Equipartition of energy, Avogadro law and ratio of specific heats

Abstract The equipartition of energy in its simplest form, which is related to the translational motion of the molecules of a gas, was announced independently by Waterston in 1845 and by Clausius in 1857. In its more general form, it was formulated by Maxwell in 1860. Together with the relation between pressure and translational motion, given by the kinetic theory of gases, one can derive the equation of state of an ideal gas. One can also derive the Avogadro law, a fundamental law of physical chemistry as stated by Meyer and Mendeleev. From the equipartition of energy Boltzmann could explain the experimental ratio γ of the specific heats of diatomic gases, an explanation that was countered by Maxwell. We discuss these two conflicting explanation, and present an account and a critical analysis of the emergence of the law of equipartition of energy and other laws that preceded it but are understood as consequences or related to it. Our account includes also the Laplace relation between the speed of sound and γ, and the Clément and Desormes experiment to determine γ.