On Classical Ideal Gases
Résumé
The air density on earth decays exponentially as a function of altitude. To derive this law one usually invokes the Boltzmann factor, itself derived from statistical considerations. We show that this (barometric) law may be derived solely from the democritian concept of corpuscles moving in vacuum. We employ a principle of simplicity, namely that this law is \emph{independent} of the laws of physics, aside from the law of conservation of energy. This view-point puts aside restrictive assumptions that are source of confusion. Similar observations apply to the ideal-gas law. It is usually derived under the assumption that the temperature is proportional to the corpuscle average kinetic energy, or else, from a form of the quantum theory. In contradistinction, we show that it follows solely from the postulate that the ideal-gas law is independent of the law of corpuscle motion. On the physical side we employ only the concept of potential energy. Most of the end results are known, but the method appears to be novel. The mathematics being elementary (no integration is needed), the present paper should facilitate the understanding of the physical meaning of the barometric and ideal-gas laws, even though not-usually-taught concepts are being introduced. The reasons for rejection of this paper by American Journal of Physics are commented upon in the last appendix of this V2.
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