Nicolas Léonard Sadi Carnot
Encyclopedia
Nicolas Léonard Sadi Carnot (1 June 1796 – 24 August 1832) was a French
military engineer
who, in his 1824 Reflections on the Motive Power of Fire
, gave the first successful theoretical account of heat engine
s, now known as the Carnot cycle
, thereby laying the foundations of the second law of thermodynamics
. He is often described as the "Father of thermodynamics", being responsible for such concepts as Carnot efficiency
, Carnot theorem, Carnot heat engine
, and others.
, Sadi Carnot was the first son of the eminent military leader
and geometer, Lazare Nicholas Marguerite Carnot, elder brother of Hippolyte Carnot
, and uncle of Marie François Sadi Carnot
(President of the French Republic (1887-1894), son of Hippolyte Carnot
). His father named him after the Persian poet Sadi of Shiraz
, and he was always known by this third given name.
From age 16 (1812), he lived in Paris and attended the École polytechnique
where he and his contemporaries, Claude-Louis Navier
and Gaspard-Gustave Coriolis
, were taught by professors such as Joseph Louis Gay-Lussac
, Siméon Denis Poisson
and André-Marie Ampère
. After graduation, he became an officer in the French army
before committing himself to scientific research, becoming the most celebrated of Fourier's contemporaries who were interested in the theory of heat
. Since 1814, he served in the military. Following the final defeat of Napoleon in 1815, his father went into exile. He later obtained permanent leave of absence from the French army. Subsequently, he spent time to write his book.
, and yet the engine was actually pretty far along in its development. It had risen to a widely recognized economic and industrial importance. Newcomen
had invented the first piston-operated steam engine over a century before, in 1712. Some 50 years after that, Watt
made his celebrated improvements which greatly increased the efficiency and practicality of the engine. Compound engines (engines with more than one stage of expansion) had already been invented. There was even a crude form of internal-combustion engine, with which Carnot was familiar and which he described in some detail in his book. Amazing progress on the practical side had been made, so at least some intuitive understanding of the engine's workings existed. The scientific basis of its operation, however, was almost nonexistent even after all this time. In 1824 the principle of conservation of energy
was still immature and controversial, and an exact formulation of the first law of thermodynamics
was still more than a decade away. The mechanical equivalent of heat
was not identified for another two decades. The prevalent theory of heat was the caloric theory
, which regarded heat as a sort of weightless, invisible fluid
that flowed when out of equilibrium
.
Engineer
s in Carnot's time had tried various mechanical means, such as high pressure steam
, or the use of some fluid other than steam, to improve the efficiency of their engines. In these early stages of engine development, the efficiency of a typical engine -- the useful work it was able to perform when a given quantity of fuel
such as a lump of coal
was burnt -- was a mere 3%.
Perhaps the most important contribution Carnot made to thermodynamics was his abstraction of the essential features of the steam engine as it was known in his day into a more general, idealized heat engine
. This resulted in a model thermodynamic system
upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engine. By idealizing the engine, he could arrive at clear, indisputable answers to his original two questions.
He showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be (T1−T2)⁄T1, where T1 is the absolute temperature of the hotter reservoir. (Note: This equation probably came from Kelvin
.) No thermal engine operating any other cycle can be more efficient, given the same operating temperature
s.
He saw very clearly, intuitively, that he could give very definite answers to the two questions set before the reader. The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. He knew that conduction of heat between bodies at different temperatures is a wasteful, irreversible process and must be eliminated if the heat engine is to have the maximum efficiency.
Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of the working fluid
. He stated this for emphasis as a general proposition: "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 the transfer of caloric takes place." For his "motive power of heat", we would today say "the efficiency of a reversible heat engine," and rather than "transfer of caloric" we would say "the reversible transfer of heat." He knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be.
He concluded:
and
Though formulated in terms of caloric, rather than entropy
, this was an early insight into the second law of thermodynamics
.
, who together derived from it the notion of entropy
and the second law of thermodynamics.
epidemic when he was only 36 in 1832. Because of the concern of cholera
, many of his belongings and writings were buried together with him after his death. Thus only a handful of his scientific writings survived besides his book.
After the publication of his book in 1824, it quickly went out of print and for some time was very difficult to obtain. For example, Kelvin
had great difficulty in getting a copy of Carnot's book. An English translation of it by R. H. Thurston in 1890 has been reprinted in recent decades by Dover
and by Peter Smith, most recently by Dover in 2005. Some of his posthumous manuscripts have also been translated into English. (See Reference.)
Carnot published his book in the days of steam engines. His theory explained why steam engines using superheated steam were better because of the higher temperature of the hot reservoir involved. Carnot's theory did not help to improve the efficiency of steam engines in the beginning; his theory only helped to explain why one existing practice was better. It was only towards the end of the nineteenth century that Carnot's idea -- that a heat engine can be made more efficient if the temperature of its hot reservoir is increased -- was put into practice by, for example, Rudolf Diesel
(1858-1913), who was fascinated by Carnot's theory and designed an engine (diesel engine
) in which the temperature of the hot reservoir is much higher than that of a steam engine, resulting in an engine which is more efficient than a steam engine. Thus, though it took time, Carnot's book eventually had a real impact on the design of practical engines.
His name is one of the 72 names inscribed on the Eiffel Tower.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
military engineer
Military engineer
In military science, engineering refers to the practice of designing, building, maintaining and dismantling military works, including offensive, defensive and logistical structures, to shape the physical operating environment in war...
who, in his 1824 Reflections on the Motive Power of Fire
Reflections on the Motive Power of Fire
In 1824, French physicist Sadi Carnot published the book Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power....
, gave the first successful theoretical account of heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...
s, now known as the Carnot cycle
Carnot cycle
The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It can be shown that it is the most efficient cycle for converting a given amount of thermal energy into work, or conversely,...
, thereby laying the foundations of the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
. He is often described as the "Father of thermodynamics", being responsible for such concepts as Carnot efficiency
Exergy efficiency
Exergy efficiency computes the efficiency of a process taking the second law of thermodynamics into account.-Motivation:...
, Carnot theorem, Carnot heat engine
Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...
, and others.
Life
Born in ParisParis
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, Sadi Carnot was the first son of the eminent military leader
French Revolutionary Army
The French Revolutionary Army is the term used to refer to the military of France during the period between the fall of the ancien regime under Louis XVI in 1792 and the formation of the First French Empire under Napoleon Bonaparte in 1804. These armies were characterised by their revolutionary...
and geometer, Lazare Nicholas Marguerite Carnot, elder brother of Hippolyte Carnot
Hippolyte Carnot
Lazare Hippolyte Carnot was a French statesman.- Early life :Lazare was the younger brother of the founder of thermodynamics Sadi Carnot and second son of the revolutionary politician Lazare Nicolas Marguerite Carnot, who also served in the government of Napoleon. He was born at Saint-Omer,...
, and uncle of Marie François Sadi Carnot
Marie François Sadi Carnot
Marie François Sadi Carnot was a French statesman and the fourth president of the Third French Republic. He served as the President of France from 1887 until his assassination in 1894.-Early life:...
(President of the French Republic (1887-1894), son of Hippolyte Carnot
Hippolyte Carnot
Lazare Hippolyte Carnot was a French statesman.- Early life :Lazare was the younger brother of the founder of thermodynamics Sadi Carnot and second son of the revolutionary politician Lazare Nicolas Marguerite Carnot, who also served in the government of Napoleon. He was born at Saint-Omer,...
). His father named him after the Persian poet Sadi of Shiraz
Saadi (poet)
Abū-Muḥammad Muṣliḥ al-Dīn bin Abdallāh Shīrāzī better known by his pen-name as Saʿdī or, simply, Saadi, was one of the major Persian poets of the medieval period. He is not only famous in Persian-speaking countries, but he has also been quoted in western sources...
, and he was always known by this third given name.
From age 16 (1812), he lived in Paris and attended the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
where he and his contemporaries, Claude-Louis Navier
Claude-Louis Navier
Claude-Louis Navier born Claude Louis Marie Henri Navier , was a French engineer and physicist who specialized in mechanics.The Navier–Stokes equations are named after him and George Gabriel Stokes....
and Gaspard-Gustave Coriolis
Gaspard-Gustave Coriolis
Gaspard-Gustave de Coriolis or Gustave Coriolis was a French mathematician, mechanical engineer and scientist. He is best known for his work on the supplementary forces that are detected in a rotating frame of reference. See the Coriolis Effect...
, were taught by professors such as Joseph Louis Gay-Lussac
Joseph Louis Gay-Lussac
- External links :* from the American Chemical Society* from the Encyclopædia Britannica, 10th Edition * , Paris...
, Siméon Denis Poisson
Siméon Denis Poisson
Siméon Denis Poisson , was a French mathematician, geometer, and physicist. He however, was the final leading opponent of the wave theory of light as a member of the elite l'Académie française, but was proven wrong by Augustin-Jean Fresnel.-Biography:...
and André-Marie Ampère
André-Marie Ampère
André-Marie Ampère was a French physicist and mathematician who is generally regarded as one of the main discoverers of electromagnetism. The SI unit of measurement of electric current, the ampere, is named after him....
. After graduation, he became an officer in the French army
French Army
The French Army, officially the Armée de Terre , is the land-based and largest component of the French Armed Forces.As of 2010, the army employs 123,100 regulars, 18,350 part-time reservists and 7,700 Legionnaires. All soldiers are professionals, following the suspension of conscription, voted in...
before committing himself to scientific research, becoming the most celebrated of Fourier's contemporaries who were interested in the theory of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
. Since 1814, he served in the military. Following the final defeat of Napoleon in 1815, his father went into exile. He later obtained permanent leave of absence from the French army. Subsequently, he spent time to write his book.
Background
The historical context in which Carnot worked was that there had been almost no scientific study of the steam engineSteam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...
, and yet the engine was actually pretty far along in its development. It had risen to a widely recognized economic and industrial importance. Newcomen
Newcomen
Newcomen may refer to:* Viscount Newcomen, an extinct viscountcyPeople with the surname Newcomen:* John Newcomen , first white settler murdered by another white settler in Plymouth Colony, Massachusetts...
had invented the first piston-operated steam engine over a century before, in 1712. Some 50 years after that, Watt
James Watt
James Watt, FRS, FRSE was a Scottish inventor and mechanical engineer whose improvements to the Newcomen steam engine were fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.While working as an instrument maker at the...
made his celebrated improvements which greatly increased the efficiency and practicality of the engine. Compound engines (engines with more than one stage of expansion) had already been invented. There was even a crude form of internal-combustion engine, with which Carnot was familiar and which he described in some detail in his book. Amazing progress on the practical side had been made, so at least some intuitive understanding of the engine's workings existed. The scientific basis of its operation, however, was almost nonexistent even after all this time. In 1824 the principle of conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
was still immature and controversial, and an exact formulation of the first law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
was still more than a decade away. The mechanical equivalent of heat
Mechanical equivalent of heat
In the history of science, the mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century....
was not identified for another two decades. The prevalent theory of heat was the caloric theory
Caloric theory
The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores in solids and liquids...
, which regarded heat as a sort of weightless, invisible fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
that flowed when out of equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
.
Engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
s in Carnot's time had tried various mechanical means, such as high pressure steam
Steam
Steam is the technical term for water vapor, the gaseous phase of water, which is formed when water boils. In common language it is often used to refer to the visible mist of water droplets formed as this water vapor condenses in the presence of cooler air...
, or the use of some fluid other than steam, to improve the efficiency of their engines. In these early stages of engine development, the efficiency of a typical engine -- the useful work it was able to perform when a given quantity of fuel
Fuel
Fuel is any material that stores energy that can later be extracted to perform mechanical work in a controlled manner. Most fuels used by humans undergo combustion, a redox reaction in which a combustible substance releases energy after it ignites and reacts with the oxygen in the air...
such as a lump of coal
Coal
Coal is a combustible black or brownish-black sedimentary rock usually occurring in rock strata in layers or veins called coal beds or coal seams. The harder forms, such as anthracite coal, can be regarded as metamorphic rock because of later exposure to elevated temperature and pressure...
was burnt -- was a mere 3%.
The Carnot cycle
Carnot sought to answer two questions about the operation of heat engines: "Is the work available from a heat source potentially unbounded?" and "Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?" He attempted to answer these in a memoir, published as a popular work in 1824 when he was only 28 years old. It was entitled Réflexions sur la puissance motrice du feu ("Reflections on the Motive Power of Fire"). The book was plainly intended to cover a rather wide range of topics about heat engines in a rather popular fashion. Equations were kept to a minimum and called for little more than simple algebra and arithmetic, except occasionally in the footnotes, where he indulged in a few arguments involving a little calculus. He discussed the relative merits of air and steam as working fluids, the merits of various aspects of steam engine design, and even threw in some ideas of his own on possible practical improvements. But the most important part of the book was devoted to a quite abstract presentation of an idealized engine that could be used to understand and clarify the fundamental principles that are of general applicability to all heat engines, independent of the particular design choices that might be made.Perhaps the most important contribution Carnot made to thermodynamics was his abstraction of the essential features of the steam engine as it was known in his day into a more general, idealized heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...
. This resulted in a model thermodynamic system
Thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....
upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engine. By idealizing the engine, he could arrive at clear, indisputable answers to his original two questions.
He showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be (T1−T2)⁄T1, where T1 is the absolute temperature of the hotter reservoir. (Note: This equation probably came from Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
.) No thermal engine operating any other cycle can be more efficient, given the same operating temperature
Operating temperature
An operating temperature is the temperature at which an electrical or mechanical device operates. The device will operate effectively within a specified temperature range which varies based on the device function and application context, and ranges from the minimum operating temperature to the...
s.
He saw very clearly, intuitively, that he could give very definite answers to the two questions set before the reader. The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. He knew that conduction of heat between bodies at different temperatures is a wasteful, irreversible process and must be eliminated if the heat engine is to have the maximum efficiency.
Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of the working fluid
Working fluid
A working fluid is a pressurized gas or liquid that actuates a machine. Examples include steam in a steam engine, air in a hot air engine and hydraulic fluid in a hydraulic motor or hydraulic cylinder...
. He stated this for emphasis as a general proposition: "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 the transfer of caloric takes place." For his "motive power of heat", we would today say "the efficiency of a reversible heat engine," and rather than "transfer of caloric" we would say "the reversible transfer of heat." He knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be.
and
Towards the second law
In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot however further postulated that some caloric is lost, not being converted to mechanical work. Hence no real heat engine could realise the Carnot cycle's reversibility and was condemned to be less efficient.Though formulated in terms of caloric, rather than entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, this was an early insight into the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
.
Reception and later life
Carnot’s book apparently received very little attention from his contemporaries at first. The only citation within a few years after his publication was a review of it in a periodical “Revue Encyclopédique,“ which was a journal that covered a wide range of topics in literature. The work only began to have a real impact when modernised by Émile Clapeyron, in 1834 and then further elaborated upon by Clausius and KelvinWilliam Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
, who together derived from it the notion of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
and the second law of thermodynamics.
Death
Carnot died in a choleraCholera
Cholera is an infection of the small intestine that is caused by the bacterium Vibrio cholerae. The main symptoms are profuse watery diarrhea and vomiting. Transmission occurs primarily by drinking or eating water or food that has been contaminated by the diarrhea of an infected person or the feces...
epidemic when he was only 36 in 1832. Because of the concern of cholera
Cholera
Cholera is an infection of the small intestine that is caused by the bacterium Vibrio cholerae. The main symptoms are profuse watery diarrhea and vomiting. Transmission occurs primarily by drinking or eating water or food that has been contaminated by the diarrhea of an infected person or the feces...
, many of his belongings and writings were buried together with him after his death. Thus only a handful of his scientific writings survived besides his book.
After the publication of his book in 1824, it quickly went out of print and for some time was very difficult to obtain. For example, Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
had great difficulty in getting a copy of Carnot's book. An English translation of it by R. H. Thurston in 1890 has been reprinted in recent decades by Dover
Dover Publications
Dover Publications is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche. It publishes primarily reissues, books no longer published by their original publishers. These are often, but not always, books in the public domain. The original published editions may be...
and by Peter Smith, most recently by Dover in 2005. Some of his posthumous manuscripts have also been translated into English. (See Reference.)
Carnot published his book in the days of steam engines. His theory explained why steam engines using superheated steam were better because of the higher temperature of the hot reservoir involved. Carnot's theory did not help to improve the efficiency of steam engines in the beginning; his theory only helped to explain why one existing practice was better. It was only towards the end of the nineteenth century that Carnot's idea -- that a heat engine can be made more efficient if the temperature of its hot reservoir is increased -- was put into practice by, for example, Rudolf Diesel
Rudolf Diesel
Rudolf Christian Karl Diesel was a German inventor and mechanical engineer, famous for the invention of the diesel engine.-Early life:Diesel was born in Paris, France in 1858 the second of three children of Theodor and Elise Diesel. His parents were Bavarian immigrants living in Paris. Theodor...
(1858-1913), who was fascinated by Carnot's theory and designed an engine (diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...
) in which the temperature of the hot reservoir is much higher than that of a steam engine, resulting in an engine which is more efficient than a steam engine. Thus, though it took time, Carnot's book eventually had a real impact on the design of practical engines.
His name is one of the 72 names inscribed on the Eiffel Tower.
External links
- Reflections on the Motive Power of Heat, English translation by R.H. Thurston
- Reflections on the Motive Power of Heat, English translation by R.H. Thurston (at Internet Archive)
- "Sadi Carnot and the Second Law of Thermodynamics", J. Srinivasan, Resonance, November 2001, 42 (PDF file)