Absolute Zero and the Conquest of Cold (14 page)

His break with the past started in Paris at the moment when colleagues at Regnault's laboratory introduced him to Clapeyron's exegesis of Carnot. This single article began to deeply affect Thomson's thinking about heat and cold, so much so that he roamed the bookstores of the city seeking a copy of Carnot's
Réflexions,
but could not find a copy to buy, nor even one to study in a library.

The second son of a professor of engineering at the University of Glasgow, William had matriculated there at the age of ten, partly to accompany his older brother, James—the boys' mother had died when William was six. The brothers' minds and interests were complementary, the future engineer James often playing the role of what a later colleague dubbed "the philosopher, who plagued his pragmatical brother." Both held firm beliefs in God, and in God as the first cause of the physical universe, though James was more doctrinaire in religious adherence.

William Thomson was a person so bursting with ideas that he seldom restrained himself enough to allow a partner in a conversation to finish a thought before voicing another of his own. At Glasgow, he studied the great French mathematicians so intently that at age seventeen he produced a paper,
On Fourier's Expansions of Functions in Trigonometrical Series.
As though to prove that was no flash in the pan, when he transferred to Cambridge the next year he wrote
On the Uniform Motion of Heat ... and Its Connection with the Mathematical Theory of Electricity,
drawing mathematical parallels between the operations of heat and electricity to help explain how heat reaches equilibrium; the certitude and depth of understanding of the eighteen-year-old were breathtaking. By 1845, when he graduated from Cambridge in the position of second "wrangler"—the first prize having gone to a man who paid more attention to his studies while Thomson busied himself writing two additional, highly praised papers—William was already viewed as belonging in the top rank of scientific intellects, and only by age a junior member of the scientific establishment.

It was with his bent toward synthesis and his growing fascination with Carnot in mind that Thomson, along with Stokes, attended a session of the British Association for the Advancement of Science (BAAS) in June 1847 and heard something that affected him—and the history of work on the cold—even more than his introduction to Carnot: the clarion call of James Joule.

The "British Ass" had begun in 1830 in response to a scathing attack on the scientific establishment that charged that British science was inadequate, poorly taught in universities, and ignored by the government. Seventeen years after its birth, the BAAS had become the most important annual colloquium of serious scientists. They swelled the lists of presenters in attendance at the June 1847 session to the point that the chairman of the Mathematics and Physics section, on the grounds that it was the end of a long day, refused to permit Joule to make a full presentation. However, in the few minutes allotted, Joule exhibited the paddle wheel he employed to measure how fluid friction generated heat.

The genius of science often expresses itself when someone recognizes as important a fact or an idea that others pass over as inconsequential. Such a fact was Joule's experimentally proved data that a paddle wheel moving through water produces heat. This fact was startling—first, because it demonstrated that heat was generated by a method no one had ever thought about in that connection, and second, because it undermined the caloric explanation of heat. Joule believed that his work on the paddle wheel would have sunk into obscurity had not a man in the back of the hall stood up and asked penetrating questions. Thomson remembered the occasion differently; he had wanted to rise with an objection—that Joule was contradicting Carnot—but realized, as he later wrote, that "Joule had a great truth and a great discovery, and a most important measurement to bring forward." So, according to Thomson, he and Stokes waited until the meeting ended to approach Joule and start a discussion.

"Joule is I am sure wrong in many of his ideas, but he seems to have discovered some facts of extreme importance, as for instance that heat is developed by the friction of fluids in motion," William wrote to brother James, enclosing two papers the Manchester brewer had given him, which he predicted would "astonish" James. His brother, who had along with William become a professor at Glasgow, agreed, finding a key inconsistency in one of Joule's conclusions but praising Joule's data as derived from experiment, and predicting that Joule's ideas would "unsettle" anyone who had become convinced by Carnot as interpreted by Clapeyron.

William Thomson was completing work on a thermometric scale inspired by Carnot, whose original book he had still not located. The Reaumur, Fahrenheit, and centigrade scales were merely "arbitrary series of numbered points of reference," Thomson argued, because each degree did not represent precisely the same amount of work. He constructed an "absolute" scale using Carnot's notion that a given amount of heat passing between two temperatures can produce only a particular amount of work. On Thomson's scale each one-degree increment represented an amount of work equal to that of every other one-degree increment. Thomson's scale was independent of the kind of material in the thermometer, and in that sense it was "absolute." Later, Rudolph Clausius suggested a mathematical change to make Thomson's absolute scale conform approximately to centigrade scales. In the previous hundred years a dozen different numbers had been suggested as the value of absolute zero, and these guesses varied by as much as 1,000 degrees Fahrenheit. Thomson was happy to have absolute zero determined by his French mentor, Victor Regnault, who—with his usual thoroughness—had averaged the calculations done by four methods to come up with—272.75°C.
^*
Years later, after Thomson was awarded the title of Lord Kelvin, his absolute scale would become known as the Kelvin scale, used in the many concerted attempts to understand the region of utmost cold.

Today Kelvin is generally known for that scale, in the short form of science history—but it was actually a lateral matter emerging from his work on the scale that more markedly advanced scientific understanding of heat and especially of cold: his interaction with James Joule. In a footnote to the absolute-scale article, Thomson paid homage to Joule's "very remarkable discoveries," but he also contended that Joule had not proved the interconvertibility of heat and work. He ignored entirely Joule's idea that caloric might not exist. Professional courtesy would have insisted that Thomson send this paper to Joule before presenting it, so Joule could have a chance to rebut the remarks about his work, but Thomson did not send it. There is something very sad about his callous treatment of Joule in this initial period; Stokes corresponded with Joule easily, as with a comrade in arms, but Thomson seems to have been unwilling to permit a brewer from Manchester, who had not trained at Cambridge or Oxford, to have thoughts on his own level, even though he could not help being troubled by Joule's ideas. When Joule read Thomson's article in a journal, he fired off a private letter to Thomson that praised him but would not let him off the hook. Joule reasserted that he had proved the interconvertibility of heat and work, as opposed to Carnot's supposition that heat could perhaps be entirely annihilated.

Agonized, Thomson responded with a nineteen-page missive, confessing his inability to answer Joule's objections, especially Joule's objection to Carnot, but saying he also believed that Carnot was correct and hoped to reconcile the two at some point in time.

He tried hard to do so—after a friend finally gave him a copy of the
Réflexions—
in an 1849 article that was a total analysis of Carnot. In it, Thomson restated a Carnot proposition, writing that "nothing can be lost in the operations of nature—no energy can be destroyed." But then Thomson went on to ask a key, Joule-inspired question: When (as Carnot contended) "thermal agency" was spent in conducting heat from a hot to a cold body, "what becomes of the mechanical effect that it might [otherwise] produce?" Thomson had as yet no answer for that question.

William's brother James tried to resolve for him what still seemed like a contradiction between Carnot and Joule. Long ago Robert Boyle had proved that water expands with "terrific" force when it becomes ice; if Carnot was correct, James argued, then that physical change from water to ice—from hotter to colder—ought to produce some useful work. But since the temperature of both water at the freezing point and ice at the melting point was the same, o°C, there seemed to be
no
work done during the change. James showed that when pressure lowered the melting point of ice, making the conversion from water to ice into an action accompanied by a fall in temperature, work was indeed done. William embraced this result as a vindication of Carnot.

Even with James's help, William Thomson in 1849 could not reconcile Carnot and Joule, and that may have stalled his train of thought about heat for a while. His research was also affected by the sudden death of his father—which, he wrote to a friend, was "of a single event, the greatest grief of my life," so dreadful that he feared it would break up the family, which it shortly did. Of course, even when William put aside heat for two years, he still managed to write a major paper on magnetism.

During those two years, Rudolf Clausius of Germany found the way to reconcile Carnot and Joule, thus opening the door for a great deal of further research into heat and cold. In 1850 Clausius was twenty-eight, and his doctorate was newly minted. During his youth in the Prussian part of Poland he had studied music, coming late to mathematics and physics—and perhaps this was the essential difference between his approach and that of Thomson: Clausius's vision was not obscured by the same Idols of the Theatre and of the Tribe that had held Thomson in thrall. Clausius had not been overly steeped in the long traditions of French mathematics and caloric theory, and so he could reach conclusions that Thomson could not yet accept. Also, Clausius drew on relatively recent writing about heat: the opus of Mayer, by this time so addled by rejection and mental illness that he had stopped writing papers; that of another medical doctor, Hermann von Helmholtz; that of Joule, whose work Helmholtz had relied upon but disparaged; and the work of Regnault, Clapeyron, and Thomson himself. The only thing Clausius had not read was Carnot's book, since he could not find a copy either.

In Clausius's view, in an engine that produced work, two things happened simultaneously: some of the heat was converted (Joule's notion),
^*
while another portion of the heat was simply transferred from the hotter body to the colder one (Carnot's notion). In other words, the ideas of Joule and Carnot were not mutually exclusive; their theories represented two events occurring at the same time, so there was no real contradiction between them. Clausius then deduced two laws of thermodynamics: the first, that the total amount of energy is always conserved, even when heat seems to disappear (because it is simply being converted to other forms of energy); and the second, that the general tendency in nature is for heat to always flow from hot to cold, not the reverse. Clausius proved the second law by showing that the opposite of it was false. He argued that if heat was able to flow from cold to hot "without any expenditure of force or any other change," then one could devise a perpetual-motion machine that would continually pour energy back and forth from hotter to colder to hotter bodies—and therefore, since everyone knew that perpetual motion was impossible, the notion of irreversible flow had to be true.

In his paper, Clausius cited the primacy of Mayer and Helmholtz, to the detriment of Joule, in an ongoing skirmish—it did not rise to the level of a battle—more based on national pride than on primacy of ideas. German and British scientific establishments had long been rivals, with most of the laurels for discoveries going to the British; but with German science coming into its maturity, Clausius wanted to refer to German antecedents. It was also payback, as Joule and Thomson appeared to have ignored Mayer and in general to have slighted German work. Actually, Joule had first been alerted only in 1848 to the possible importance of Mayer's early papers, and since then he had struggled to personally translate them into English. Thomson, too, had never read Mayer, but he would shortly go out of his way to cultivate the friendship of Helmholtz. Also, as historians of science confirm, the interconvertibility of heat and work, and the conservation of energy, were better and earlier stated by Joule than by Helmholtz or Mayer.

When Thomson in February 1851 came to his own formulation of the laws of thermodynamics, he claimed to have evolved them mostly by himself, not having learned about Clausius's paper until after completing his own first draft. He seems also to have avoided accepting the insights of the Scottish engineer and physicist W. J. M. Rankine, who had reached much the same conclusions in a paper that also had been published in the interim.

It might seem to the layperson that the first law of thermodynamics, that energy is conserved in the universe, is a pretty straightforward concept and one rather easy to comprehend. But Thomson's path to this and to the second law was tortuous. His seminal article that states the laws made it clear that Thomson's work derived from that of Joule and from the observations of Regnault, and also owed a great deal to his changed understanding of God's relationship to the natural world. Splitting theological hairs, Thomson wrote, in his version of the first law, that "mechanical effect" could be

lost to man
irrecoverably though
not lost in the material world,
[because although] no destruction of energy can take place in the material world without an act of power possessed only by the supreme ruler, yet transformations take place which remove irrecoverably from the control of man sources of power which, if the opportunity of turning them to his own account had been made use of, might have been rendered available.