Prof. Fred L. Wilson

Rochester Institute of Technology

Teaching at RIT


21. Mechanical Theory of Heat

Mechanistic theory achieved a number of triumphs in the eighteenth and nineteenth century, outside the areas in which Newton had written. The first of these triumphs was Rumford's series of experiments that put the caloric theory of heat to light.

Benjamin Thompson, Count Rumford (1753-1814)

Benjamin Thompson (better known as Count Rumford) was born only two miles from the birthplace, a half century before, of that other Benjamin, Benjamin Franklin. He began life quietly as an apprentice to a storekeeper in Salem, but in 1766 he was nearly killed in the explosion of some fireworks he was making. After recovery, he returned to Boston to become an assistant in another store. At nineteen he married a rich widow considerably older than himself and lived with her in Rumford (now Concord), New Hampshire. All would have gone well were it not that the Revolutionary War broke out and young Thompson's sympathies were with the king. Indeed, he served the British troops by spying on his countrymen.

When the British troops left Boston, Thompson went with them (leaving wife and child behind) and spent the war in minor government offices in England, ending with a short stay in the still embattled colonies as a lieutenant colonel in the king's forces. When the Revolutionary War was over and the colonials had won their independence, Thompson knew himself to be in permanent exile.

Thompson's character did not improve in England. He took bribes and was suspected of selling war secrets to the French. In 1783, with the permission of George III, he found it safer to go to the Continent in search of adventure. There he fell in with Elector Karl Theodor of Bavaria, for whom he worked as an intelligent and capable administrator. He established workhouses for Munich beggars, for instance, and had them turn out army uniforms with an efficiency that helped both the beggars and the army. He also introduced James Watt's steam engine and the potato to the Continent.

The Elector expressed his gratitude in 1790 by making Thompson a count, and Thompson chose Rumford as his name, for that was the town in which his wife was born and near which he had had an estate. In the Bavarian service he grew interested in the problem of heat and that was the occasion for his most important contribution to science.

In the eighteenth century heat was looked upon as an imponderable fluid, like phlogiston. Lavoisier, who demolished phlogiston, continued to think of heat as a fluid that could be poured from one substance to another and called it caloric. Rumford, however, while boring cannon in Munich in 1798, noticed that the blocks of metal grew hot as blazes as the boring tool gouged them out, so that they had to be cooled constantly with water. The orthodox explanation was that caloric was being loosened from the metal as the metal was broken down into shavings by the boring. Rumford noticed that the heating continued as long as the boring did, with no letup, and that enough caloric was removed from the brass to have melted the metal if it were poured back in. In other words, more caloric was being removed from the brass than could have been contained in it. In fact, if the boring instruments were dull so that no metal was ground to shavings, the caloric did not stop pouring out of the metal. On the contrary, the metal heated up more than ever.

Rumford's conclusion was that the mechanical motion of the borer was being converted to heat and that heat was therefore a form of motion, a view that had been groped toward for a century and more by such men as Francis Bacon, Boyle, and Hooke. And in this, they and Rumford are now considered to have been right.

Rumford even tried to calculate how much heat was produced by a given quantity of mechanical energy. He was thus the first to set a figure for what we now call the mechanical equivalent of heat. His figure was far too high, however, and a half century passed before Joule reported the correct value.

Rumford, through his arrogance and the general unpleasantness of his character, finally outwore his welcome in Bavaria too, particularly after the death of the Elector. That, and the pressure of Napoleon's victories, made it advisable for Rumford to return to England in 1799, and there his achievements were recognized and he was admitted into the Royal Society. In that year he weighed a quantity of water both as water and as ice and could detect no change in weight with the most delicate balance. Since water lost beat when it froze and gained it when it melted, as had been demonstrated by Black, it followed that caloric, if it existed, must be weightless. The fate of phlogiston made weightless fluids suspect and this experiment weakened the caloric theory, too.

Rumford, with the encouragement of Sir Joseph Banks, founded the Royal Institution in 1799 and obtained young men such as Young and Davy as lecturers. Rumford was a little dubious about the latter until he heard him give a lecture. That resolved all doubts, and indeed Davy was to grow famous through his lectures. In addition Davy had just conducted some experiments that led him to the same conclusions as Rumford. Davy had arranged for ice to be rubbed mechanically, the entire system being kept one degree below the freezing point. There was insufficient caloric in the whole system, according to the orthodox view, to melt the ice, and yet it melted. Davy decided that the mechanical motion was converted to heat. Certainly this experiment didn't hurt Davy in Rumford's regard. (Historians of science doubt that the experiment could have worked as described by Davy, but Davy believed it worked and described the results in his first publication.)

In any case, neither Rumford's nor Davy's experiment was convincing to physicists. The caloric theory, which seemed to be substantiated by the work of Prevost, and was strongly backed by such men as Berthollet, lived on for another half century until Maxwell settled it once and for all.

In 1804 Rumford went to Paris, though Great Britain and France were at war and France was threatening an invasion. (Political passions were milder then, it would seem.) While he was in Paris, his path crossed that of the dead Lavoisier a second time. Having produced evidence against Lavoisier's theory of heat, he (having outlived his first wife) proceeded to marry Lavoisier's widow (who was rich and who kept the famous name of her martyred first husband). It was a late marriage -- he being slightly over fifty, she slightly under -- and an unhappy one, their first quarrel coming the day after their marriage. After four years they separated and Rumford was so ungallant as to hint that she was so hard to get along with that Lavoisier was lucky to have been guillotined. However, it is quite obvious that Rumford was no daisy himself.

In 1811 his American daughter by his first wife joined him and cared for him in his last years. Incidentally, despite all the unpleasant messes of Rumford's character, there was a strong streak of idealism in him. He believed it better to make people happy first as a way of making them virtuous later (rather than the reverse, which has been the seemingly hopeless tactic of religions for so long). Then, too, like Franklin he refused to patent his inventions, which included a double boiler, a drip coffeepot, and a kitchen range. He even attempted a reconciliation with the United States in the end, and though he died, as he had lived, in exile, he left most of his estate to the United States and endowed a professorship in applied science at Harvard.

Rumford's "Caloric Theory"

The idea that heat was a motion of particles was voiced by the Greek atomists and echoed duly in the days of the scientific renaissance. One of the few correct statements made by Bacon on physical problems was his dictum that "heat itself, its essence and quiddity, is motion and nothing else." So spoke Boyle, Hooke, and Newton. But in the course of what Whittaker called the most amazing vicissitude in the history of science, the true theory had to yield temporarily to a concept that pictured heat as an "igneous fluid," a "heat fluid," or "caloric," the latter word having been coined as late as 1787 by Lavoisier and other French scientists. Rumford, however, found that there were heat producing processes that, if the caloric theory were true, should postulate the presence of the "heat fluid" in practically unlimited quantities in any body subjected to continuous friction. There was only one alternative and Rumford put it forcefully: "It appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in these experiments, except it be motion."

Rumford made no pretense of knowing "by what mechanical contrivance that particular kind of motion in bodies which is supposed to constitute heat is excited, continued and propagated." This problem, however, was only a matter of detail within the overall framework of mechanism. Rumford himself was quick to recall the case of Newton who, while not claiming to know the ultimate cause of gravity, nevertheless considered his discoveries genuine mechanical laws. In the phenomenon of heat Rumford saw a mechanical feature of the universe no less fundamental than the mechanism underlying the gravitational attraction. "The effects," he wrote, "produced in the world by the agency of heat are probably just as extensive, and quite as important as those which are due to the tendency of the particles of matter toward one another; and there is no doubt but that its operations are, in all cases, determined by laws equally immutable." If any conjectures were to be made about the mechanical cause of heat, the supporters of Rumford's theory were not in the least reluctant to make an educated guess. Thus the young Humphry Davy defined the mechanical contrivance whereby heat was produced as the "vibration of the corpuscles of bodies."

The caloric theory, however, was a long time dying. The number of scientists who were unable to see in heat a mode of motion decreased but slowly as the nineteenth century approached its midpoint. The actual situation, however, was not reflected in the "Heat" article of the 1860 edition of the Encyclopaedia Britannica in which the mechanical theory of heat was dismissed as "vague and unsatisfactory," while the view that "heat or caloric is a material agent of a peculiar nature" was described as the theory most generally accepted among men of science. Those working on the subject did not lend a great deal of credibility to the concept either. As we've already seen, Rumford was incorrigible. And Robert Mayer turned to the study of heat from his observations on blood.

Julius Robert Mayer (1814-1878)

Originally trained as a physician at the University of Tübingen, Mayer, the son of an apothecary, was not a particularly good scholar and did not enjoy medical practice. He served as ship's doctor under conditions which gave him little to do but think and about 1840, during a trip to Java, he began to interest himself in physics, while considering the problem of animal heat.

In 1842 he presented a figure for the mechanical equivalent of heat, based on an experiment in which a horse powered a mechanism which stirred paper pulp in a caldron. He compared the work done by the horse with the temperature rise in the pulps. His experiments were not as detailed and careful as those by Joule but Mayer saw their significance and clearly presented his belief in the conservation of energy before either Joule or Helmholtz did.

He had some difficulty getting his paper on the subject published but Liebig finally accepted it for the important journal he edited. Though Mayer was five years ahead of Joule his paper aroused no interest, and in the end it was Joule, with his imposing experimental background, who received credit for working out the mechanical equivalent of heat. And it was Helmholtz who received credit for announcing the law of conservation of energy because he announced it so much more systematically. Yet Mayer went further than either of the other two, for he included the tides, the heating of meteorites, and even living phenomena in the realm of energy conservation (a daring step in a decade when vitalism, with its view that the laws of inanimate nature did not apply to living systems, was still a considerable force).

Mayer argued that solar energy was the ultimate source of all energy on earth, both living and nonliving. He further suggested that solar energy was derived from the slow contraction of the sun, or by the fall of meteors into the sun, in either case kinetic energy being converted to radiant energy. Helmholtz and Kelvin got credit for this latter idea.

Mayer's failure to be appreciated and the fact that he was on the losing side in controversies as to priority affected him strongly. The year 1848 saw additional disasters, with the death of two of his children and his brother's involvement with revolutionary activities. Mayer tried to commit suicide in 1849 by jumping from a third-story window but failed in that too, merely injuring his legs severely, and laming himself permanently. In 1851 he was taken to a mental institution where primitive and cruel methods for treating the sick prevailed. He was eventually released but he never fully recovered. He lived in such obscurity that when Liebig lectured on Mayer's views in 1858 he referred to the man as being dead.

That, however, proved a turning point. It was as though the world's conscience smote it. Tyndall lectured on his work during the early 1860s and labored to secure him proper recognition. Mayer was granted the right to add "von" to his name, which was roughly the equivalent of an English knighthood. Then, in 1871, he received the Copley medal.

Mechanical Theory Gains Popular Support

Actually by 1860 the majority opinion defined heat as the effect of the motion of molecules. True, only fifteen years earlier the caloric theory claimed physicists of note among its supporters. Among them was Philipp Gustay von Jolly, an influential figure in mid-nineteenth-century German physics, who had remarked during a hurried meeting with a somewhat eccentric physician, Robert Mayer, that water should warm up by shaking if Mayer's theory of the mechanical equivalence of heat were correct. To Jolly's consternation, Mayer rushed into his office a few weeks later shouting "It is so!" It took some explanation on Mayer's part, however, to make Jolly realize that mechanical processes like stirring and shaking do indeed produce a rise in temperature.

These were also the years that saw Joule give the mechanical equivalent of heat and heard Helmholtz, a youth of twenty-six, read a paper entitled "Die Erhaltung der Kraft." In that paper the various forces of the mechanical universe were tied together for the first time in an even more general concept, energy. Gravity, electrical force, magnetic force, and heat all had one thing in common -- they could perform mechanical work, and in a measure that remained always the same under similar circumstances. Heat, a necessary by-product of all actually performed work, occupied a central position in this synthesis. As Helmholtz admitted in the fall of 1862, the recognition of the true nature of heat was of decisive importance in establishing the validity of the Law of the Conservation of Force in all natural processes. This was why physicists chose, as Helmholtz put it, to "designate that view of Nature corresponding to the law of the Conservation of Force with the name of Mechanical Theory of Heat."

James Prescott Joule (1818-1889)

Joule was the second son of a wealthy brewer, which meant he had the means to devote himself to a life of research. He also suffered poor health as a youngster, having some sort of spinal injury, which meant he could withdraw to his books and studies. His father encouraged him and supplied him with a home laboratory. He had some instruction from Dalton but by and large he was self-educated and, like Faraday, remained innocent of mathematics.

Joule was almost a fanatic on the subject of measurement, and even on his honeymoon he took time out to devise a special thermometer to measure the temperature of the water at the top and bottom of a scenic waterfall his wife and he were to visit. (His wife died in 1853, after only six years of marriage.) In his teens he was publishing papers in which he was measuring heat in connection with electric motors.

Despite the fact that illness forced his father to retire in 1833 and that young Joule had then to do his share toward running the brewery, he continued his scientific labors. By 1840 he had worked out the formula governing the development of heat by an electric current (the heat developed is proportional to the square of the current intensity multiplied by the resistance of the circuit). He went on to devote a decade to measuring the heat produced by every process he could think of. He churned water and mercury with paddles. He passed water through small holes to heat it by friction. He expanded and contracted gases. Even his honeymoon measurement of the waterfall temperature was based on the thought that the energy of falling water should be converted to heat once it was stopped so that the temperature at the bottom of the waterfall should be higher than that at the top.

In all those cases he calculated the amount of work that had entered the system and the amount of heat that came out and he found, as Rumford had maintained fully half a century before, that the two were closely related. A particular quantity of work always produced a particular quantity of heat. In fact, 41,800,000 ergs of work produced one calorie of heat. This is called the "mechanical equivalent of heat."

Joule's first full description of his experiments and conclusion appeared in 1847. It did not commend itself to most scientists at the time. This may have been due partly to the fact that Joule was a brewer and not an academician. (He never received a professorial appointment though he was proposed for one at least once and was rejected, in part because of his spinal injury.) It may have been due partly, too, to the fact that his conclusions were based on small temperature differences in many eases (he used thermometers which could be read to 0.020 F. and, eventually, to 0.0050 F.), so his experiments were not spectacular.

His original statement of his discovery was rejected by various learned journals as well as by the Royal Society and he was forced to present it at a public lecture in Manchester and then get his speech published in full by a reluctant Manchester newspaper on which his brother was music critic. A few months later he finally managed to present it before an unsympathetic scientific gathering and his presentation would have passed almost unnoticed but for a twenty-three-year-old in the audience. His name was William Thomson, and he was later to be known as Lord Kelvin. His comments on Joule's work were shrewd enough and logical enough to rouse interest and even enthusiasm, and Joule's reputation was made. Later, Stokes also supported Joule's work with enthusiasm. Full recognition came in 1849 when Joule read a paper on his work before the Royal Society, with Faraday himself as his sponsor.

Joule was not the first to determine the mechanical equivalent of heat. Rumford had attempted it but had come out with a value that was far too high. Mayer produced a fairly good value before Joule did, but it was Joule who was most accurate (up to his time), who backed up his figure with a large variety of careful experimental data, and who (with Thomson's help) forced the view on the world of science. He therefore gets the credit, and in his honor a unit of work, equal to 10,000,000 ergs, is called the joule (4.18 joules of work equal 1 calorie of heat).

The determination of the mechanical equivalent of heat led to something very fundamental. Ever since the time of Newton and even of Galileo it was understood that the energy of an object hurtling upward did not really decline as its movement slowed. To be sure, that movement steadily diminished under the pull of gravity, but as the object lost kinetic energy (the energy of movement) it gained potential energy (the energy of position). When the object reached its maximum height, it was momentarily stationary and had no kinetic energy at all, hut it had a good deal of potential energy. As it started falling, potential energy was reconverted into kinetic energy and when it reached the ground again, it was with all the kinetic energy with which it had originally been hurtled upward.

Theoretically, potential energy and kinetic energy interchanged without loss and this was the "conservation of mechanical energy." In reality the conservation was not perfect. Some energy was lost through air resistance and friction. However, if heat is recognized as a form of energy; and if it is further recognized that the loss of mechanical energy through friction or air resistance is balanced by a gain of heat; and if Joule's point is clear, that the loss of other forms of energy is always exactly balanced by the gain in heat, then the suspicion arises that total energy is conserved.

This is the law of conservation of energy, which states that energy can neither be created out of nothing nor destroyed into nothing, but that it can be changed from one form to another. This is one of the most important generalizations in the history of science. It is so important in connection with the study of the interactions of heat and work (the thermodynamics first founded as a science by Carnot two decades earlier) that it is frequently called "the first law of thermodynamics."

In the century and a quarter since Joule's time this law has trembled on occasion, notably when radioactivity was discovered and again when the radioactive emission of electrons was studied in detail. Always, through the work of such men as Einstein and Pauli the first law has been reestablished more firmly than before -- at least so far.

Although Joule recognized the principle of the conservation of energy, and so did Mayer before him, the first to present it to the world as an explicit generalization was Helmholtz and it is usually Helmholtz who is given credit for its discovery.

During the 1850s Joule went on to collaborate with his young friend Thomson. Together the two men showed that when a gas is allowed to expand freely, its temperature. drops slightly. This observation, established in 1852, is called the Joule-Thomson effect and it is taken as evidence for the fact that molecules of gases have a slight attraction for their neighbors. It is in overcoming this attraction while moving apart during expansion that individual molecules lose energy and therefore temperature. This turned out to be a very important consideration in obtaining extremely low temperatures toward the end of the nineteenth century. Men such as Dewar took full advantage of it.

Joule also discovered, in 1846, the phenomenon of magnetostriction, whereby an iron bar changes its length somewhat when magnetized. This seemed purely academic at the time, but nowadays the effect is used in connection with ultra-sonic sound-wave formation.

Joule was elected to the Royal Society in 1850, received its Copley medal in 1866 and was president of the British Association for the Advancement of Science in 1872 and in 1887. That he remained a brewer all his life and was never a professor did not seem to matter in the intellectual democracy of the world of science.

Toward the end of his life he suffered economic reverses, but Queen Victoria granted him a pension in 1878. He was a modest and unassuming man, a sincerely religious one, and toward the end of his life bitterly regretted the increasing application of scientific discoveries to the art of warfare.

Kinetic Theory of Gases

What Mayer, Joule, and Helmholtz established on the macroscopic level, the kinetic theory of gases did on the molecular level: the behavior and properties of gases came to be reduced to the kinetic energy of their molecules. In the kinetic theory of gases the mechanical conception of nature indeed reached its widest development. It expressed a world view in which, to use Planck's words, "all physical phenomena can be completely reduced to movements of invariable and similar particles or elements of mass." It gave the impression of unveiling at last the most fundamental aspect of the world as nothing more than a "billiard ball universe."

According to the definition of A. Kronig, one of the creators of the theory, "gases consist of atoms that behave like solid, perfectly elastic spheres moving with definite velocities in void space." Maxwell's paper of 1859, entitled "Illustration of the Dynamical Theory of Gases," which put kinetic theory on solid foundations, voiced the same view "on the motions and collisions of perfectly elastic spheres." His aim was to formulate the laws, the "strict mechanical principles," for the behavior of an "indefinite number of small, hard, and perfectly elastic spheres acting on one another only during impact."

The conviction that such an imagery closely paralleled the physical reality was rooted not only in the apparently unassailable truth of mechanical philosophy, but also in the truly spectacular successes of the kinetic theory. The theory made it possible to calculate quantities like the free mean path of gas molecules, the viscosity of some gases and their specific heat. All these results followed from the same mechanical postulates that treated, for instance, the diatomic molecules as dumbbells that could move, vibrate, and rotate. Mechanics reached its boldest extremes and for a fleeting decade or two was on the threshold of final triumph. So at least the body of physicists preferred to believe.

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Fred L. Wilson (
July 28, 1996