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The History of the Cooling Law: When the Search for Simplicity can be an Obstacle

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Abstract

This paper presents an historical overview of the research on the cooling law, from Newton until the beginning of 20th century, and provides some suggestions for the use of this history as a resource for teaching. This history begins with a description and an interpretation of Newton’s earlier work in 1701 and an overview of studies confirming or confuting Newton’s law during the 18th century. Subsequently, it presents the early studies on cooling due to radiant heat, the fundamental work of Dulong and Petit published in 1817, and a brief overview of the research conducted after 1850 on the laws of thermal radiation and of natural and forced convection. It is shown that many scientists persisted in maintaining Newton’s law, despite numerous evidence to the contrary, by attributing the found discrepancies to empirical errors or to other disturbance factors. Many scientists considered this law as a fundamental principle rather than a conjecture to be tested by means of experiments, while others were searching for a different but general and unique cooling law. The faith in the simplicity of natural laws and the spontaneous idea of proportionality between cause and effect seem to have strongly influenced Newton and many later scientists. A discussion of epistemological, methodological and pedagogical implications is offered.

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Notes

  1. See: http://www.nap.edu/catalog/4962.html, Chap. 6a, p. 107.

  2. See: Ruffner J. A. (1963); Molnar G. W. (1969); Grigull U. (1984); Winterton R. H. S. (1999); Simms D. L. (2004); Cheng K. C. (2009).

  3. The Scotsman Joseph Black (1728–1799) was the first to clearly understand, around 1760, the distinction between heat and temperature, but his ideas only diffused slowly after 1770 and his Lectures were published after his death in 1803. In his Lectures on the Elements of Chemistry (1803), he wrote that in a situation of thermal equilibrium usually scientists imagined that “there is an equal quantity of heat in every equal measure of space, however filled up with different bodies. The reason they give for this opinion is that to whichever of those bodies the thermometer be applied, it points to the same degree. But this is taking a very hasty view of the subject. It is confounding the quantity of heat in different bodies with its general strength or intensity, though it is plain that these are two different things, and should always be distinguished … The quantities of heat which different kinds of matter must receive, … to raise their temperature by an equal number of degrees, are not in proportion to the quantity of matter in each, but in proportions widely different from this, and for which no general principle or reason can yet be assigned… different bodies, although they be … of the same weight, when they are reduced to the same temperature or degree of heat, … may contain very different quantities of the matter of heat”.

  4. See Jones (1991).

  5. To be more precise, Newton did not consider that phase changes of pure substances take place at constant temperature, but rather over a small temperature interval. For example, he wrote: “Water begins to boil with a degree of heat of 33 parts, and by boiling scarcely acquires any greater degree than that of 34½ (Incipit aqua ebullire calore partium 33 & calorem partium plusquam 34½ ebulliendo vix concipit)”; and “96. Least degree of heat that melts lead; lead, by growing hot, is melted with the heat of 96 or 97 parts, and cooling it hardens with 95 parts.”.

  6. Ruffner (1963) had already remarked this aspect: “he [Newton] intends, ultimately, to define a scale of heat by means of his cooling law” (p. 149). Previously, E. Mach (1896) sustained that Newton’s argument was circular (Mach 1896, p. 60).

  7. The works of Richmann were considered very authoritative, so that some authors made reference to the cooling law (1–2) as Richmann’s law.

  8. Unless different indications are given, all quotations that were in Latin, in French or in German in the original were translated in English by the author of the present paper.

  9. Mackenzie (1989) develops an interesting presentation of the Martine’s life and works, but he writes erroneously (p. 1829) that Martine argued that the cooling law coincides with “that obeyed by a heavy body descending perpendicularly in a medium…” whilst it is matter of a body ascending vertically. Moreover, he specifies that this law “according to Newton’s Principia is a hyperbolic curve” represented by the Fig. 2. On the contrary, this law is not represented by a hyperbola, because it is an exponential function, and in the Martine’s paper Fig. 2 did not represent this law, but the cases in which this law is not valid.

  10. Manuscripts Copy of Journal Book of the Royal Society of London, 15 November 1716, quoted by Simms (2010), pp. 73–74.

  11. The quotations in the text make references to the book Rumford (1873) The Complete Works of Count Rumford, Vol. 2, which contains also a Historical Review Of The Various Experiments Of The Author On The Subject Of Heat, at pp. 188–240.

  12. The ideas of frigorific rays and of reflection and focusing of cold were previously sustained by G. Della Porta (1589) and confirmed by the Accademia del Cimento of Florence, in Italy (Saggi di Naturali Esperienze fatte nell’Accademia del Cimento (1667), p. 176, English translation in: Essayes of Natural Experiments made in the Academia del Cimento, trans. by R. Waller, London, 1684, p. 103). By contrast, Marc-Auguste Pictet, Pierre Prevost and other sustainers of material nature of heat interpreted these phenomena as a result of a peculiar arrangement of caloric transmission. An interesting controversy took place between Rumford and Prévost about the existence of cold radiation and the nature of heat. In fact, Rumford considered the existence of frigorific radiation as a strong argument against the caloric theory (see also Chang 2002).

  13. «Dans un milieu de température constant, un corps s’échauffe ou se refroidit, de sorte que les différences de sa chaleur à celle du milieu sont en progression géométrique, tandis que les tems de l’échauffement ou du refroidissement sont en progression arithmétique» (Prévost 1809, pp. 46–47).

  14. “Quelque cause trouble-t-elle la loi au-delà de certaines limites ?”.

  15. He wrote in French (Delaroche 1812, pp. 215 et 220) : «La quantité de chaleur qu'un corps chaud cède dans un temps donné par voie de rayonnement à un corps froid situé à distance, croît, toutes choses égales d'ailleurs, suivant une progression plus rapide que l'excès de la température du premier sur celle du second. Cette proposition n'est pas d'accord avec les opinions reçues. M. Leslie a même fait des expériences dont le résultat semble lui être directement contraire. Aussi ai-je cru devoir répéter plusieurs fois les expériences qui établissent sa justesse, et les varier de plusieurs manières… Je crois qu'en général la quantité de chaleur reçue est d'autant plus éloignée d'être proportionnelle à l'excès de la température du corps chaud sur celle du corps froid, que la température du premier devient plus élevée ; mais je n’ai pas multiplié assez mes observations, pour établir avec quelque précision, la loi suivant laquelle se fait l’accroissement de cette quantité de chaleur.».

  16. «lorsqu'un corps chaud A agit sur un autre corps B à distance et à travers l'air, la quantité de calorique rayonnant que celui-ci reçoit à chaque instant infiniment petit, n'est pas simplement proportionnelle à l'excès de la température de A sur la sienne, mais croit suivant une loi plus rapide, qui, dans les expériences citées, est exprimée par les deux premières puissances impaires de la température» (p. 24).

  17. «M. Dalton, en considérant la même question sous un point de vue beaucoup plus élevé, a essayé d'établir des lois générales applicables à la mesure de toutes les températures. Ces lois, il faut en convenir, forment un ensemble imposant par leur régularité et leur simplicité. Malheureusement cet habile physicien s'est trop empressé de généraliser des aperçus fort ingénieux, il est vrai, mais qui ne reposaient que sur des évaluations incertaines : aussi n'est-il presqu'aucune de ses assertions qui ne se trouve contredite par les résultats des recherches que nous allons faire connaître», p. 15.

  18. «c'est sans doute à l'extrême complication de cette loi qu'il faut attribuer le peu de succès des tentatives faites jusqu'à ce jour pour la découvrir. On ne pouvait évidemment y parvenir qu'en étudiant à part chacune des causes qui contribuent à l'effet total», p.367.

  19. In the original article in German, Boltzmann wrote: “In meinem Aufsatze über eine von Bartoli entdeckte Beziehung der strahlenden Wärme zum zweiten Hauptsatze habe ich gezeigt, dass sich zwischen den beiden Funktionen ψ und f aus dem zweiten Hauptsatze die Beziehung ergibt f = t ∫ψdt/t 2 , deren Differential lautet: tdf−fdt = ψdt, wenn also, wie aus der elektromagnetischen Lichttheorie folgt, f = 1/3ψ gesetzt wird, so erhält man: t·dψ/3 = 4ψdt/3 und durch Integration ψ = ct 4 , ein Gesetz, welches bekanntlich schon vor längerer Zeit von Stefan empirisch aufgestellt und in guter Übereinstimmung mit den Beobachtungen gefunden wurde”.

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    Ugo Besson

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Besson, U. The History of the Cooling Law: When the Search for Simplicity can be an Obstacle. Sci & Educ 21, 1085–1110 (2012). https://doi.org/10.1007/s11191-010-9324-1

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