A prova teórica de Boltzmann
article, Poincaré stated that both mechanical collision processes and Döpler-Fizeau's law lead to the same energy-
sharing law. Poincaré also promised to write a theory that would be able to include ether in the interaction processes
between radiation and matter. This article published by Poincaré, will be discussed in a future publication.
Boltzmann had already published preliminary studies on this topic in the years 1866 (Boltzmann, 1968)and 1884
(L. Boltzmann, 1884), based on Maxwell's work in relation to the Kinetic Theory of Gases and the distribution of veloc-
ities. Thomas Kuhn (Khun, 1978) considers these works fundamental for the further development of Quantum Theory.
In this sense, Boltzmann is, when reinterpreting the laws of thermodynamics based on the notions of probability,
statistics and entropy, one of the main theoretical contributors of Quantum Theory, as well as Poincaré (Khun, 1978),
whose participation in the first Solvay Council in 1911 was fundamental to the developments later. We fully translated
the 1912 Poincaré article and published it in the Doctoral Thesis (Rosa, 2019). Charles Galton Darwin published a
commented English translation of Poincaré's article, which contributed to the acceptance of Planck's theory, since
English scientists were more likely to accept Wien's theory.
Based on the Kinetic Theory of Gases, Boltzmann theoretically demonstrated the empirical law of Dulong-Petit
(Laranjeiras, 2002) for ideal gases, but without using the Planck hypothesis, which appeared only in 1900. Einstein in
1907 (Einstein, 1906) when deducing an adjustment equation for the behavior of solid bodies, proved to be valid the
notion of quantization of harmonic oscillators proposed by Planck.
In the next topic, we will address the conceptual character of the Dulong-Petit law, analyzing the original publica-
tion (Dulong, Pierre L. y Petit, 1819) in French, as well as some controversial aspects about whether this law was
conceived by both or if it belonged to François Arago (Fox, 1968). This law was discovered during a period when there
was a fruitful debate about the corpuscular and undulating interpretation of the theory of heat (Brush, 1970).
II. THE DULONG-PETIT LAW AND THE CONTROVERSY WITH ARAGO
According to Fox (Fox, 1968), what the history of physics knows as Dulong-Petit's law, in fact, would have its origin in
Arago's research. The 1881 account of French chemist Jean Baptiste Dumas (Dumas, 1881) (Dumas, 1883) seems to
cast some doubt on the discovery of the law of specific heats for solid bodies.
Monday, April 5, 1819, a memorable date, Petit secretly showed his brother-in-law Arago a piece of paper, containing the
reports of how the simple bodies combine, and the quantities of heat required for each to heat in the same way, having the
same weight. At first, it seemed pure disorder, but when the two columns multiplied, all the products led to the same result.
An hour later, the illustrious perpetual secretary, convinced that Dulong, always hesitant, could oppose the disclosure of this
beautiful law, spoke of this to his colleagues, for a calculated indiscretion. Eight days later, the two collaborators announced
themselves to the Academy (Fox, 1968)
Fox omitted the passage in which Dumas comments about the misfortune of Petit's premature death, “ , dont un
an plus tard la science déplorait la mort prémature ”. The correct page of Dumas's text would be xlviij, not xlviii, as it
is in the footnote to Fox's article10. The publication date of the text also appears to be incorrect. Dumas's text was
published by the French Academy of Sciences on March 14, 1881 (Dumas, 1881)and Fox quotes it as being published
in 1883 (Dumas, 1883).
Perhaps Robert Fox's quotes are from publications after the original date. We are going to analyze Petit and Du-
long's text on the specific heat for solid bodies from the historical point of view, as it is an important empirical law
that does not appear in basic education textbooks and that in some way is associated with theoretical modification in
basics and mechanical interpretation of natural phenomena.
Initially Petit and Dulong's 1819 (Dulong et al, 1819)article makes clear the need to obtain simpler laws for the
composition of chemical compounds. These less complicated and more regular laws would be possible considering
that the material properties would be linked to the actions of individual molecules. Petit and Dulong observed that
Crawford and Irvine assumed that the amount of heat contained in the bodies would be proportional to their thermal
capacity, thus, whenever the specific heat of the compound was very high or the average chemical composition of its
elements, at the time of the combination, there would be absorption or release of heat.
According to Fox, all Dumas biographers claim that he came to Paris only in 1823, approximately three years after
Petit's death, strongly suggesting that the account had its origin in Arago. Fox, doubts Dumas' account, considering
that it is not correct in relation to the priority of the law. Due to Dumas` conflicting report, Fox decided to examine
their publications in the years immediately preceding the discovery of the law (Fox, 1968). What can be concluded is
that Arago, in fact, is acting as a defender and promoter of the Dulong-Petit law.
Petit and Dulong's article, Sur quelques points importants de la théorie de la chaleur, it can be considered histori-
cal, since it describes the empirical construction of a fundamental law of physicochemistry: the microscopic behavior
of atoms and molecules from the thermal point of view.
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REVISTA DE ENSEÑANZA DE LA FÍSICA, Vol. 35, n. o 2 (2023)