# Teaching Heat: the Rise and Fall of the Caloric Theory

Michael Fowler, University of Virginia

In my experience, there is much to be gained from teaching physics with some historical perspective. Unfortunately, the trend in physics textbooks these days is in the opposite direction. Thirty years ago, most standard texts included some discussion of how and when basic concepts in physics developed. Recent editions of these same books, much heavier and more colorful, have dropped that material in favor of endless detailed instruction on how to solve textbook problems. This may be, in part, a necessary response to less well prepared students, and possibly teachers, but the new texts, despite four color artwork on shiny paper, are rather dreary. My solution is simply to use the text as a source of problems and for back up reading, to use a fair amount of historical material (and demonstrations) in class, and to post my class notes on the web. Homework assignments include calculations based on historical experiments (for example: Estimate the mechanical equivalent of heat using Rumford's cannon-boring data and Watt's estimate of one horsepower.) >Most of the students enjoy this approach.

I strongly believe that it is not a waste of time to discuss some earlier theories that turned out to be wrong. In fact, these earlier theories are often close to the students' current thinking, so challenging them as to why those ideas were finally abandoned can stir the critical faculties and lead to better understanding. A case in point is the caloric theory of heat. Of course, the students are vaguely aware that it's not right, but their intuitive ideas of heat, based on everyday experience, have probably led them to construct an operational model not too different from the caloric one, so we go ahead and discuss heat from this naive point of view, and mention the first recorded systematic experiments on heat and heat flow. For example, Ben Franklin measured heat flow down rods of different materials by seeing how long it took to melt wax, and thereby compared the thermal conductivities of different materials, a matter of real practical importance in designing stoves, for example. Franklin believed some weightless (or almost weightless) caloric fluid was flowing down those rods. Recall he'd thought the same thing about electricity—there was some electric fluid flowing when an object was being charged electrically—and there he was absolutely correct. Like the electric fluid, Franklin believed the caloric fluid would flow from one object to another, but overall there was always the same amount of fluid: it was conserved. That is the basic Caloric Theory.

We next discuss Joseph Black's ideas and careful experiments on heat, how it always flows from hot to cold things, and evens out in a room with no heat source after a time. (I should mention that the evolution of thermometers up to Fahrenheit was covered immediately before this review of caloric theory.) At this point, the quantitative concept of heat capacity is introduce (deviating only slightly from historical correctness by using Celsius and grams from the start). We perform one of Black's experiments in the lecture, using a calorimeter to find the specific heat of a piece of metal. The students are asked to discuss and predict it first. Almost all of them expect the specific heat of copper to be greater than that for water, so the opposite result gets their attention. This naturally leads to a presentation of a wider range of results, and the mysterious finding of Dulong and Petit that the heat capacity per atom seems to be a constant, no matter what the weight of the atoms.

Once we start thinking about atoms, it becomes clear that some kind of microscopic picture of the caloric fluid flow must be constructed. OK, it wasn't clear to everyone at the time—even almost a century later, some eminent German scientists, such as Ostwald and Mach, were arguing against atomic models. They felt the business of science was the discovery of laws relating observable quantities, such as pressure, volume and temperature of a gas, and attempts to interpret these laws in terms of unobservable entities such as atoms were unverifiable fantasies. Time has shown how wrong they were. Now only string theorists have to endure that kind of criticism! Anyway, back to the subject: our students certainly agree that some microscopic theory is needed, so how do we begin to construct one?

We know that heat expands a gas (in class, we'd recently discussed Galileo's thermometer). How does the caloric theory explain that? Newton imagined atoms in a gas rather like soft oranges in a crate, taking up most of the room available, and coated with this caloric fluid, so that on pouring in more caloric the atoms swelled in size. The atoms in a solid or liquid had a lot less caloric, that's why it took so much heat (pumping in caloric) to boil water.That sounds reasonable. But the caloric theory did much more: the whole theory of heat flow in solids, including important problems like the cooling of the earth over geological time, were analyzed quantitatively using sophisticated mathematical techniques developed in France (by Fourier and others) applied to the caloric theory, and these methods and results are all still good. Furthermore, as we shall see shortly, Carnot developed a theory of the steam engine based on caloric theory, which was largely correct and shed new light on some of the most pressing technological problems of the era.

But a caloric theory has to explain other things. For example, why does friction cause heating? The standard argument was that the stress of rubbing surfaces together forced some caloric fluid to be pushed out from between the atoms, and it appeared as heat. This was the real weak point of the theory, and this was where Rumford attacked. In manufacturing cannons for the Bavarian military, he found the necessary grinding to hollow out the barrel produced huge amounts of frictional heat, which continued to flow as long as the grinding was maintained. This apparently endless supply of caloric posed a big problem—why should an ordinary piece of metal contain an apparently infinite amount of caloric fluid? Rumford decided a better explanation was that the friction of grinding caused some kind of internal invisible microscopic motion in the metal, and the flowing out of heat was nothing but this motion being communicated, the jiggling atoms causing neighboring atoms to jiggle as they came into contact. The caloric fluid flow was perhaps just a useful large-scale picture of the microscopic motion spreading through the material. If Rumford's picture was correct, the "fluid" was mechanically created by the friction, and, unlike electricity, was not a conserved quantity.

But Rumford's work, published in 1798, did not kill the caloric theory. After all, the caloric theory had explained a lot. Rumford's critics suggested that maybe somehow the fragments of metal shaved off had lost all their caloric. He had tried to check for that, but his method was not completely convincing.

To appreciate the next major advance in understanding heat, the backdrop of the developing industrial economy must be borne in mind. The first modern factories were textile mills, with many power looms driven by a large water wheel, so the water falling under gravity was the source of power. By the early 1800's, the water wheels were being replaced by steam engines. The first attempt to construct a theory of the steam engine was by Sadi Carnot, in the1820's. His idea was that just as water flows downhill, caloric flows from hot to cold: and the steam engine utilizes this caloric flow just as a water wheel takes energy from falling water. His analysis led to many correct conclusions, such as that the amount of work that a given amount of heat would provide depended on the height of the temperature drop, and there was a limit to how much work could be extracted. Carnot proved that the limit was the work provided by a reversible engine, one with no friction and heat exchange only between objects at the same temperature. (We go over an analysis of why you can't do better than a reversible engine in class.) These results, drawn from an analysis of a flawed theory, nevertheless are central to our present understanding of steam engines and internal combustion engines. Sad to report, Carnot died at a young age, and his work was almost unknown until the 1850's.

Another scientist-to-be fascinated with water wheels in the 1820's was Julius Robert Mayer, born in the mill town of Heilbronn, Germany, on the river Neckar, in 1814. The town's whole economy was based on water power. The ten year old Mayer had a great idea: why not use part of a water wheel's output to drive an Archimedean screw which would pump the water back up again? That way you wouldn't have to rely on the river at all! He decided to build a model. His first try didn't quite work—some water was pumped back up, but not enough. But surely that could be taken care of by putting in a gear train to make the screw run faster? Disappointingly, he found the water wheel had a tougher time turning the screw faster, and he needed to supply more water over the wheel, putting him back to square one. Increasingly ingenious—but unsuccessful—fixes finally convinced him that in fact there was no solution: there was no way to arrange a machine to do work for nothing. This lesson stayed with him for life.

Mayer studied to become a medical doctor (his studies included one physics course) and in 1840, at age 25, he signed on as a ship's doctor on the Java, bound for the tropics. Shortly after reaching the Dutch East Indies, some of the sailors became ill and Mayer's treatment included bloodletting. He was amazed to find that the venous blood was a bright red, almost the same as arterial blood. Back in Germany, the venous blood was much darker, and there was a reason: the chemist Lavoisier had explained that the body's use of food, at least in part, amounted to burning it in a controlled way to supply warmth. The darker venous blood in effect contained the ashes, to be delivered to the lungs and expelled as carbon dioxide. Mayer concluded that less burning of food was needed to keep warm in the tropics, hence the less dark blood.

Now, Lavoisier had claimed that the amount of heat generated by burning, or oxygenation, of a certain amount of carbon didn't depend on the sequence of chemical reactions involved, so the heat generated by blood chemistry oxygenation would be the same as that from uncontrolled old-fashioned burning in air. This quantitative formulation led Mayer to think about how he would measure the heat generated in the body, to equate it to the food burned. But this soon led to a problem. Anyone can generate extra heat, just by rubbing the hands together, or, for example, by turning a rusty, unoiled wheel: the axle will get hot. Does this "outside" heat also count as generated by the food? Presumably yes, the food powers the body, and the body generates the heat, even if indirectly. Mayer was convinced from his childhood experience with the water wheel that nothing came from nothing: that outside heat couldn't just appear from nowhere, it had to have a cause.

But he saw that if the indirectly generated heat must also be included, there's a problem. His analysis ran something like this: suppose two people are each steadily turning large wheels at the same rate, and the wheels are equally hard to turn. One of them is our rusty unoiled wheel from the last paragraph, and all that person's efforts are going into generating heat. But the other wheel has a smooth, oiled axle and generates a negligible amount of heat. It's equally hard to turn, though, because it's raising a large bucket of water from a deep well. How do we balance the "food = heat" budget in this second case?

Mayer was forced to the conclusion that for the "food = heat" equation to make sense, there had to be another equivalence: a certain amount of mechanical work, measured for example by raising a known weight through a given distance, had to count the same as a certain amount of heat, measured by raising the temperature of a fixed amount of water, say, a certain number of degrees. In modern terms, a joule has to be equivalent to a fixed number of calories. Mayer was the first to spell out this "Mechanical Equivalent of Heat" and in 1842 he calculated the number using results of experiments done earlier in France on the specific heats of gases. French experimenters had measured the specific heat of the same gas at constant pressure (Cv) and at constant pressure (Cp). They always found Cp to be greater than Cv. The way to understand this is as follows: consider two identical vertical cylinders, closed at the top by moveable pistons, the pistons resting on the gas pressure, each enclosing the same amount of the same gas at the same temperature. Now supply heat to the two gases, for one gas keep the piston fixed, for the other allow it to rise. Measure how much heat is needed to raise the gas temperature by ten degrees, say. It is found that extra heat is needed for the gas at constant pressure, the one where the piston was allowed to rise. Mayer asserted this was because in that case, some of the heat had been expended as work to raise the piston: this followed very naturally from his previous thinking, and the French measurements led to a numerical value for the equivalence. Mayer understood the sequence: a chemical reaction produces heat and work, that work can then produce a definite amount of heat. This amounted to a statement of the Conservation of Energy. Sad to report, Mayer was not part of the German scientific establishment, and this ground-breaking work was ignored for some years.

Meanwhile, in Manchester, England , the center of the industrial revolution, the same problem was being approached from quite a different direction by James Joule, the son of a prosperous brewer. Joule was lucky in that as a teenager, he was tutored at home, along with his brother, by John Dalton, the chemist who founded the atomic theory. Manchester was at the cutting edge of technological progress, and one exciting idea in the 1830's was that perhaps coal-driven steam engines could be replaced by battery-driven electric motors. Joule, in his twenties, set himself the task of improving the electric motor to the point where it would be competitive with the steam engine. But it was not to be—after years of effort, he concluded that at best it would take five pounds of zinc consumed in a battery to deliver the work from one pound of coal. But he learned a lot. He found an electric current in a wire produced heat at a rate I 2R, now known as Joule heating. The caloric theory interpretation was that caloric fluid originally in the battery was released along with the electric current and settled in the wire. However, Joule discovered the same heating took place with a current generated by moving the wire past a permanent magnet. It was difficult to see how the caloric fluid got into the wire in that situation. Joule decided the caloric theory was suspect. He generated a current by applying a measured force to a dynamo, and established that the heat appearing in the wire was always directly proportional to the work done by the force driving the dynamo. Finally, it dawned on him that the electrical intermediary was unnecessary: the heat could be produced directly by the force, if instead of turning a dynamo, it turned paddle wheels churning water in an insulated can. In this way, he found the mechanical equivalent of heat, the same number Mayer deduced from the French gas experiments.

Joule's initial reception by the scientific establishment was not too different from Mayer's. He, too, was a provincial, with a strange accent. But he had a lucky break in 1847, when he reported his work to a meeting of the British Association, and William Thomson was in the audience. Thomson had just spent a year in Paris. He was fully familiar with Carnot's work, and believed the caloric theory to be correct. But he knew that if Joule really had produced heat by stirring water, the caloric theory must be wrong—he said there were "insuperable difficulties" in reconciling the two.

In fact, by this time, although many still believed in the caloric theory, it had run into other difficulties. Before the 1820's, almost everyone believed, following Newton , that light was a stream of particles. Around 1800, Herschel discovered that on passing sunlight through a prism, and detecting the heat corresponding to the different colors, in fact there was heat transmitted beyond the red. This suggested that radiant heat was caloric particles streaming through space, and no doubt very similar in character to light. But in the 1820's it was unambiguously established that light was really a wave. Did this mean heat was a wave too? Perhaps the caloric fluid was oscillations in the ether. Things were now very confused. In 1841, Joule wrote diplomatically: "let the space between these compound atoms be supposed to be filled with calorific ether in a state of vibration, or, otherwise, to be occupied with the oscillations of the atoms themselves."

It transpired, though, that the difficulties in reconciling Carnot's theory and Joule's experiments were not as insuperable as Thomson had claimed. In 1850, a German professor, Rudolph Clausius, pointed out that Carnot's theory was still almost right: the only adjustment needed was that there was a little less heat emerging from the bottom of the "caloric water wheel" than went in at the top—some of the heat became mechanical energy, the work the steam engine was performing. For real steam engines, the efficiency—the fraction of ingoing heat delivered as useful work—was so low that it was easy to understand why Carnot's picture had been accepted for so long. For the first time, with Clausius' paper, a coherent theory of heat emerged, and the days of the caloric theory drew to a close.

Books I've used in teaching this subject and writing these notes:

Statistical Physics and the Atomic Theory of Matter, Stephen G. Brush, Princeton , 1983.

Robert Mayer and the Conservation of Energy, Kenneth L. Caneva. Princeton , 1993.

James Joule: A Biography, Donald S. L. Cardwell, Manchester University Press, 1989.

Joule's Scientific Papers, Dawsons, 1887, 1963.

James Prescott Joule and the Concept of Energy, Henry J. Steffens, Dawsons , 1979.

Maxwell's Demon, Hans Christian von Baeyer, Random House, 1998.

July, 2003