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 naïve 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.
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?
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
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
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
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
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,
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,
Robert Mayer and the Conservation of Energy, Kenneth
James Joule: A Biography,
Joule’s Scientific Papers,
James Prescott Joule and the Concept of Energy, Henry J. Steffens,
Maxwell’s Demon, Hans Christian von Baeyer, Random House, 1998.