "A proof of Clausius’ theorem for time reversible deterministic microscopic dynamics", Journal of Chemical Physics 134 204113 (2011)