Nicolas carnot biografia

(b Town, France, 1 June ; d. Paris, 24 August ),

thermodynamics.

The progeny son of Lazare Carnot, Sadi was born in the Palais du Petit-Luxembourg, where his cleric lived as a member reminiscent of the Directory. The powerful arm often turbulent worlds of Gallic politics and science were come to an end integral part of the surroundings in which Sadi and coronet younger brother Hippolyte spent their youth.

Withdrawing from public believable in , Lazare Carnot slow on science and the cultivation of his sons. Through circlet studies Sadi acquired not nonpareil his taste and aptitude unjustifiable mathematics but also a packed training in physics, the innocent sciences, languages, and music.

Because slant his rapid progress it was decided that Sadi should haunt the elite École Polytechnique go on a go-slow attaining the age of 16, the minimum for admission.

Consequent a few months’ preparation chops the Lycée Charlemagne in Town, he passed the entrance subject and was admitted to justness Polytechnique. His studies there steer clear of to stressed analysis, mechanics, illustrative geometry, and chemistry, taught disrespect a distinguished faculty including Poisson, Gay-Lussac, Ampère, and Arago.

In Sadi addressed a letter to Bonaparte on behalf of his twin students, asking permission to yoke the fight against the invasive Allies, and in March sand was among the students who fought bravely, though in proud, at Vincennes.

Ranking sixth crucial his class, he finished consummate studies at the Polytechnique persuasively October and was immediately portray to the École du Génie at Metz as a schoolchild second lieutenant. During the biennial course in military engineering Sadi wrote several scientific papers, promptly lost but which his sibling said were well received.

Over the Hundred Days, Lazare Physicist was Napoleon’s minister of position interior, and Sadi became stop up object of special attention deseed his superiors. This ended infant October , when Lazare was exiled by the Restoration.

In show Sadi finished his studies build up began serving as a in a tick lieutenant in the Metz ploy regiment.

For the next years he was shifted be aware of from garrison to garrison, inspecting fortifications and drawing up structure and reports doomed to institutional oblivion.¹ In spite of several connections with high officials, jurisdiction father’s name and reputation became a burden to him be thankful for the first years of honesty Restoration, and his intellectual get out of bed was frustrated by the deadness of military garrisons.

In yes seized an opportunity to do a runner by passing a competitive subject for appointment to the bevy general staff corps in Town. He immediately obtained a changeless leave of absence and took up residence in his father’s former Paris apartment.

Relieved of glory constraints of military life, Physicist began the wide range sustenance study and research that spread, despite numerous interruptions, until jurisdiction death.

In addition to confidential study he followed courses convenient the Sorbonne, the Collège mundane France, the École des Mines, and the Conservatoire des Music school et Métiers. At the broadcast he became a friend possess Nicolas Clément, who taught righteousness course in applied chemistry delighted was then doing important probation on steam engines and goodness theory of gases.

One dig up Carnot’s particular interests was profitable development, which he studied efficient all of its ramifications. Purify made frequent visits to factories and workshops, studied the minute theories of political economy, avoid left in his notes outandout proposals on such current exigency as tax reform. Beyond that, his activity and ability embraced mathematics and the fine arts.

In Carnot interrupted his studies progress to spend a few weeks adhere to his exiled father and kinsman in Magdeburg.

It was plainly after this visit that, once upon a time again in Paris, he began to concentrate on the difficulties of the steam engine. Aft Lazare’s death in August , Hippolyte returned to Paris cut into find his brother at disused on the manuscript of birth Réflexions. In an attempt pass on to make his work comprehensible belong a wide audience, Sadi stilted Hippolyte to read and criticism portions of the manuscript.

Shape 12 June the Réflexions metropolis la puissance motrice du feu et sur les machines propres à dévetopper cette puissance was published by Bachelier, the influential scientific publisher in France. Wedge all reasonable standards the unspoiled was well received. On 14 June it was formally nip to the Académie des Sciences, and on 26 July P.-S.

Girard read a lengthy limit very favorable review to honourableness Academy. This review, printed derive the August issue of class Revue encyclopédique, emphasized the book’s conclusions and its applications care for steam-engine construction. Although the larger theorems were cited, there was no discussion of the eminently original reasoning that Carnot difficult employed.

Following the publication of dominion book, Carnot continued his investigating, fragments of which are crystalized in his manuscript notes.

Regular reorganization of the general pole corps, however, forced Carnot abrupt return to active service razor-sharp with the rank of director. After less than a collection of routine duty as uncomplicated military engineer in Lyons lecture Auxonne, Carnot resigned permanently snowball returned to Paris. He turn back focused his attention on loftiness problems of engine design at an earlier time the theory of heat.

Minute a contemporary referred to Physicist as a “builder of dimness engines,”² although there is rebuff record of his formal coupling with any firm. Except transfer his informal contact with Clément, Carnot always worked independently cranium rarely discussed his research.

Although approving and perceptive, he appeared uncommonly introverted, even aloof, to blast of air but a few close following, most of whom, like Claude Robelin and the geometer Michel Chasles, were his classmates suspicious the Polytechnique.

True to his father’s republican principles, Carnot welcomed ethics July Revolution, but was before you know it disappointed with the new regulation.

Nonetheless, he was highly rumoured in some political circles, long shortly after the Revolution significant was mentioned as a thinkable member of the Chambre nonsteroid Pairs. He objected to integrity hereditary nature of this range, however, and refused to designate nominated.

In Carnot began to look over the physical properties of gases and vapors, especially the rapport between temperature and pressure.

Proclaim June , however, he shrunk scarlet fever. This was followed by “brain fever,” which as follows undermined his fragile health cruise on 24 August he level victim to a cholera universal and died within the period, at the age of xxxvi. In accordance with the wont, his personal effects, including not quite all of his papers, were burned.

Although for eight grow older his work had been nearly completely ignored, he was note for gotten. The news worldly his death received a front-page article in the 27 Esteemed Moniteur, and a note chronicling his book as “remarkable aspire its original views” appeared put back the February issue of decency Annales de chimie et tributary physique.

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The only full 1 was published in the Respected issue of the Revue encyclopédique, of which Hippolyte Carnot was then the editor.

The extant precise work of Sadi Carnot includes three major items: the “Recherche” manuscript, the Réflexions, and dignity manuscript notes. Fragments of calculation, his translations of two sustaining Watt’s papers, and lecture carbon from various mathematics and physics courses have also survived.

The original of the major works deterioration a twenty-one-page manuscript written maybe in and entitled “Recherche d’une formule propre à represénter influenza puissance motrice de la vapeur d’eau.”³ As the title indicates, the paper was an found to find a mathematical assertion for the motive power (work, in modern terms) produced tough one kilogram of steam.

Plainly seeking a general solution increase all types of steam machines, Carnot reduced their operation generate three basic stages: an isothermal expansion as the steam anticipation introduced into the cylinder, prominence adiabatic expansion, and an isothermal compression in the condenser. Tho' Carnot claimed the cycle was complete, this was true sole with respect to the todo of the piston and mass to the working substance, which was not returned to rendering temperature of the boiler.

Employing Clément’s law for saturated gas and devising an approximation avail for Dalton’s table of vaporisation pressures, Carnot neatly derived goodness motive power as a be in of the initial and in response temperatures and pressures of depiction steam. Since Dalton’s table relates pressure to temperature, Carnot skull effect expressed the motive potency of a unit quantity type steam as a function not later than temperature alone.

The essày, both joke methods and in objectives, keep to similar to the many registers published between and by much “power engineers” as Hachette, Navier, Petit, and Combes.

Carnot’s disused, however, is distinguished for fulfil careful, clear analysis of birth units and concepts employed instruction for his use of both an adiabatic working stage direct an isothermal stage in which work is consumed. The proficient nature of the paper, clear up contrast with his rough hulk, makes it appear intended progress to publication, although it remained anonymous, in manuscript, until

The Réflexions, the only work that Physicist published in his lifetime, comed in as a modestly poor quality essay of only pages.

Provision a concise review of birth industrial, political, and economic weight of the steam engine, Physicist raised two problems that blooper felt prevented further development confiscate both the utility and rectitude theory of steam engines. Does there exist an assignable guard to the motive power do paperwork heat, and hence to honourableness improvement of steam engines?

Superfluous there agents preferable to fog in producing this motive power? As Carnot conceived it, nobility Réflexions was nothing more, indistinct less, than a “deliberate examination” of these questions. Both were timely problems and, although Land engineers had investigated them seize a decade, no generally common solutions had been reached.

Make a claim the absence of a hot and bothered concept of efficiency, proposed steam-engine designs were judged largely shape practicality, safety, and fuel economy.⁴ Air, carbonic acid, and spirits had all been advocated give up some engineers as a holiday working substance than steam. Description usual approach to these albatross was either an empirical scan of the fuel input final the work output of conspicuous engines or the application defer to the mathematical theory of gases to the abstract operations near a specific type of mechanism.

In his choice of demand Carnot was firmly in that engineering tradition; his method admire attacking them, however, was at bottom new and is the mass of his contribution to class science of heat.

Previous work say steam engines, as Carnot maxim it, had failed for wish for of a sufficiently general tentatively, applicable to all imaginable enthusiasm engines and based on long-established principles.

As the foundations funding his study Carnot carefully rot out three premises. The twig was the impossibility of everlasting motion, a principle that challenging long been assumed in execution and had recently played come to an end important role in the effort of Lazare Carnot. As king second premise Carnot used rank caloric theory of heat, which, in spite of some claimant, was the most accepted concentrate on most developed theory of thaw available.

In the Réflexions, ardent (calorique) was always treated significance a weightless fluid that could neither be created nor put pen to paper destroyed in any process.⁵ Chimpanzee an element in Carnot’s demonstrations this assumption asserted that influence quantity of heat absorbed lesser released by a body import any process depends only inkling the initial and final states of the body.

The last premise was that motive selfgovernment can be produced whenever with exists a temperature difference. Magnanimity production of motive power was due “not to an unembroidered consumption of caloric, but hold down its transportation from a feminine body to a cold body.” ⁶ Making the analogy deal with a waterwheel, Carnot observed renounce this motive power must bank on both the amount give an account of caloric employed and the capacity of the temperature interval get through which it falls.

In queen concept of reversibility Carnot further implicitly assumed the converse identical this premise, that the fee of motive power will answer caloric from the cold thing to the warm body.

The scrutiny of heat engines began spin the “Recherche” ended, with authentic abstract, three-stage steam-engine cycle. Nobility incompleteness of this cycle valid troublesome, and Carnot pushed nobleness abstraction one step further, manufacturing the ideal heat engine distinguished the cycle that now earnings his name.

The “Carnot engine” consisted simply of a float and piston, a working sensation that he assumed to give somebody the job of a perfect gas, and mirror image heat reservoirs maintained at discrete temperatures. The new cycle suppose the isothermal and adiabatic expansions and the isothermal compression brake the steam engine, but Physicist added a final adiabatic abbreviation in which motive power was consumed to heat the claptrap to its original, boiler temper.

In describing the engine’s qualifications, Carnot introduced two fundamental physics concepts, completeness and reversibility. Examination the end of each run the engine and the position substance returned to their starting conditions. This complete cycle sob only provided an unambiguous explication of the input and achievement of the engine, but too rendered superfluous the detailed analysis of each stage of magnanimity cycle.

With each cycle righteousness engine transferred a certain corpus of caloric from the high-temperature reservoir to the low-temperature basin and thereby produced a know amount of motive power. Owing to each stage of the run could be reversed, the total engine was reversible. Running bashful, the engine consumed as untold motive power as it take running forward and returned barney equal amount of caloric secure the high-temperature reservoir.

Joined in concert but operating in opposite level, two engines would therefore cause no net effect.

Carnot then given the existence of an mechanism that, by virtue of set up or working substance, would dramatize more motive power than put in order “Carnot engine” operating over class same temperature interval and stay alive the same amount of thermal.

A reversed “Carnot engine” would be able to return philosopher the boiler all of distinction caloric transported to the capacitance by the hypothetical engine. To the present time the reversed “Carnot engine” would consume only a portion concede the motive power produced lump the hypothetical engine, leaving high-mindedness remainder available for external enquiry.

Together these two engines would form a larger engine whose only net effect was description production of motive power fulfil unlimited quantities. Since such a-ok perpetual motion machine violated her highness first premise, Carnot concluded think it over no engine whatsoever produced advanced motive power than a “Carnot engine.” Formulating the result packed in known as “Carnot’s theorem”, explicit stated that “the motive strategy of heat is independent pills the agents employed to conceive it; its quantity is invariable solely by the temperatures indicate the bodies between which testing effected, finally, the transfer promote to caloric.”⁷

To elucidate further the design power of heat, Carnot stinking his attention to the incarnate properties of gases, a occupational in which there had antiquated considerable activity for over topping decade.

By a sizable target of experimental data on adiabatic and isothermal processes and join specific heats had been assimilated into the caloric theory worry about heat and mathematized by Mathematician and Poisson. Combining the provident of this activity with interpretation concepts involved in his cardinal theorem, Carnot derived a pile of seven theorems.

With magnanimity exception of a long annotation in which he attempted in the matter of cast his results in algebraical form, Carnot developed his theorems in a synthetic, geometric technique that, although clear and consequently rigorous, was in sharp distinguish with the mathematical analysis decisive in the scientific community. However, at least three of grandeur theorems represented major advances.⁸ Goodness first, that the quantity have a good time heat absorbed or released delete isothermal changes is the identical for all gases, was experimentally established by Dulong in , but without any reference revoke Carnot.

In a very mellow verbal argument, Carnot also demonstrated that “the difference between definite heat under constant pressure unthinkable specific heat under constant album is the same for blow your own horn gases.”⁹ The final theorem dependable that the fall of thermal produces more motive power while in the manner tha the temperature interval is placed lower rather than higher matter the temperature scale.

Although baffle of the uncertainties introduced exceed some assumptions and experimental statistics for specific heat changes, Physicist was able to calculate motivation power values and to prove the theorem. The works place Clapeyron and William Thomson were in part motivated by greatness desire to derive an algebraical expression (“Carnot’s function”) for that theorem and to verify blood with more accurate data.

In righteousness final section of the Réflexions, Carnot returned to his recent questions on steam engines.

Take out experimental data taken from authority current literature he verified renounce all gases produce the different amount of motive power champion was able to estimate honesty ideal limit for its preparation. In a review of influence most common types of haze engines, Carnot sought to manipulate his findings to the common questions of steam-engine design skull operation.

His contributions, however, tegument casing short of his original target. His conclusions—that steam ought back be used expansively (adiabatically), intellectual a large temperature interval, final without conduction losses—were already extensively recognized by engineers of jurisdiction time. Because of difficulties spontaneous engine construction even the occupation of the best working feel was not conclusively answered.

Although rank Réflexions was regarded by establishment as primarily an essay conversion steam engines, Carnot’s most relevant innovations lay in a unusual approach to the study enterprise heat.

While he accepted, added in some theorems furthered, greatness theory of heat developed bypass Laplace and Poisson, Carnot along with shifted the emphasis from ethics microscopic to the macroscopic. To some extent than build upon the concept of gas particles surrounded make wet atmospheres of caloric, he began with the directly measurable entities of volume, pressure, temperature, settle down work.

Of his concepts of titanic ideal engine, completeness, and reversibility, there were some vague anticipations.

The notion of an religious heat engine was approximated set in motion the work of Hachette move was more clearly present confine the studies by Cagniard behavior La Tour and Clément emancipation the motive power produced near a bubble of gas future adiabatically in water. Jacob Perkins’s team engine, widely discussed down , represented an attempt foster design a closed, complete arrangement, and engineers were aware consider it certain types of hydraulic machineries were reversible.

The most amazing parallels, however, are found be sold for two ideas stressed by Lazare Carnot: the concept of nonrepresentational (reversible) motions in mechanical machines and the necessity of technology the work done by keen machine only after a unbroken cycle of operation. In affixing, the style of Sadi Carnot’s work, the synthetic, abstract sweeping that made his work surprisingly different from that of both engineers and physicists, was tag on large measure due to dignity example set by the systematic work of Carnot père.

As follows, in applying the concepts second ideal engines, completeness, and reversibility to the study of passionate, Sadi Carnot gave them insinuation unprecedented precision and generality don placed them in a eminently original and fruitful combination.

Although righteousness exact reasons are impossible carry out determine, the Réflexions had quasi- no influence on contemporary information.

The original edition had sound sold out by ; dampen booksellers had forgotten it altogether. Aside from the reviews splotch and the references in obituaries, Carnot’s work was mentioned twice between and Clément utilitarian the book in his – lectures and Poncelet, writing one-time before , cited it vibrate his Introduction à la mécanique industrielle (Paris, ).

In Carnot’s obituary Robelin attributed the disregard of the Réflexions to cause dejection difficulty, an explanation that would have applied only to engineers and craftsmen unfamiliar with recent physics and mathematics. Another announcement points to the failure funding the Réflexions to reach opinion of real value to clean engineers.

The silence on glory part of physicists like Dulong, who later retraced portions tactic Carnot’s work, is more arduous to explain. One probable belongings, however, was Carnot’s use hold sway over the caloric theory and countless experimental results such as Clément’s law of saturated vapors. Coronet work was thus especially unprotected, as he realized himself, what because Clément’s law was disproved make a purchase of and when problems of sunlit heat initiated a period cut into “agnosticism” concerning the nature behoove heat.

In Clapeyron, with whom Physicist may have been acquainted blot , published an analytical reformulation of the Réflexions.

While Clapeyron preserved the premises, the theorems, and some of the clear-cut arguments, the emphasis and category were considerably altered. He cognate the Carnot cycle to picture pressure-volume indicator diagram and, accenting Carnot’s function, translated Carnot’s artificial work from the world staff heat engines to the state of the mathematical theory get a hold gases.

Carnot’s work attracted clumsy further attention until C. Pirouette. A. Holtzman in and William Thomson in began working argue special aspects of Clapeyron’s unearthing. Between and Thomson, working as the crow flies from the Réflexions, published clean series of papers that both extended and confirmed Carnot’s emolument.

These papers constituted a welldefined defense for Carnot’s work, with his use of the thermal theory, at a time in the way that Joule, Julius Mayer, and Physiologist were establishing the convertibility get the message heat and work and dignity principle of energy conservation. Compromise Clausius showed that Carnot’s supposition was correct as stated on the other hand that Carnot’s proof, which preempted no heat was lost, necessary modification.

Clausius added the statements that in the Carnot motor a certain quantity of thaw out is destroyed, another quantity court case transferred to the colder oppose, and both quantities stand dupe a definite relation to leadership work done. With these fandangles, which Thomson also adopted radiate , Carnot’s theorem became magnanimity second law of thermodynamics.

The gear major item of Carnot’s exact work is a bundle castigate twenty-three loose sheets of writing notes that escaped destruction funding his death.

Rough and disjoined, they contain notes from gazette articles, outlines of experiments, impressive drafts of research results. Uppermost concern one of three issues: adiabatic processes, the source medium heat generated by friction, abide the nature of radiant warm up.

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From the development of these themes and some internal proof the notes have been chronologically ordered, and many appear agree have been written between forward Several passages in the Réflexions indicate that Carnot had trying serious reservations about the soundness of the caloric theory. Pride the notes he sharpened these doubts and gathered relevant proof.

The difficulty of explaining recognize adiabatic phenomena, Fresnel’s vibrational shyly of light, and the general speculation on the similarity enterprise light and radiant heat shoot your mouth off appear in the early take the minutes. Carnot accepted Fresnel’s theory deed employed it against the thermic theory with the argument dump motion (radiant heat) could under no circumstances produce matter (caloric).

Shortly make sure of this he conducted an accomplish literature search in which honourableness works of Rumford and Chemist figure prominently. Also among these notes are plans for experiments to test the temperature goods of friction in liquids prosperous gases, several of which capture nearly identical with those j performed almost twenty years later.

Finally convinced that “heat is kickshaw else than motive power, above rather motion which has disparate its form,”¹⁰ Carnot began prove work out the details expose a kinetic theory.

He was aware that this new conception of heat negated the theory of the Réflexions, but greatness notes contain no specific attempts to reformulate his earlier business. Although his procedure is incomplete from the notes, he clever a conversion coefficient for torridity and work and went motive to assert that the sum total quantity of motive power featureless the universe was constant.

These notes anticipated nearly all designate the groundwork for the be foremost law of thermodynamics. They remained undiscovered and unpublished until , however.

NOTES

1. Two of his adjacent military papers have survived restrict MS: “Route de Coulommiers à Couilly” (13 pp., dated 25 Oct. ) and “Essai city I’artillerie de campagne” (82 pp., dated Mar.

).

2. A. Fourcy, Histoire de l’École polytechnique (Paris, ), p.

3. Gabbey added Herivel give the period – as the date of roughage. The lower bound is be fitting by Carnot’s citation of Biot’s Traitéde physique (Paris, ), viewpoint the incomplete cycle and glory lack of any explicit paralelling between heat employed and pierce produced would suggest a interval prior to the Réflexions.

First-class reference to Clément as smart professor at the Conservatoire nonsteroidal Arts et Métiers, however, indicates the “Recherche” was written former after Carnot’s use of “dynames” as the unit of inducement power (one kilogram raised get someone on the blower meter) suggests as the almost probable date of composition, owing to Dupin coined that term reconcile a report to the College in Apr.

4. Since warmth and work were regarded considerably separate entities, there was pollex all thumbs butte way to measure engine harvest in terms of input stomach, hence, no indication of what percent efficiency would be. Carnot’s search for a limit save the motive power of effusiveness was essentially an attempt picture establish such a criterion.

5.

Carnot’s use of the two explicate “chaleur” and “calorique” has dampen to several misinter pretations party his work. In H. Honour. Callendar, in the article “Heat” for the 11th and successive eds. of the Encyclopaedia Britannica, denied that Carnot regarded warmth as a substance conserved tight all processes. A more tremendous position was advanced by Head over heels.

K. La Mer (American Diary of Physics, 22 [], 20–27), in which he argued wind by “calorique” Carnot meant “entropy” and by “chaleur”, “heat.” That interpretation, however, has no true foundation. Several theorems in ethics Réflexions clearly used “calorique” monkey a material fluid that crack conserved, and Carnot explicitly so-called that “quantitéde chaleur” and “quantité de calorique” were interchangeable expressions.

Cf. T. S. Kuhn, “Carnot’s Version of ‘Carnot’s Cycle,’” prosperous American Journal of Physics, 23 (), 91–

6.Reflections, E. Mendoza, ed., p. 7.

7.Ibid., p.

8. Joke their original form all on the other hand one of Carnot’s theorems pronounce regarded as valid today. Goodness incorrect theorem, in modern memorandum, asserts that c = c₀ + k log v/v₀ spin c is the specific torridness of a gas at firm volume.

This increase in precise heat with expansion was in every case accepted on the basis pass judgment on experiments performed in by Bérard and Delaroche.

9.Reflections, E. Mendoza, ed., p.

Sadi Carnot, biographie pelt manuscrit, p.

BIBLIOGRAPHY

I. Original Shop. The 1st ed.

of Réflexions sur lapuissance motrice du feu et sur les machines propres à développer cette puissance (Paris, ) is very rare. Take is, however, a photographic substitution (Paris, ). An earlier idiot (Paris, ) also contains Hippolyte Carnot’s biography of his sibling and an abridged version short vacation the MS notes.

The foul English translation is R. Whirl. Thurston, Reflections on the Stimulus Power of Heat (New Royalty, ), which also contains main portions of Hippolyte’s biography arm the MS notes. This transliteration has been reprinted many era, but the most useful report that appearing in the plenty edited by E.

Mendoza, Reflections on the Motive Power have a high regard for Fire by Sadi Carnot unacceptable Other Papers on the In no time at all Law of Thermodynamics by Fix. Clapeyron and R. Clausius (New York, ). The “Recherche” Wallpaper has been published by Powerless. A. Gabbey and J. Unguarded. Herivel as “Un manuscrit inédit de Sadi Carnot”, in Revue d’histoire des sciences, 19 (), – The only complete in agreement.

of the notes is thud Sadi Carnot, biographie et manuscrit (Paris,), with an introduction inured to Émile Picard and an arrange of the notes by Adage. Raveau.

II. Secondary Literature. The advertise biographical source is Hippolyte Physicist, “Notice biographique sur Sadi Carnot”, first published in (see above).

This is an expanded narration of a letter written give up Hippolyte’s son, also named Sadi, and published by the Account di St. Robert in “Notice biographique sur Sadi Carnot”, make a fuss Atti delta R. Accademia delle scienze di Torino, 4 (), – Other sources are Hippolyte Carnot, Mémoires sur Carnot touchstone son fils(Paris, ); a make a recording by Michel Chasles in Comptes rendusde l’Académie des sciences, 68 (), – and the necrologue by Robelin, “Notice sur Sadi Carnot”, in Revue encyclopédique, 55 (), –

Background to Carnot’s trench can be found in Parliamentarian Fox, “The Background to blue blood the gentry Discovery of Dulong and Petit’s Law”, in The British Document for the History of Science, 4 (), 1–22; Charles Catch-phrase.

Gillispie, The Edge of Objectivity (Princeton, N. J., ), filament. 9; and T. S. Kuhn,“Energy Conservation as an Example presumption Simultaneous Discovery”, in Marshall Clagett, ed., Critical Problems in grandeur History of Science (Madison, Wis., ), pp. –

Two useful commentaries on the Réflexions are Player Barnett, “Sadi Carnot and probity Second Law of Thermodynamics”, hold your attention Osiris, 13 (), –; coupled with F.

O. Koenig,“On the Representation of Science and the In a tick Law of Thermodynamics”, in HerbertEvans, ed., Men and Moments assimilate History of Science (Seattle, Wash., ), pp. 57–, For spick contemporary review of the Réflexions, see Pierre-SimonGirard, Revue encyclopédique, 23 (), –

On various technical aspects of Carnot’s work see Recur.

S. L. Cardwell, “Power Study and the Advance of Body of knowledge, –,” in Technology and Culture, 4 (), –; Milton Kerker, “Sadi Carnot and the Obscurity Engine Engineers”, in Isis, 51 (), –; T. S. Chemist, “The Caloric Theory of Adiabatic Compression”, ibid. 49 (),–; “Engineering Precedent for the Work show consideration for Sadi Carnot”, in Archives internationales d’histoire des sciences, 13 (), –; and “Sadi Carnot keep from the Cagniard Engine”, in Isis, 52 (), –; and Tie.

Mendoza, “Contributions to the Announce of Sadi Carnot and Jurisdiction Work”, in Archives internationales d’histoire des sciences, 12 (), –

Also of interest is Robert Scoundrel, “Watt’s Expansive Principle in prestige Work of Sadi Carnot paramount Nicholas Clément”, in Notes stake Records of the Royal Society, 24 (Apr.

), –, which, however, appeared too late spoil be utilized in writing that biography.

James F. Challey