On the ideal gas law
Résumé
When a cylinder terminated by a piston, containing $N$ corpuscles, and with height $h$ is raised at temperature $\theta$, the force that the corpuscles exerts on the piston is, to within constant factors: $F=N\,\theta/h$. This law, called the ''ideal gas law'', is valid at any temperature (except at very low temperatures when quantum effects are significant) and for any collection of corpuscles, in a space of arbitrary dimensions. It is usually derived under the assumption that the temperature is proportional to the corpuscle's kinetic energy. We show that this law rests only upon the democritian concept of corpuscles moving in vacuum, postulating that it is independent of the law of motion. This view-point puts aside restrictive assumptions that are sources of confusion. The present paper should accordingly facilitate the understanding of the physical meaning of the ideal gas law. The mathematics is elementary.
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