Eur. J. Phys. 20 (1999) 183–192. Printed in the UK PII: S0143-0807(99)97568-2Sadi Carnot, ‘Founder of the SecondLaw of Thermodynamics’Herman ErlichsonDepartment of Engineering Science and Physics, College of Staten Island, City University ofNew York, Staten Island, NY 10314, USAE-mail: [email protected] 5 September 1998Abstract. Sadi Carnot was one of the giants of physics. Although he used the incorrect calorictheory of heat in his R´eflexions, nevertheless he may rightfully be considered to be ‘the Founder ofthe Second Law of Thermodynamics’.1. IntroductionSadi Carnot (1796–1832) may rightfully be considered the ‘Founder of the Second Law ofThermodynamics’—despite having used the subsequently discredited caloric theory of heatin the only work he published during his lifetime, his R´eflexions sur la puissance motrice dufeu et sur les machines propres a d´evelopper cette puissance [1]. After the publication of hisR´eflexionshe continued his research, and his Notes [2, 3] indicate that he abandoned the calorictheory for the mechanical theory of heat. These Notes were only published posthumously. Inthis paper we will try to show how Carnot’s theoretical ideas on heat engines in his slim (118pages), partly incorrect, book secured for him a major position in the history of physics.2. Historical backgroundSadi Carnot had one of the shortest lifetimes, just 36 years, of any of the giants in the historyof physics. Carnot’s period was that of the Industrial Revolution and the steam engine. Sadiwas the son of Lazare Carnot, a prominent figure in the era of the French Revolution andNapoleon, and no mean scientist in his own right. Mendoza [4, p xii] attributed Sadi’s abilityto generalize to his father and said of Carnot’s R´eflexions that:The Memoir transcended technical details because Sadi had inherited from his fatherthe capacity to generalize, to see the fundamental processes animating a complicatedmechanism. Thus he saw that in an engine—any engine—an amount of caloric fellfrom a high to a low temperature; he extended some of his father’s ideas on mechanicstoapplytothermal processes—theimpossibility ofperpetual motion, theneed toavoidirreversible changes.Sadi was trained at the prestigious´Ecole Polytechnique from 1812 to 1814, following whichhe studied military engineering for two years at the´Ecole du G´enie in Metz. In 1819 he wasgranted a permanent leave of absence from the army and embarked on a highly productiveperiod of study and research in Paris. On 12 June 1824 his R´eflexions book [1] was published0143-0807/99/030183+10$19.50 © 1999 IOP Publishing Ltd 183184H Erlichsonby Bachelier. After that, except for a short period when he returned to military service, Carnotcontinued his research in thermodynamics. He died at age 36 on 24 August 1832, a victim ofa cholera epidemic.Carnot’s Refl´exions was basically ignored by the community of his contemporaries inscience at the time of its publication. We hazard the guess that this is because Carnot wasoutside of the scientific establishment. He had been trained as a military engineer and servedin the army. How could a book written by such a person command the interest of the trainedphysicists of the period? J F Challey, in his article on Carnot for The Dictionary of ScientificBiography [5], writes that ‘In 1828 a contemporary referred to Carnot as a “builder of steamengines”, although there is no record of his formal connection with any firm’. We maintain thatit was this association of the name of Sadi Carnot with engineering, as distinct from science,that delayed the recognition of Carnot’s fertile ideas on thermodynamics.Once the belatedrecognitionofCarnotoccurred, people had to dealwithhisuseofthenowobsolete caloric theory in the R´eflexions, and more importantly, the absence in that work of theprinciple of conservation of energy. It was nevertheless recognized that after the publicationof the R´eflexions he had come to grips with both the mechanical theory of heat and with theFirst Law of Thermodynamics. The R´eflexions, which had made so small a stir on its originalpublication in 1824, was republished in 1878 in a new edition [2], which also contained a letterfrom Sadi’s brother, Hippolyte Carnot, to the French Academy of Sciences, and some of theunpublished Notes written by Sadi after the publication of his R`eflexions. Hippolyte saw hisbrother as the founder of the science of thermodynamics. He wrote (English translation by HErlichson):We are therefore justified in saying that if, in his first work, published in 1824,he formulated the principle to which his name is preserved, by his later work healso discovered the principle of equivalence, which makes up, with the first, thefundamental basis of thermodynamics.We will also have occasion to refer to a 1953 photographic reprint [3] of the original 1824R´eflexions including some of the material in [2], and to the most recent English translation ofCarnot’s R´eflexions made by Robert Fox [6] in 1986.3. Carnot’s intention to study heat engines from a general viewpointCarnot opens his R´eflexions by stressing the practical importance of heat engines [4, p 3]:The study of these engines is of the greatest interest, their importance is enormous,theiruseiscontinuallyincreasing,andtheyseemdestinedtoproduceagreatrevolutionin the civilized world.This kind of opening is what one would expect from a practical engineer enthusiasticabout practical progress. But, shortly thereafter, we find [4, p 6]:The phenomenon of the production of motion by heat has not been considered from asufficiently general point of view. . . . In order to consider in the most general way theprinciple of the production of motion by heat, it must be considered independentlyof any mechanism or any particular agent. It is necessary to establish principlesapplicable not only to steam-engines, but to all imaginable heat-engines, whateverthe working substance and whatever the method by which it is operated.Herewehavethevoiceofthescientist, not that oftheengineer. And, in the verynextparagraph,Carnot calls for a physical theory which can be used to achieve for heat engines what has beenachieved for mechanical devices such as waterfalls or windmills [4, p 6]:We shall have it only when the laws of physics shall be extended enough, to makeknown beforehand all the effects of heat acting in a determined manner on any body.Sadi Carnot,