HAL : hal-00615244, version 5
 arXiv : 1108.3744
 Versions disponibles : v1 (18-08-2011) v2 (23-01-2012) v3 (29-03-2012) v4 (18-06-2012) v5 (20-04-2013)
 On Classical Ideal Gases
 (27/03/2012)
 The ideal gas laws are derived from the democritian concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion aside from the law of energy conservation. A single corpuscle in contact with a heat bath and submitted to a $z$ and $t$-invariant force $-w$ is considered, in which case corpuscle distinguishability is irrelevant. The non-relativistic approximation is made only in examples. Some of the end results are known but the method appears to be novel. The mathematics being elementary the present paper should facilitate the understanding of the ideal-gas law and more generally of classical thermodynamics. It supplements importantly a previously published paper: The stability of ideal gases is proven from the expressions obtained for the force exerted by the corpuscle on the two end pistons of a cylinder, and the internal energy. We evaluate the entropy increase that occurs when the wall separating two cylinders is removed and show that the entropy remains the same when the separation is restored. The entropy increment may be defined at the ratio of heat entering into the system and temperature when the number of corpuscles (0 or 1) is fixed. In general the entropy is defined as the average value of $\ln(p)$ where $p$ denotes the probability of a given state. Generalization to $z$-dependent weights, or equivalently to arbitrary static potentials, is made.
 1 : Institut d'Electronique du Sud (IES) CNRS : UMR5214 – Université Montpellier II - Sciences et techniques 2 : Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM) CNRS : UMR5506 – Université Montpellier II - Sciences et techniques
 Équipe de recherche : INFO/ARITH
 Domaine : Physique/Physique/Physique ClassiquePhysique/Matière Condensée/Mécanique statistiquePhysique/Physique/Physique Générale
 Mots Clés : Ideal gas law – Relativistic gases submitted to gravity – Corpuscular concepts – Classical gas theory – Democritus Physics – Canonical single-corpuscle thermodynamics
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 idealJacques.ps(1.1 MB)
 hal-00615244, version 5 http://hal.archives-ouvertes.fr/hal-00615244 oai:hal.archives-ouvertes.fr:hal-00615244 Contributeur : Laurent Chusseau <> Soumis le : Vendredi 19 Avril 2013, 16:41:29 Dernière modification le : Samedi 20 Avril 2013, 10:46:09