Celebrating Sadi Carnot

June 1, 2021, is the 225th birthday of Sadi Carnot, an original thinker who was not afraid to ask the questions that nobody else had thought. His attempts to answer them were hampered by deficiencies in the scientific theory of the day, and sadly he died in a cholera outbreak at the age of 36 before he had managed to untangle himself from the contemporary understanding of the nature of heat that was holding him back.
Carnot is often portrayed as a maverick loner, working outside the establishment, whose ideas about heat popped out of nowhere and failed to make an impact at the time because of his isolation from mainstream scientific thought. Like most of history this is partly true, but misses a lot of the detail that helps to put his work in context.

Carnot trained for three years from the age of 16 at the École Polytechnique in Paris, where the staff at that time included Ampère, Gay-Lussac, Arago and Poisson and their international contacts included Biot, von Humboldt, Foucault and Faraday. However, he had the misfortune to graduate in 1814 as a second lieutenant in the Corps of Engineers in Napoleon’s army the year before the Battle of Waterloo.

Carnot’s father, who had been Minister of the Interior in Napoleon’s government, was exiled and shortly afterwards Carnot left active military service and transferred to the General Staff in Paris. This gave him the opportunity to reconnect with scientific thinking and he furthered his education by attending lectures in industrial chemistry by Professor Clément, striking up a friendship with the Professor in 1819 and working with him on the improvement of steam engine efficiency. Clément was also responsible for defining the calorie as a unit of
heat—the amount of heat required to heat one kilogram of water by one degree Celsius.

Rather than popping out of nowhere, Carnot’s now famous publication “Réflexions sur la Puissance Motrice du Feu” (“Reflections on the Motive Power of Fire”) was the result of five years of intense study with Clément and his colleagues, probing the shortcomings of existing theory. Carnot’s major significant breakthrough was the observation that “The motive power of a waterfall depends on its height and on the quantity of liquid; the motive power of heat depends also on the quantity of caloric used, and on what may be termed, on what in fact we will call, the height of its fall. (The matter here dealt with being entirely new, we are obliged to employ expressions not in use as yet, and which are perhaps less clear than is desirable.)” His insight that the “height of the fall” of heat set limits on the process took another quarter-century to travel from the fringes of scientific thought to the mainstream. His big idea was almost lost to posterity because most of his papers were burned after his death due to fear of cholera infection and it was a descriptive interpretation of Réflexions by Clapeyron, published two years after Carnot’s death, that provided a picture signpost to the next generation of heat investigators by plotting Carnot’s ideal cycle on a graph of pressure against volume.

I am indebted to ASHRAE Journal reader Bob Hanlon who has produced an excellent (and very accessible) textbook called Block by Block: The Historical and Theoretical Foundations of Thermodynamics. The extract from Réflexions quoted above and much of the historical context comes from Bob’s book, which he says took 20 years to write. It should be on every refrigeration engineer’s bookshelf.

Celebrating Sadi Carnot