Inventing Temperature

by Hasok Chang

  The tradition of caloric theories described as "chemical" in chapter 2, led by Lavoisier, could avoid the experimental failure of Irvinism because it had postulated two different states of caloric (free/sensible vs. combined/latent). In the chemical caloric theory, temperature was conceived as the density (or pressure) of free caloric only, since latent caloric was usually conceived as caloric deprived of its characteristic repulsive force, hence unable to effect the expansion of thermometric substances. But it was impossible to refute the various chemical-calorist doctrines by direct experiment, since there was no direct way to measure how much caloric was going latent or becoming sensible again in any given physical or chemical

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  process, not to mention how much total latent caloric was contained in a body. Rumford came up against this irrefutability when he tried to argue against the caloric theory on the basis of his famous cannon-boring experiment. In Rumford's own view, his experiment disproved the caloric theory because it showed that an indefinite amount of heat could be generated by friction (motion). For the leading calorists, Rumford's experiment only showed the disengagement of combined caloric as a consequence of the mechanical agitation, and no one knew just how much combined caloric was there to be released in such a manner.15

  The chemical calorists also refused to accept the Irvinist identification of specific heat and heat capacity. For them the very concept of Irvinist heat capacity was meaningless, and specific heat was simply a measure of how much heat a body required to go from temperature T° to temperature (T + 1)°, which was actually a variable function of T. We have seen in Haüy's critique of De Luc, in "Caloric Theories against the Method of Mixtures" in chapter 2, how indeterminate the relation between temperature and heat input became under the chemical caloric theory. Haüy's work was probably among the best contributions from that tradition to thermometry, but still it could only play a negative role. As discussed in "The Calorist Mirage of Gaseous Linearity" in chapter 2, the later theoretical work by Laplace further weakened the link between the theory and practice of thermometry, despite his aims to the contrary. Laplace redefined temperature as the density of the "free caloric of space," to which one had no independent observational access at all, and which was postulated to be so thinly spread that it would have been undetectable for that reason in any case. Laplace's derivations of the gas laws only amounted to a spurious rationalization of the existing practice of gas thermometry, rather than adding any real insight or concrete improvement to it. All in all, it is not surprising that the serious practitioners of thermometry, including Regnault, mostly disregarded the latter-day caloric theory for the purposes of their art.

  If the caloric theories failed to link thermometry effectively to the theoretical concept of temperature, did other theories do any better? Here the modern commentator will jump immediately to the collection of theories that can be classified as "dynamic" or "mechanical," built on the basic idea that heat consists of motion, since that is the tradition that eventually triumphed, though after many decades of neglect during the heyday of caloric theories. Note, however, that the dynamic theories that were in competition with the caloric theories bore very little resemblance to the dynamic theories that came after thermodynamics. Despite a very long history including a phase of high popularity in the context of seventeenth-century mechanical philosophy, dynamic theories of heat were not developed in precise and quantitative ways until the nineteenth century.

  15. This famous experiment is described in Rumford [1798] 1968. For typical examples of calorist rebuttals, see Henry 1802, and Berthollet's discussion reproduced in Rumford [1804a] 1968, 470-474. Rumford's own conception of the caloric theory was clearly of the Irvinist variety, as shown in his attempt to argue that the heat could not have come from changes in heat capacity by confirming that the specific heat (by weight) of the metal chippings was the same as the specific heat of the bulk metal.

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  The first dynamic theorist that we should take note of is indeed Rumford, who has often been hailed as the neglected pioneer whose work should have toppled the caloric theory but did not. However, as intimated by his advocacy of positive cold radiation discussed briefly in the previous section, Rumford's theory of heat was very far from the modern kinetic theory. As was common during that time, Rumford envisaged molecules of matter as vibrating around fixed positions even in gases, not bouncing around in random motion. Rumford presumed temperature to be defined by the frequency of the vibrations, but he vacillated on this point and expressed a suspicion that it might really depend on the velocities that the molecules took on in the course of their oscillations.16 It is important not to read modern conceptions too much into Rumford's work. He believed that the vibrating molecules would continually set off vibrations in the ether without themselves losing energy in that process. He also rejected the idea of absolute zero because he did not consider temperature as a proper quantity: Hot and cold, like fast and slow, are mere relative terms; and, as there is no relation or proportion between motion and a state of rest, so there can be no relation between any degree of heat and absolute cold, or a total privation of heat; hence it is evident that all attempts to determine the place of absolute cold, on the scale of a thermometer, must be nugatory. (Rumford [1804b] 1968, 323)

  This opinion regarding the absolute zero was shared by Humphry Davy (1778-1829), Rumford's protégé in the early days of the Royal Institution, and fellow advocate of the dynamic theory of heat: "Having considered a good deal the subject of the supposed real zero, I have never been satisfied with any conclusions respecting it. … [T]emperature does not measure a quantity, but merely a property of heat."17

  Instead of Rumford, we might look to the pioneers of the kinetic theory of gases, who believed in the random translational motion of molecules, because they are the ones who created the modern theoretical idea that temperature is a measure of the kinetic energy of molecules. But even there the situation is not so straightforward. (On the history of the kinetic theory, I will largely rely on Stephen Brush's [1976] authoritative account.) Very early on Daniel Bernoulli (1700-1782) did explain the pressure of gases as arising from the impact of molecular collisions and showed that it was proportional to the vis viva of individual molecules (mv2 in modern notation), but he did not identify molecular vis viva as temperature. The first theoretical conception of temperature in the kinetic theory seems to have been articulated by John Herapath (1790-1868) in England, who composed an important early article on the subject in 1820. But Herapath's idea was that temperature was proportional to the velocity of the molecules, not to the square of the velocity as the modern theories would have it. In any case, Herapath's work was largely ignored by the scientific establishment in London, and for a time he was reduced to publishing some of his scientific articles in the Railway Magazine, which

  16. See Rumford [1804b] 1968, 427-428; see also the brief yet interesting commentary on this matter in Evans and Popp 1985, 749.

  17. Letter from Davy to John Herapath (6 March 1821), quoted in Brush 1976, 1:118.

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  he edited. The only real impact his work had was made through James Joule, who made use of some of Herapath's ideas in the late 1840s.18

  Even worse reception than Herapath's awaited the work of the Scottish engineer John James Waterston (1811-1883), who is the first person on record to have identified temperature as proportional to mv2, starting in 1843. Waterston's paper submitted to the Royal Society in 1845 was flatly rejected and did not see the light of day until Lord Rayleigh discovered it in the Society's archives in 1891 and had it published in the Philosophical Transactions finally. The same idea was put into real circulation only through the work of Rudolf Clausius (1822-1888), whose publications on the matter started in 1850.19 By that time Thomson had already published his first definition of absolute temperature, and macroscopic thermodynamics was to be the most important vehicle of progress in the theory of heat for a time.

  In short, up
to the middle of the nineteenth century there was a good deal of disagreement about what temperature meant in a dynamic theory of heat. Besides, even if one accepted a certain theoretical definition, it was not easy to make a successful bridge between such a definition and actual measurement. In fact Herapath was probably the only one to build a clear operational bridge, by declaring that the pressure of a gas was proportional to the square of its "true temperature." But both his theoretical conception and his operationalization were seen as problematic, and there is no evidence that anyone took up Herapath's thermometry.20 Meanwhile neither Waterston nor Clausius came up with a method of operationalizing their concept of temperature as proportional to the average kinetic energy of molecules. In fact, even in modern physics it is not entirely clear how easily that concept can be operationalized (except by sticking an ordinary thermometer in a gas).

  William Thomson's Move to the Abstract

  We can appreciate the true value of Thomson's work on thermometry when we consider the failure in both of the major traditions of heat theory, discussed in the last section. He crafted a new theoretical concept of temperature through an ingenious use of the new thermodynamic theory and also made that concept measurable. William Thomson (1824-1907), better known to posterity as Lord Kelvin, was one of the last great classical physicists, who made many key advances in thermodynamics and electromagnetism, and worked tenaciously to the end of his life to create a viable physical theory of the ether. Son of a Belfast-born Glasgow professor of mathematics, precocious Thomson received just about the best conceivable

  18. See Brush 1976, 1:20 on Bernouilli's work, 1:69, 110-111 on Herapath's ideas, and 1:115-130 on Herapath's general struggle to get his views heard (not to mention accepted). See Mendoza 1962-63, 26, for Joule's advocacy of Herapath's ideas.

  19. See Brush 1976, 1:70-71, for Waterston's basic idea; 1:156-157, for the circumstances of its publication; and 1:170-175, for Clausius's contribution.

  20. See Brush 1976, 1:111-112, for an explanation of Herapath's conception of temperature.

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  scientific education: early study at home was followed by attendance at Glasgow University, then a Cambridge degree in mathematics, rounded out by further study and apprenticeship in the heart of the scientific establishment in Paris. At the unlikely age of 22, Thomson was appointed to the chair of natural philosophy at Glasgow, which he held from 1846 to 1899. His early reputation was made in mathematical physics, especially through his able defense of Fourier's work and its application to electrodynamics. Later in life Thomson became absorbed in various practical applications of physics, including the laying of the much-celebrated Atlantic telegraph cable. It was characteristic of Thomson's work to insist on an abstract mathematical formulation of a problem, but then to find ways of linking the abstract formulation back to concrete empirical situations, and his work in thermometry was no exception.21

  It is important to keep in mind just how much Thomson's thermometry arose out of an admiring opposition to Victor Regnault's work, which I examined in detail in chapter 2. Thomson's sojourn in Paris occurred when Regnault was beginning to establish himself as the undisputed master of precision experiment. Following an initial introduction by Biot, Thomson quickly became one of Regnault's most valued young associates. In the spring of 1845 he reported from Paris to his father: "It has been a very successful plan for me going to Regnault's laboratory. I always get plenty to do, and Regnault speaks a great deal to me about what he is doing. … I sometimes go to the lab as early as 8 in the morning, and seldom get away before 5, and sometimes not till 6." Thomson's duties in the lab evolved from menial duties, such as operating an air pump on command, to collaboration with Regnault on the mathematical analysis of data. By 1851 we find Thomson paying a visit back to Paris, and subsequently spending a good deal of time writing out an account of the new thermodynamic theory for Regnault. To the end of his life Thomson recalled Regnault's tutelage with great fondness and appreciation. At a Parisian banquet held in his honor in 1900, Thomson (now Lord Kelvin) recalled with emotion how Regnault had taught him "a faultless technique, a love of precision in all things, and the highest virtue of the experimenter—patience."22

  Thomson's first contribution to thermometry, a paper of 1848 presented to the Cambridge Philosophical Society, began by recognizing that the problem of temperature measurement had received "as complete a practical solution … as can be desired" thanks to Regnault's "very elaborate and refined experimental researches." Still, he lamented, "the theory of thermometry is however as yet far from being in so satisfactory a state" (Thomson [1848] 1882, p. *100). As I discussed in detail in "Regnault: Austerity and Comparability" in chapter 2, Regnault had just consolidated his precision air thermometry by shrinking from theoretical speculations

  21. The most extensive and detailed existing accounts of Thomson's life and work are Smith and Wise 1989 and Thompson 1910. A briefer yet equally insightful source is Sharlin 1979.

  22. For records of Thomson's work with Regnault, see Thompson 1910, 117, 121-122, 126, 128, 226, 947-948, 1154. Thomson's letter to his father (30 March 1845) is quoted from p. 128 and his 1900 speech from p. 1154.

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  about the nature of heat and temperature. Consonant with the disillusionment with abstract theory that was particularly widespread in France (see "Regnault and Post-Laplacian Empiricism" in chapter 2), Regnault's attitude was that basic measurements had to be justified in themselves. Those who wanted to found measurements on some theory which in itself was in need of empirical verification, had got the epistemic order of things exactly backwards. Much as the young Glaswegian professor admired Regnault's work, this austere antitheoretical manner of doing science apparently did not appeal to Thomson.

  Thomson did appreciate quite well the powerful way in which Regnault had used the comparability criterion for rigorous practical thermometry, demonstrating that the air thermometer was a good instrument to use because it gave highly consistent readings even when its construction was made to vary widely. Even so, Thomson complained: Although we have thus a strict principle for constructing a definite system for the estimation of temperature, yet as reference is essentially made to a specific body as the standard thermometric substance, we cannot consider that we have arrived at an absolute scale, and we can only regard, in strictness, the scale actually adopted as an arbitrary series of numbered points of reference sufficiently close for the requirements of practical thermometry.23

  So he set about looking for a general theoretical principle on which to found thermometry. He needed to find a theoretical relation expressing temperature in terms of other general concepts. The conceptual resource Thomson used for this purpose came from something that he had learned while working in Regnault's laboratory, namely the little-known theory of heat engines by the army engineer Sadi Carnot (1796-1832), which Thomson himself would help to raise into prominence later. It is useful here to recall that "Regnault's great work" was the result of a government commission to determine the empirical data relevant to the understanding of steam engines.24 As Thomson was attempting to reduce temperature to a better established theoretical concept, the notion of mechanical effect (or, work) fitted the bill here. A theoretical relation between heat and mechanical effect is precisely what was provided by a theory of heat engines. Thomson explained: The relation between motive power and heat, as established by Carnot, is such that quantities of heat, and intervals of temperature, are involved as the sole elements in the expression for the amount of mechanical effect to be obtained through the agency of heat; and since we have, independently, a definite system for the measurement of quantities of heat, we are thus furnished with a measure for intervals according to which absolute differences of temperature may be estimated. (Thomson [1848] 1882, 102; emphases original)

  23. Thomson [1848] 1882, 102; emphases original; see also Joule and Thomson [1854] 1882, 393.

  24. See the introductory chapter in Regnault 1847 for the way he conc
eptualized the operation of a heat engine, which was actually not so different from Carnot's framework.

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  Carnot's theory provides a theoretical relation between three parameters pertaining to an abstractly conceived heat engine: heat, temperature, and work. If we can measure heat and work directly, we can infer temperature from the theory.

  It is necessary to explain at this point some elements of Carnot's theory and its background. (This is a digression, but a necessary one for a true understanding of Thomson's work, which is the end point of our narrative. Readers who are already familiar with the history of heat engines and the technical aspects of Carnot's theory can skip this part and proceed directly to page 181.) The widespread interest in the theory of heat engines in the early nineteenth century owed much to the impressive role that they played in the Industrial Revolution. The phrase "heat engine" designates any device that generates mechanical work by means of heat. In practice, most of the heat engines in use in Carnot's lifetime were steam engines, which utilize the great increase in the volume and pressure of water when it is converted into steam (or their decrease when steam is condensed back into liquid water). Initially the most important use of steam engines was to pump water in order to drain deep mines, but soon steam engines were powering everything from textile mills to ships and trains. It is not the case that the steam engine was invented by the Scottish engineer James Watt (1736-1819), but he did certainly make decisive improvements in its design. I will note some aspects of his innovations here, because they are closely linked with certain features of Carnot's theory. Watt, like Wedgwood (see "Adventures of a Scientific Potter" in chapter 3), worked on a very interesting boundary between technology and science. Early in his career Watt was a "mathematical instrument-maker" for the University of Glasgow, where he worked with Joseph Black and John Robison. Later he established his firm with Matthew Boulton near Birmingham and became a key member of the Lunar Society, associating closely with Priestley and Wedgwood among others, and with De Luc, who was an occasional but important visitor to the Lunar circle.25