Julius Robert Mayer was born in the mill town of
He decided to build a model. His first try didn’t 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 a lot more water over the wheel, so he was 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 Mayer 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 a ship 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 did not 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 could not just appear from nowhere, it had to have a cause.
But he saw that if the indirectly generated heat must also be included, there is a problem. His analysis ran something like this (I’ve changed the illustration slightly, but the idea’s the same): 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 is equally hard to turn, though, because it is 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 volume (Cv) and at constant pressure (Cp). They always found Cp to be greater than Cv. Mayer interpreted this with the following thought experiment: 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.
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. The picture below shows his apparatus:
The paddle wheels turn through holes cut in stationary brass sheets, churning up the water. This is all inside an insulated can, of course. In this way, Joule measured the mechanical equivalent of heat, the same number Mayer had 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
Mayer and Joule, using entirely different approaches, arrived almost simultaneously at the conclusion that heat and mechanical work were numerically equivalent: a given amount of work could be transformed into a quantitatively predictable amount of heat. Which of the two men deserves more credit (not to mention other contenders!) has been argued for well over a century. Briefly, it is generally conceded that Mayer was the first to spell out the concept of the mechanical equivalent of heat (although closely followed, independently, by Joule) and Joule was the first to put it on a firm experimental basis.
In fact, by the 1840’s, 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 used in writing these notes…
Caneva, K. L.: 1993, Robert Mayer and the Conservation of
Cardwell, D. S. L.: 1989, James Joule: A Biography,
Cardwell, D. S. L.: 1971, From Watt to Clausius,
Joule, J. P.: 1963, Scientific Papers, Vol. I, Dawsons of Pall Mall,
Magie, W. F.: 1935, A Source Book in Physics,
Roller, D.: 1957, ‘The Early Development of the Concepts of Temperature and Heat: The Rise and Decline of the Caloric Theory’, in J. B. Conant and L. K. Nash (eds.), Harvard Case Histories in Experimental Science, Harvard University Press, Cambridge, Massachusetts, 1957, 117-215.