|1813 portrait of Sadi Carnot, at the age of 17 in his Polytecnique uniform, by Louis Boilly.|
Heat | Work
In 1824, Carnot, when he published his now famous memoir On the Motive Power of Fire, adhered to the “caloric” model of heat.
In c.1827, Carnot, in his manuscripts notes (made available when in 1878 Hippolyte Carnot deposited them to the French Academy of Sciences), according to Robert Thurston (1880) and Robert Fox (1986), had recognized the doctrine of the equivalence of heat and mechanical energy; the following, below left, is an extract of what he had written in these notes: (Ѻ)
|French | Carnot | manuscript notes (c.1927)||English | Thurston (1880) translation|
|“La Chaleur n'est autre que la puissance motive, ou plutót, que le mouvement qui a changé de forme. C'est un mouvement dans les particules des corps. Partout ou il y a destruction de puissance motive, il y a, en même temps, production de chaleur en quantité précisément proportionelle à la quantité de puissance motive détruite. Réciproquement, partout on ily a destruction de chaleur, il y a production de puissance motive.” |
On peut donc poser en thèse générale que la puissance motive est en quantité invariable dans la nature, qu’elle n'est jamais, a proprement parler, détruite. A la vérité, elle change de forme, c'est-a-dire qu’elle produit tantôt un genre de mouvement, tantôt un autre; mais jamais elle n'est anéantie.”
| “Heat is nothing else than motive power (energy), or rather, a motion which has changed its form. It is a motion of the molecules of bodies. Whenever motive power is destroyed, there is, at the same time, a production of heat in quantity precisely proportional to the quantity of power destroyed. Reciprocally, wherever there is destruction of heat, there is production of power of motion. |
We may then state as a general law, that energy is, in nature, invariable in amount; that is, is never, properly speaking, either created or destroyed. In fact, it changes form; that is, it causes sometimes one kind of motion, sometimes another; but it is never destroyed.”
|English | Google translation|
English | Fox (1880) translation
|"Heat is none other than motive power, or rather, movement that has changed form. It is a movement in the particles of bodies. Wherever there is a destruction of motive power, there is at the same time a production of heat in proportion to the quantity of motive power destroyed. Conversely, everywhere there is a destruction of heat, there is a production of motive power. |
It may therefore be posited in general theory that motive power is in invariable quantity in nature, that it is never, strictly speaking , destroyed. In truth, it changes its form, that is to say, it produces sometimes a kind of movement, sometimes another; but it is never destroyed."
|“Heat is nothing but motive power, or rather motion, which has changed form. It is motion of the particles of bodies. Whenever motive power is destroyed, there is a simultaneous production of an amount of heat exactly proportional to the motive power that is destroyed. Conversely, whenever there is destruction of heat, motive power is produced.|
Hence, we may state, as a general proposition, that the quantity of motive power in nature is fixed, and that, strictly speaking, motive power is neither produced nor destroyed. It is true that it changes its form' that is, it simetimes produces one kind of motion, sometimes another. But it is never annihilated.” 
Here, we see Thurston reading into the French to English translation, a bit more than Carnot had intuited.
Sadi was born June 1796 in Paris to French mathematical engineer Lazare Carnot, founder of the world's leading engineering school the École Polytechnique (first so-called "school of thermodynamics") of the day, and Sophie Dupont, the daughter of a well-off family of Saint-Omer. In August of 1807, Lazare decided to take care of the education of his two sons, Sadi and younger brother Hippolyte Carnot, and teaches them math, science, languages, and music. In 1812, Sadi entered the École Polytechnique, graduating two years later.
In 1818, Carnot retired into a general staff position, at half pay, into “voluntary obscurity” in Paris. There, however, he was said to gravitate to the Conservatoire des Arts et Metiers, a recently founded technological museum, offering lectures to the general public. Here, supposedly, Carnot fell into the association of brother-in-laws Nicholas Clement and Charles Bernard Desormes, who did joint research on the physics of steam engines. All three, were said to have felt a need to boost France’s mills and factories industry operations, and that the way to do this was to better understand the principles behind the operation of steam engines. Carnot devoted the years 1820 to 1824 to this effort. 
|Men of the Carnot family: Lazare Carnot (father), Sadi Carnot (thermodynamicist), and Hippolyte Carnot (brother).|
In 1824, Sadi self-published his treatise Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power, in an edition of 600 copies. In this work, Carnot's overall aim, stimulated by the earlier work of his father, on the universal nature of geometric operation and force constraints of machines, was to outline the general principles and laws of the phenomenon of the production of motion by heat not only to steam engines but to all imaginable heat-engines, whatever the working substance and whatever the method by which it is operated. Other terms or concepts introduced by Carnot include: working substance, motive power, "re-establishment of equilibrium in the caloric", thermodynamic efficiency, among others.
In 1834, Carnot's Reflections was put on a graphical footing by French physicist Émile Clapeyron.  It was through Clapeyron that Carnot's theories were introduced to German physicist Rudolf Clausius who, beginning in 1850, was thus stimulated to spend 15-years writing the monumental Mechanical Theory of Heat, through which "entropy" and the second law of thermodynamics were introduced.
The key point of Carnot's work that goaded Clausius to such an effect was Carnot's postulate, based on the faulty caloric theory, that "no change occurs in the condition of the working body" in a complete heat engine cycle. Clausius sought to remidy this statement by introducing a new variable to science dQ/T called "entropy" that in any heat engine process (cycle), which is in any way possible, increases, meaning that energy is used by the molecules of the working body on each other as they change their physical condition of state or configuration during each step of an expansion or contraction due to the action of a heat gradient.
|Sadi Carnot at age 34 (1830) |
The paragraph that interested Clausius to such an effect, via his reading of Clapeyron's 1834 paper, in reference to the process in which work is done by heat through the medium of a working body in alternate contact with a heat gradient, is Carnot’s postulate that (as quoted by Clausius): 
“No heat is lost in the process, but that the quantity of heat remains unchained … this fact is not doubted; it was assumed at first without investigation, and then established in many cases by calorimetric measurements. To deny this would overthrow the whole theory of heat, of which it is the foundation.”
This paragraph is the core of the science of thermodynamics. The term "quantity of heat" here refers to French physicist Antoine Lavoisier's 1787 theory of particles of caloric, which were considered to be indestructible entities responsible for the expansion of bodies by the action of heat. 
Quotes | On
The following are tributes and praise:
“The celebrated memoir on the motive power of heat, published in 1824 by Sadi Carnot, then only 28 years of age, has become extremely rare. The work passed long without notice, and did not acquire any fame until it was perceived to be the true origin of the magnificent researches of Clausius, Rankine, Joule, and several others in thermo-dynamics. Physicists will be pleased to learn that Hyppolyte Carnot, brother of the author, and Senator, has reedited this work, which has so much historical interest; also that the new edition is enriched with notes hitherto unpublished, and one of which, at least, has considerable importance. It proves, in fact, that Sadi Carnot, by the end of his too short life, had come to regard thermodynamics in their true light, perceiving that the work done by the steam-engine represents a transformation of heat. The manuscript of the memoir and the notes will be deposited in the Library of the French Academy.”— Anon (1879), notice (Ѻ), English Mechanic and World of Science, 717:418, Jan 3
“Nicolas-Leonard-Sadi Carnot was, perhaps, the greatest genius, in the department of physical science at least, that this century has produced.”— Robert Thurston (1890) 
“Carnot’s argument is perhaps the most original in physical science.”— Joseph Larmor (1918), “On the Nature of Heat” 
“In the annals of science, Carnot’s Motive Power of Fire is almost unique, for it had no discernible predecessors and was built up from the assemblage of unordered opinions and problems, concepts, theories and measurements that were available at the time. Carnot, in short, was not standing on the shoulders of giants; he saw further than his contemporaries because he had a much clearer vision.”— Donald Cardwell (1971), From Watt to Clausius (pg. 193)
“The most original work ever written in the physical sciences, with a core of abstraction comparable to the best of Galileo”— Tom Shachtman (1999), Absolute Zero and the Quest for Absolute Cold 
Quotes | By
The following are noted quotes:
“Say little about what you know and nothing at all about what you don’t know. When a discussion degenerates into a dispute, keep silent. Do not do anything which the whole world cannot know about.”— Sadi Carnot (c.1820), “Rules of Conduct”, personal notes 
1. Carnot, Sadi. (1824). Reflections on the Motive Power of Fire: and on Machines Fitted to Develop that Power. Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55.
2. Clapeyron, Emile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX,  446, 566).
3. Clausius, Rudolf. (1865). The Mechanical Theory of Heat: with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst.
4. Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws Which can be Deduced From it for the Theory of Heat." Poggendorff's Annalen der Physik, LXXIX, 368, 500.
5. Lavoisier, Antoine. (1787). Elements of Chemistry. Edinburgh: G.G. and J.J. Robinsons.
6. (a) Personal notes of Sadi Carnot (category: rules of conduct).
(b) In: Mendoza, E. (1960). “Introduction” (section) in Carnot, Sadi. (1824). “Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power.” Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55. (1960, Dover edition).
7. Thurston, Robert H. (1890). ch. 1: “The Work of Sadi Carnot” (pg. 1); In: Carnot, Sadi, Thurston, Robert H., Carnot, Hippolyte, Thomson, William, and Smith, Albert W. (1890). Reflections on the Motive Power of Heat and on Machines Fitted to Develop that Power: From the Original French of N.L.S. Carnot. John Wiley & Sons.
8. Carnot, Sadi. (1988). Reflections on the Motive Power of Fire and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius (edited with an introduction by E. Mendoza). (Carnot photo, pg. v). Dover.
9. Shachtman, Tom. (1999). Absolute Zero and the Quest for Absolute Cold (pg. 81). Mariner Books.
10. (a) Larmor, Joseph. (1918). “On the Nature of Heat” (pg. 326), Philosophical Transactions of the Royal Society.
(b) Cardwell, Donald S.L. (1971). From Watt to Clausius: the Rise of Thermodynamics in the Early Industrial Age (pgs. 119-20). Cornell University Press.
11. Fox, Robert. (1986). Reflections on the Motive Power of Fire: a Critical Edition with the Surviving Scientific Manuscripts (heat quote, pgs. 26, 191). Manchester University Press.
● Carnot, Sadi, Hippolyte Carnot, and Thomson, William. (1890). Reflections on the Motive Power of Fire and on Machines fitted to Develop this Power. J. Wiley.
● Lervig, Philip. (1972). “On the Structure of Carnot’s Theory of Heat” (abstract), Archive for the History of Exact Sciences, Vol. 9, No. 3, pgs. 222-39.
● Carnot, Sadi. (1986). Reflections on the Motive Power of Fire: a Critical Edition with the Surviving Scientific Manuscripts (editor and translator: Robert Fox). Publisher.
● Gillispie, Charles; Pisano, Raffaele. (2014). Lazare and Sadi Carnot: a Scientific and Filial Relationship. Springer.
● Nicholas Leonard Sadi Carnot – Wikipedia.