Second law of thermodynamics: Difference between revisions
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Carl McBride (talk | contribs) m (New page: For a reversible change :<math>dQ=TdS</math> Thus for a closed system (<math>n</math> fixed): :<math>dU=TdS -PdV</math> For an open system: :<math>dU=TdS -PdV + \mu dN</math> For <ma...) |
Carl McBride (talk | contribs) (→References: Added a book by Arieh Ben-Naim) |
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The '''second law of thermodynamics''' for a reversible change (that is to say that the system evolves through a succession of equilibrium states) can be written as | |||
:<math>\left.dQ\right.=TdS</math> | |||
Thus for a closed system, having a fixed number of atoms/molecules, one has | |||
:<math>\left.dU\right.=TdS -PdV</math> | |||
where <math>U</math> is the [[internal energy]]. | |||
For an open system: | For an open system: | ||
:<math>dU=TdS -PdV + \mu dN</math> | :<math>\left.dU\right.=TdS -PdV + \mu dN</math> | ||
where <math>\mu</math> is the [[chemical potential]]. | |||
For <math>U(S,V)</math> one has the following total differential | For <math>U(S,V)</math> one has the following total differential | ||
:<math>dU=\left(\frac{\partial U}{\partial S}\right)_V dS + \left(\frac{\partial U}{\partial V}\right)_S dV</math> | :<math>dU=\left(\frac{\partial U}{\partial S}\right)_V dS + \left(\frac{\partial U}{\partial V}\right)_S dV</math> | ||
==See also== | |||
*[[Entropy]] | |||
*[[Non-equilibrium thermodynamics#Fluctuation theorem | Fluctuation theorem]] | |||
*[[H-theorem]] | |||
==References== | |||
<references/> | |||
;Related reading | |||
*Nicolas Léonard Sadi Carnot "Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance" (1824), printed in [http://www.numdam.org/item?id=ASENS_1872_2_1__393_0 Annales scientifiques de l'École Normale Supérieure Sér. '''2''', 1 pp. 393-457 (1872)] | |||
*[http://arxiv.org/abs/1205.6894v1 Esther Hänggi and Stephanie Wehner "A violation of the uncertainty principle implies a violation of the second law of thermodynamics", arXiv:1205.6894v1 <nowiki>[</nowiki>quant-ph<nowiki>]</nowiki> Thu, 31 May 2012] | |||
*[http://dx.doi.org/10.1063/1.4921558 K. S. Glavatskiy "Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics", Journal of Chemical Physics '''142''' 204106 (2015)] | |||
* Arieh Ben-Naim "Discover Entropy and the Second Law of Thermodynamics: A Playful Way of Discovering a Law of Nature" World Scientific Publishing (2010) ISBN: 978-981-4299-75-6 | |||
* Arieh Ben-Naim "Entropy and the Second Law Interpretation and Misss-Interpretations", World Scientific Publishing (2012) ISBN 978-981-4407-55-7 | |||
[[Category: Classical thermodynamics]] | |||
Latest revision as of 18:04, 25 November 2015
The second law of thermodynamics for a reversible change (that is to say that the system evolves through a succession of equilibrium states) can be written as
Thus for a closed system, having a fixed number of atoms/molecules, one has
where is the internal energy. For an open system:
where is the chemical potential.
For one has the following total differential
See also[edit]
References[edit]
- Related reading
- Nicolas Léonard Sadi Carnot "Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance" (1824), printed in Annales scientifiques de l'École Normale Supérieure Sér. 2, 1 pp. 393-457 (1872)
- Esther Hänggi and Stephanie Wehner "A violation of the uncertainty principle implies a violation of the second law of thermodynamics", arXiv:1205.6894v1 [quant-ph] Thu, 31 May 2012
- K. S. Glavatskiy "Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics", Journal of Chemical Physics 142 204106 (2015)
- Arieh Ben-Naim "Discover Entropy and the Second Law of Thermodynamics: A Playful Way of Discovering a Law of Nature" World Scientific Publishing (2010) ISBN: 978-981-4299-75-6
- Arieh Ben-Naim "Entropy and the Second Law Interpretation and Misss-Interpretations", World Scientific Publishing (2012) ISBN 978-981-4407-55-7