Joule and the Conservation of Energy

James Joule was born in 1818, the second son of a prosperous brewer in Manchester, England. His father hired John Dalton (who had proposed the atomic theory of chemistry in 1803) as a private tutor for his two sons.  Dalton met with the boys twice a week, guided them through Euclid’s books on geometry, and covered a vast range of natural phenomena.  There was also a wilder side to Joule’s science education: he blew his eyebrows off in a gun experiment; he flew kites in thunderstorms. He asked a servant girl to report her sensations as he gave her increasing electric shocks, but stopped when she fell unconscious. (Cardwell, page 16).


But Joule worked with meticulous care in the laboratory. In 1840, at the age of 22, he established that a conductor carrying an electric current became hot, and that the rate of heating for a current I flowing through a resistance R was given by I2R for any kind of wire, and even for electric currents in fluids.  This was a kind of heat production no-one had seen before—previously, heat had only come from either chemical combustion, or friction, or radiation. And, sad to relate, Rumford’s assertions had had little impact on the scientific community, so the big question was: how did the electric current deliver caloric fluid into the wire?   Well, actually, this wasn’t too difficult to explain.  In the battery, caloric was no doubt being released in the chemical reactions involved in producing the electric current, and the caloric was then transported down the wire by the current. 


(Cultural footnote: Cardwell, page 35)  From a London perspective, Manchester was (and maybe still is) the boondocks.  When Joule submitted his paper on the discovery of the electrical I2R heating (now known as Joule heating) to the Royal Society, it was rejected, except for a short abstract.  Much later, when asked if that cursory treatment surprised him, he replied: “I was not surprised—I could imagine those gentleman in London sitting round a table and saying to each other ‘what good can come out of a town where they dine in the middle of the day?’”


Next, Joule did an experiment that was tougher for the caloric theory to explain.  He found that the very same heating of the wire took place if the electrical current involved, instead of being generated by chemical reactions in a battery, came from a dynamo, a simple coil of wire rotating in a magnetic field.  Now where was the “caloric fluid” coming from?  The only explanation anyone could come up with was that rotating the coil in the magnetic field must be somehow pumping caloric out of it.  So the coil should cool down.  Joule tested this hypothesis, and found that instead the coil heated up a little. It was impossible to reconcile this finding with the caloric theory—heat could not be a conserved fluid after all. Joule wrote that in magneto electricity, we have an agent capable by simple means of … generating heat.  (Cardwell, page 56).


So “caloric fluid” could be manufactured!  The basic assumption of the caloric theory, that this was a conserved fluid, was wrong!  Joule next asked if a given amount of work always produced the same amount of heat (we’ll say “heat” instead of the discredited “caloric fluid” from now on). He drove his electrical generator at a steady pace by wrapping fine string around the axle, and tying a weight to the end of it.  As the weight fell, the generator settled to a steady pace, which he timed. He then turned the generator at that pace by hand for fifteen minutes, and measured how much heat was generated in a piece of wire immersed in a calorimeter.  From that measurement, he was able to calculate that the amount of heat required to raise the temperature of one pound of water by 1°F (that is, one British Thermal Unit of heat, usually written one BTU) could be generated by an 896 pound weight falling through one foot—or a one pound weight falling through 896 feet, etc., in other words, 896 foot×pounds of mechanical work.  This figure is in the right ballpark, but almost 20% too high—his later, much more accurate, measurement was 772 foot×pounds per BTU. This was the first time anyone had stated that a measured quantity of heat was equivalent to a corresponding amount of mechanical work.


Finally, in 1845, Joule realized that the electrical apparatus was an unnecessary intermediary—heat could be produced directly by a falling weight.  He arranged for the falling weight to drive paddle wheels in a calorimeter, churning up the water.  This led to a slight but measurable rise in temperature. He found one BTU was generated by an energy expenditure of 772 foot×pounds (switching his results to the metric system, that one calorie was the equivalent of 4.2 newton.meters, or, as we now say, 4.2 joules).  Incidentally, Joule amused himself by demonstrating that Rumford’s detailed records of bringing the water to a boil in the cannon boring could be used to find the mechanical equivalent of heat.  Rumford had claimed that he had two horses working for two and a half hours, but he was working them lightly, they were only really doing the work of one.  Joule used Watt’s estimate that one horse can work at 33,000 foot×pounds per minute to find an equivalence of over 1000 foot×pounds per BTU, about fifty percent too high, but not a bad estimate in view of all the uncertainties involved. 


Joule also calculated that the water just beyond the bottom of a waterfall will be one degree Fahrenheit warmer than the water at the top for every 800 feet of drop, approximately, the kinetic energy turning to heat as the water crashed into rocks at the bottom.  Joule spent his honeymoon at Chamonix in the French Alps, and Lord Kelvin claimed later that when he chanced to meet the honeymooners in Switzerland, Joule was armed with a large thermometer to check out the local waterfalls (but it is generally believed that Kelvin made this up).


Joule also did a series of beautiful experiments on electrolysis and combustion. Batteries work because some of the ions in solution are chemically attracted to the metal plates. For example, oxygen ions move to a zinc or iron plate, become chemically attached and deliver charge.  By carefully measuring currents, Joule was able to find the “affinity” of oxygen with plates of various elements.  He then compared this with the heat produced when zinc or iron, say, were burned in an oxygen atmosphere. He saw, correctly, that this was just another way for oxygen to attach itself to these metals, and he was able to confirm that the same heat was released in these very different-seeming reactions.  These chemical investigations, carried out in 1842, were no doubt in the back of his mind when he found that heat was interchangeable with mechanical and electrical energy, and suggested that chemical energy, too, must be in the list.


Joule’s work was so impressive that his provincial origins were forgiven, and by the late 1840’s he was regularly presenting papers to the British Association and the Royal Society.  His experiments establishing the equivalence of heat and mechanical work, the cornerstone of the principle of conservation of energy, are among the greatest achievements of nineteenth-century science.

But was Carnot so wrong?

On the face of it, once it became clear that the caloric fluid wasn’t conserved, and therefore didn’t exist in the way Carnot and others had imagined, one would think that Carnot’s elegant analysis of the heat engine as a water wheel using caloric fluid had little remaining value.  But that turned out not to be the case.  In particular, his analysis of the efficiency of a heat engine was right.


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