Editing Nicolas Léonard Sadi Carnot (section)

==''Reflections on the Motive Power of Fire''==
{{Main|Reflections on the Motive Power of Fire}}
[[File:Carnot title page.png|thumb|Title page of Sadi Carnot's ''Réflexions sur la puissance motrice du feu'' ("Reflections on the motive power of fire"), published in Paris in June 1824]]

Sadi Carnot's contribution to the development of [[thermodynamics]] is contained in his only published work, a short book titled ''Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance'' ("Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power") published in Paris in June of 1824 by Bachelier, with Carnot himself paying for the printing of the 600 copies.<ref>{{Harvnb|Almanza|Horsin Molinaro|Lo Bue|2024|p=7}}</ref>  The work attracted little attention during his lifetime and virtually disappeared from booksellers and libraries.<ref>{{Harvnb|Klein|1974|p=26}}</ref>  An article published in 1834 (two years after Carnot's death and ten years after the publication of his book) by the engineer and fellow ''polytechnicien'' [[Émile Clapeyron]] finally succeeded in calling attention to Carnot's work, which some years later was used by [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] and [[Rudolf Clausius]] to define the concepts of [[absolute temperature]], [[entropy]], and the [[second law of thermodynamics]].<ref>{{Harvnb|Klein|1974|pp=26–28}}</ref>

===Background===
[[Thomas Newcomen]] invented the first practical piston-operated [[steam engine]] in 1712.  Some 50 years after that, [[James Watt]] made his celebrated improvements, which were responsible for greatly increasing the usefulness of steam engines.  When Carnot became interested in the subject in the 1820s, steam engines were in increasingly wide application in industry and their economic importance was widely recognized.  Compound engines (engines with more than one stage of expansion) had already been invented, and there was even a crude [[internal combustion engine]], known as the ''[[pyréolophore]]'' and built by the brothers [[Claude Niépce|Claude]] and [[Nicéphore Niépce]], with which Carnot was familiar and which he described in some detail in his book.

That practical work on steam engines and the intuitive understanding among engineers of some of the principles underlying their operation co-existed, however, with an almost complete lack of a scientific understanding of the physical phenomena associated with [[heat]].  The principle of [[conservation of energy]] had not yet been clearly articulated and the ideas surrounding it were fragmentary and controversial.  Carnot himself accepted the view, prevalent in France and associated with the work of [[Antoine Lavoisier]], that heat is a weightless and invisible [[fluid]], called "[[caloric theory|caloric]]", which may be liberated by chemical reactions and which flows from bodies at higher [[temperature]] to bodies at lower temperature.

In his book, Carnot sought to answer basic questions: ''Is there a limit to the work that can be generated from a given heat source?'' and ''Can the performance of an engine be improved by replacing steam with a different [[working fluid]]?''.  Engineers in Carnot's time had tried, using highly pressurized steam and other fluids, to improve the [[thermodynamic efficiency|efficiency]] of engines. In these early stages of engine development, the efficiency of a typical engine —the useful work it was able to do when a given quantity of [[fuel]] was burned— was only about 5–7%.<ref>{{Harvnb|Asimov|1982|p=332}}</ref>

Carnot's book was only 118 pages long and covered a wide range of topics about heat engines in what Carnot must have intended to be a form accessible to a wide public.  He made minimal use of mathematics, which he confined to elementary algebra and arithmetic, except in some footnotes.  Carnot discussed the relative merits of air and steam as working fluids, the merits of various aspects of steam-engine design, and even included some ideas of his own regarding possible practical improvements.  However, the central part of the book was an abstract treatment of an idealized engine (the [[Carnot cycle]]) with which the author sought to clarify the fundamental principles that govern all heat engines, independently of the details of their design or operation.  This resulted in an idealized [[thermodynamic system]] upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engines.

===Carnot cycle===
{{main|Carnot heat engine|Carnot cycle}}
[[File:Carnot-engine-1824-vector.svg|thumb|150px|right|Cross section of Carnot's heat engine. In this diagram, ''abcd'' is a cylindrical vessel, ''cd'' is a movable piston, and ''A'' and ''B'' are thermal reservoirs at different temperatures. The vessel may be placed in contact with either reservoir or removed from both.  This is Figure 1 in Carnot's book.<ref>{{Harvnb|Carnot|1890|p=63}}</ref>]]

Carnot considered an idealized process in which heat from a [[thermal reservoir]] at a high temperature flows very slowly (and thus [[thermodynamic reversibility|reversibly]]) into the gas contained in a cylinder enclosed by a movable piston.  This gives an [[Isothermal process|isothermal expansion]] of the gas that pushes out the piston and can be used to perform useful work.  This does not yet constitute an engine because the piston must be returned to its original position in order for the machine to run cyclically.

Carnot then proposed reducing the temperature of the gas by an [[Adiabatic process|adiabatic expansion]], during which the cylinder is thermally isolated so as to prevent heat from entering or leaving the gas.  Once the temperature of the gas has reached the same value as that of the colder reservoir, the cylinder is put into thermal contact with that reservoir and the gas undergoes an isothermal compression, during which it very slowly (and thus reversibly) rejects heat into the reservoir.

To close the cycle, the temperature of the gas in the cylinder can be raised by adiabatic compression, until it reaches a value equal to the temperature of the hotter reservoir.  This succession of isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression can then be repeated as many times as desired, generating a net amount of work each time, at the expense of a transfer of heat from the hotter reservoir to the colder reservoir.

As Carnot explained, such a cycle constitutes the most efficient heat engine possible (given the temperatures of the two reservoirs), not only because of the (trivial) absence of friction, heat leakage, or other incidental wasteful processes: The main reason is that it involves no conduction of heat between parts of the engine at different temperatures. Carnot understood that the conduction of heat between bodies at different temperatures is a wasteful and [[irreversible process]], which must be minimized if the heat engine is to achieve its maximum efficiency.

[[File:Carnot cycle p-V diagram.svg|thumb|250px|Carnot cycle in a [[pressure]] vs. [[volume]] diagram.  This graphical representation of Carnot's cycle was introduced by [[Émile Clapeyron]] in 1834.]]

Because Carnot's cycle is reversible, it can also be used as a [[refrigerator]]: if an external agent supplies the needed mechanical work to move the piston, the sequence of transformations of the gas will absorb heat from the colder reservoir and reject it into the hotter reservoir.  Carnot argued that no engine operating between reservoirs at two given temperatures could deliver more work than his reversible cycle.  Otherwise, the more efficient engine could run Carnot's cycle in reverse as a refrigerator, thus returning all of the "caloric" from the colder back to the hotter reservoir, with some positive amount of work left over to perform a further useful task.  Carnot assumed that such a process, in which no net "caloric" was consumed while positive work could be done forever, would be a [[perpetual motion]] and therefore forbidden by the laws of physics.

This argument led Carnot to conclude that 

{{quote|The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.<ref>{{Harvnb|Carnot|1890|p=68}}</ref>}}

Carnot understood that his idealized engine would have the maximum possible [[thermal efficiency]] given the temperatures of the two reservoirs, but he did not calculate the value of that efficiency because of the ambiguities associated with the various temperature scales used by scientists at the time:

{{quote|In the fall of caloric, motive power undoubtedly increases with the difference of temperature between the warm and cold bodies, but we do not know whether it is proportional to this difference.<ref>{{Harvnb|Carnot|1890|p=61}}</ref>}}

=== Phase transitions ===
{{main|Clausius–Clapeyron relation}}

Later in his book, Carnot considered a heat engine operating very close to the [[boiling point]] of water, alcohol, or some other working fluid.  The transition between the liquid and vapor phases involves a sudden change in [[density]] (and therefore in the volume occupied by the fluid) while a [[latent heat]] is needed to transform some amount of the fluid from one phase to the other.  By requiring that the volume change associated with such a transition not be available to construct what he characterized as a perpetual motion device, Carnot arrived at what would later be formalized mathematically as the "[[Clausius–Clapeyron relation]]".  In the ''[[The Feynman Lectures on Physics|Feynman Lectures on Physics]]'', theoretical physicist [[Richard Feynman]] stresses that this result is due to Carnot and gives a modernized version of Carnot's original argument.<ref>{{Harvnb|Feynman|1963}}</ref>

In 1849, [[James Thomson (engineer)|James Thomson]] (the elder brother of [[Lord Kelvin]]), applied Carnot's reasoning to the [[freezing]] of water (i.e., the phase transition between liquid water and ice), and concluded that it predicted that the [[melting point]] of ice must decrease if an external pressure is applied to it, an effect that no one had ever proposed or studied before.  James Thomson's prediction was later confirmed experimentally by his brother (the future Lord Kelvin), who found that the data agreed fully with Carnot's analysis.<ref>{{Harvnb|Klein|1969|p=130}}</ref>  Kelvin later said of Carnot's argument that "nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning."<ref>{{Harvnb|Thomson|1849|p=564}}</ref>

=== Reception ===
Carnot published his book in June 1824, and it was presented at that time to the [[French Academy of Sciences]] by [[Pierre-Simon Girard]].  Girard also published a praiseful but rather broad review of the book in the ''Revue encyclopédique'', but after that the book seems to have fallen into obscurity.  It was only after the publication of an extensive commentary and explication of Carnot's work by [[Émile Clapeyron]] in 1834 that engineers and scientists began to take an interest in Carnot's contributions.  Clapeyron's article was translated into English in 1837 and into German in 1843.<ref>{{Harvnb|Klein|1974|p=26}}</ref>

[[Lord Kelvin|Kelvin]] read Clapeyron's paper in 1845, while visiting the Paris laboratory of [[Henri Victor Regnault|Henri Regnault]], but it was only at the end of 1848 that Kelvin was able to read Carnot's original work, in a copy provided to him by [[Lewis Gordon (civil engineer)|Lewis Gordon]].  Independently of Kelvin, the German physicist [[Rudolf Clausius]] also based his study of [[thermodynamics]] on Carnot's work.  Clausius modified Carnot's arguments to make them compatible with the [[Mechanical equivalent of heat|mechanical equivalence of heat]].  This then led Clausius to define the concept of [[entropy]] and to formulate the [[second law of thermodynamics]].

Carnot's text was re-printed in 1871 in the ''Annales Scientifiques'' of the [[École normale supérieure (Paris)|École normale supérieure]], and again by Gauthier-Villars in 1878 with the collaboration of Hippolyte Carnot.  In 1890 an English translation of the book was published by [[Robert Henry Thurston|R. H. Thurston]].<ref>{{Harvnb|Carnot|1890}}</ref>  That version has been reprinted in recent decades by [[Dover Publications|Dover]].  In 1892, Lord Kelvin referred to Carnot's essay as "an epoch-making gift to science."

Carnot published his book in the heyday of steam engines. His theory explained the advantage of engines that use superheated steam, since they absorb heat from a reservoir at a higher temperature.  Carnot's work did not, however, lead to any immediate practical improvements of steam technologies.  It was only towards the end of the nineteenth century that engineers deliberately implemented Carnot's key concepts: that the efficiency of a heat is improved by increasing the temperature at which heat is drawn and by minimizing the flow of heat between bodies at different temperatures.  In particular, [[Rudolf Diesel]] used Carnot's analysis in his design of the [[diesel engine]], in which heat is injected at a much higher temperature than in the older steam engines, and in which the heat from the combustion of the fuel goes primarily into expanding the air in the cylinder (rather than into increasing its temperature).<ref>{{Harvnb|Bryant|1976|p=435}}</ref>