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.

Max Planck’s Determination of the Avogadro Constant

“…Although the expression pv = RT appeared before, as in the work of É. Clapeyron and R. Clausius [9] the quantity R was not yet to be considered an universal constant because it depended on the gas being used. Nernst attributes to Horstmann [10] the use of Avogadro's rule to make this conclusion about the gas constant [11,12].…”

Sobre a Dedução do Axioma de Carathéodory da Segunda Lei da Termodinâmica dos Princípios de Clausius e Kelvin

“…Já perceba aqui a distinção física que esse formalismo nos fornece ao nos dizer matematicamente que a energiá e uma função de estado do sistema e, portanto, está 6 Existem outros caminhos possíveis para isso [7,[14][15][16].…”

“…Com isso, Gibbs influenciou várias obras populares de termodinâmica clássica que surgiram posteriormente [4,5]. Essas obras construíram uma termodinâmica clássica de postulados, introduzindo noções termodinâmicas fundamentais como a entropia na forma de conceitos elementares dos quais os outros conceitos da teoria se derivam [6]. De forma geral, chamamos aqui de formalismo de Gibbs os formalismos devidos ao pioneiro trabalho de Gibbs.…”

Determination of the adiabatic heat capacity of gases using the Clément-Desormes method

“…Although the Clément-Desormes method with initial rarefaction (P2 < P1) can be used to determine CA or CP, the accuracy will be not high. In the first experiment carried out by Clément and Desormes in 1819 [12] , the values used were P1 = 766.5, P2 = 752.69, and P3 = 762.889 mm Hg. When the stopcock is open, the atmospheric pressure begins to compress the air in the bottle.…”