Dulong-Petit’s law and Boltzmann’s theoretical proof from the Kinetic Theory of Gases

Abstract

The main aspect that we will address in this work is the introductory presentation of the empirical law of the specific heats of material bodies, published by Dulong and Petit on April 12, 1819, in the magazine Comptes Rendus. The analytical demonstration of this law appeared for the first time in 1866 in the Doctoral Thesis of the Austrian physicist Ludwig Boltzmann, according to the research carried out by Cássio C. Laranjeiras and presented in his Doctoral Thesis in 2002. In the introduction we discussed how Dulong’s law and Petit played a key role in the subsequent development of a new physics (Quantum Mechanics), when Max Planck changed his research program from electrodynamics to thermodynamics, evidenced in the book: Black Body Theory and the Quantum Discontinuity, 1894-1912, published by Thomas Khun in 1978. Between 1900 and 1912, we observed that fundamental works published by Albert Einstein, Henri Poincaré and Peter Debye explained the mathematical relationship of this empirical law based on Planck’s hypothesis of the quantum of action of blackbody radiation. Despite the controversy over the authorship of the law, whether it would have been formulated in advance by Arago, we agree with Robert Fox that it was the results of Dulong and Petit’s experiments that led to the formulation of the law.