Absolute Zero and the Conquest of Cold (12 page)

He gravitated to the Conservatoire des Arts et Métiers, a recently founded technological museum that scandalized establishment scientists by offering lectures to the general public. In addition to being a temple of the practical, the Conservatoire was a hotbed of liberal, antiroyalist sentiments, which Sadi shared. Among its stalwarts were two men who came from the same region as Carnot, Nicolas Clément and Charles Bernard Desormes, brothers-in-law who did joint research on the physics of steam engines. All three felt keenly France's military loss to England, understood that French industry needed a boost to prevent England's burgeoning mills and factories from eclipsing France's own, and believed that the way to improve industry was to better understand the principles behind the operation of machines.

Sadi Carnot devoted the years from 1820 to 1824 to the 118-page
Réflexions,
which he self-published in an edition of 600 copies. The book remained obscure until well after his death. Among the reasons for its being ignored during his lifetime: it was not written by an Académie-certified expert, was not published in an establishment periodical, and did not contain original experimental results. Pointing out that the steam engine had become more important for the economic health of England than its navy, Carnot set out to explain why the newer steam engines were more efficient than James Watt's original, to establish the maximum efficiency of an engine under ideal conditions, and to deduce from that inquiry the general relationship between heat and mechanical work. His thesis was that the action in the steam engine was a function of temperatures and that the power of the engine had to do with the fall in temperature from hotter to colder. He drew on earlier attempts—by his father, among others—to improve the water-wheel engine, in which power derived from the volume of water and the length of time it was in contact with the wheel, during which the water was carried from high point (entry) to low point (exit). The action in the steam engine, he insisted, was analogous, the "motive power" of its heat depending "on what we shall call the height of its fall, that is, on the temperature difference of the bodies between which the caloric flows."

Carnot's central tenet was that mechanical work was produced in proportion to the fall (of caloric) between higher- and lower-temperature bodies. He undermined his argument somewhat by relying on the theory of caloric. Antoine Lavoisier, the father of French chemistry, had died on the guillotine in 1794, but his theory of caloric had lived on. Carnot was actually uneasy with caloric; acknowledging critics of caloric such as Count von Rumford and Humphry Davy, he wrote that the basic principles of the caloric theory of heat needed "close attention" because "many experimental results would seem to be nearly inexplicable according to the present state of the theory." But he also balanced their criticism by citing a series of prizewinning French experiments done in 1812 on the specific heat of gases in relation to their density, the results of which seemed to shore up the notion of caloric.

Unknown to Carnot, the figures obtained in the 1812 experiments were wrong, an error that the historian of caloric, Robert Fox, calls "one of the most influential in the whole history of the study of heat. Backed by the prestige associated with victory in [an official] competition, the result quickly became standard and ... misled many calorists."

With hindsight, we can see that Carnot's discovery did not depend on caloric: he asserted that mechanical work would not be produced unless heat was transferred from a body at a high temperature to a body at a lower temperature, and that the greater the temperature difference between those two bodies, the more work done. Carnot's four-stage ideal engine required, for backward operation, the same input of work as the output when run forward. This alternation was crucial to his contention that the maximum amount of work possible was done in an engine with reversible processes. But while the processes might be reversible, the temperature direction of the flow emphatically was not. Donald Cardwell, a modern historian of thermodynamics, points out that only Carnot, of all who wrote about engines in this era, recognized that "the vast majority of thermal and thermomechanical changes are ... irreversible."
A quarter century later, after the theory of caloric had been disproved, that irreversibility led Rudolf Clausius and Lord Kelvin (William Thomson) to formulate the second law of thermodynamics; in the late twentieth century, Carnot's understandings of the working of the ideal steam engine led to many advances in the generation of ever lower temperatures achieved by means of a "Carnot cycle" used to produce cold close to absolute zero.

Among the reasons Carnot could not accept all the implications of the irreversibility he postulated was that he agreed with a pillar of the mechanistic universe, the notion of the conservation of all matter and forces. This idea contended that everything in the universe was already in existence, and nothing could be created or destroyed. It was a belief with religious origins, and Carnot could not afford emotionally to accept the damage to it that his own insight would bring. The idea that matter could indeed be irrevocably destroyed or changed in some not-yet-understood way was a frightening concept to this otherwise clear-eyed scientist.

Carnot presented
Réflexions
before the Académie. There was a long and appreciative review of it in one journal, a brief notice in another, and an encomium by Clément recommending it to students, but the book brought the author no renown. After the publication, Carnot was briefly activated again in the army, then returned to Paris, where he described himself in 1828 as a "constructor of steam engines." His studies, now more specifically dealing with the physics of gases, were interrupted by the revolution of 1830, which toppled Charles X, restored a degree of popular sovereignty, and established a new king. Carnot became part of a cohort of École Polytechnique graduates who supported the new order. In the spring of 1832 an inflammation of the gorge confined him to his bed; by summer he was so weak that he could not fight off cholera, and he died in August. That Carnot died at Charenton, a hospital associated with the insane, occasioned some historians to say he went mad; but Charenton was used for cholera patients in 1832 because other hospitals were overcrowded, and in the hope that isolating those with cholera would halt the progress of the disease through the population.

Unknown at the time of Carnot's death, but of importance to our story, was that around 1830 he had come to the realization that the caloric theory was wrong. The corpuscular theory of the transmission of light had been disproved, and experiments were demonstrating the likelihood that electricity, light, and magnetism were not the products of separate "forces" but were interrelated. In terms of heat and caloric, Carnot asked, "How can one conceive of the forces agitating the molecules, if they are never in contact with one another, if each [molecule] is perfectly isolated? Supposing that there is a subtle fluid interposed doesn't reconcile the difficulties, because that fluid would necessarily be composed of molecules." This reasoning led to an important conclusion:

Heat is nothing other than motive power, or perhaps motive power that has had a change of form. If there is a destruction in the particles of a body, there is at the same time heat production in a quantity precisely proportional to the quantity of motive power that is destroyed; reciprocally, in every configuration, if there is destruction of heat, there is production of motive power.

This understanding of how heat was transformed into motive power pushed Carnot to boldly state a modification of the everything-in-nature-is-preserved notion that he had been unwilling to make in 1824 but that he could no longer avoid:

that the quantity of motive power in nature is invariable, that it is never properly speaking produced nor destroyed. Truly it changes form, sometimes manifesting itself as one kind of movement, sometimes as another, but it is never annihilated.

Carnot was reaching here for a concept that he could not elucidate and that would take another quarter century to be defined and understood: energy. It is energy that is never annihilated, merely manifested as one or another kind of movement. Carnot didn't quite get the concept right, but he came close. In 1830 it would have been shocking to contend publicly that heat was not conserved, because it would call into question all of French science based on the work of Lavoisier and Marquis Pierre Simon de Laplace, considered France's greatest mathematician. Equally disturbing would have been Carnot's new contention that matter could be completely transformed into motive force, which countermanded the idea that the Artificer of the universe would permit some aspect of His creation to vanish into thin air. Cardwell suggests that Carnot's most compelling reason for not publishing these notes during his lifetime, though, was that to do so he would have had to revise his major work in the light of his new understandings, and that task was beyond the capacity of a single individual; the complete revision and integration of his new ideas would required the combined talents of some of the century's most ingenious thinkers.
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The French engineer Émile Clapeyron was a contemporary of Sadi Carnot, having passed through the École Polytechnique a few years after him, and having possibly been in touch with him during the 1830 uprising. Two years after Carnot's death, Clapeyron published an exegesis of Carnot that did what Carnot had been at pains not to do: it used mathematical formulas, graphs, and diagrams, for instance, to extrapolate from Carnot's analysis "Clapeyron's equation," which holds that the maximum amount of work a unit of heat can perform when it vaporizes a liquid cannot be larger than the amount it would perform if it were doing another task. Clapeyron also proved mathematically Carnot's contention that the amount of work done during the course of a one-degree fall of a unit of heat decreases as the temperature increases. More widely circulated than Carnot's book, Clapeyron's paper was also translated into English and German, which made it accessible to those doing research in what would become known as thermodynamics, the study of the transformations of energy, leading to its further influence on the exploration of the cold.

As pointed out in the previous chapter, during the 1820s and 1830s science's growing ability to produce cold was ignored. In the same year as Clapeyron's publication, 1834, and also in France, an amateur scientist of independent means used electricity to directly produce heat and cold in a way that in the twentieth century would become quite important. Jean-Charles-Athanase Peltier, who had retired from clockmaking when the death of his wife's mother resulted in a small inheritance that allowed him to follow his scientific interests, had been intrigued by the research of an earlier Estonian-born German physicist, Thomas Johann Seebeck. Peltier passed a continuous current along a circuit of two conductors, made from different metals and connected by two junctions, and found that the temperature of one junction rose and the temperature of the other junction fell.
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In other words, electricity could be used either to cool or to heat: Seebeck and Peltier had discovered an entirely new field, thermoelectricity. In 1838, using Peltier's thermoelectric method, the German scientist H. F. E. Lenz froze a drop of water. He, too, was ignored. In other words, by 1838 the technical means of providing cold to those who might need or want it had been demonstrated in several scientific laboratories, but neither the pure scientists, nor the technologists, nor the few would-be entrepreneurs of refrigeration seemed interested in the process or the goal.

Aboard the Dutch ship
Java
in Jakarta in 1840, ship's doctor Julius Robert Mayer observed something unusual while trying to prevent the spread of an infection through his crew. As he later recalled, "The blood let from the vein in the arm had an uncommon redness, so that from the color I could believe I had struck an artery." Mayer, the twenty-six-year-old son of a German apothecary, had an unusual mind, by turns highly religious and full of humor, and was given to doing card tricks, solving rebuses, winning at billiards, and writing aphorisms—"What is insanity? The reason of an individual. What is reason? The insanity of man." Mayer decided that the blood of his shipmates was brighter red in Jakarta because in the hotter climes, human bodies required a lower rate of oxidation, and since their bodies used less oxygen to metabolize food, their venous blood was redder; this led him to ponder the relationship between the body heat of an animal and the work done by that animal—which, in turn, spurred him to think about the relationship between heat and work in any configurations of matter.

Back home in Heilbronn, in February 1841 Mayer collected his thoughts in an article that he sent off to the leading German natural-science journal. It included this typical, nearly unfathomable sentence:

If two bodies find themselves in a given difference [chemical difference or spatial separation], then they could remain in a state of rest after the annihilation of [that] difference if the forces that were communicated to them as a result of the leveling of the difference could cease to exist; but if they are assumed to be indestructible, then the still-persisting forces, as causes of changes in relationship, will again re-establish the originally present difference.

This actually meant something important—it was a statement of what would later be called the first law of thermodynamics, that energy cannot be destroyed, it can only be converted to other forms—but it was almost impossible to understand from Mayer's writing. Mayer also harmed his cause by couching his argument in the context of Immanuel Kant's phenomenological approach to the study of nature, suggesting that indestructible forces such as heat and mechanical work were halfway between inert matter and soul. This was precisely the sort of philosophic blather that serious physicists were endeavoring to move beyond, and so Mayer's article was ignored by the journal, as were his three follow-up letters to the editor about it.