A Carnot heat engineIn French, Carnot uses machine à feu, which Thurston translates as heat-engine or steam-engine. In a footnote, Carnot distinguishes the steam-engine (machine à vapeur) from the heat-engine in general. (Carnot, 1824, p. 5 and Carnot, 1890, p. 43) ( , ) is a theoretical heat engine that operates on the Carnot cycle. The basic model for this engine was developed by French military engineer Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, work that led to the fundamental thermodynamic concept of entropy. The Carnot engine is the most efficient heat engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.
A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator or heat pump rather than a heat engine.
Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine.
The Carnot engine is a theoretical construct, useful for exploring the efficiency limits of other heat engines. An actual Carnot engine, however, would be completely impractical to build.
History and context
The Carnot engine was publicized in Sadi Carnot's sole work: Reflections on the Motive Power of Fire (1824). A short book addressed to practical engineers in popular language, it has been described as "remarkably accessible to modern readers"; "very clearly written ... [the] mathematical arguments are consigned to footnotes". It is known that Carnot was anxious to be understood by non-specialists.
Carnot's motivation was practical. "The purpose of Reflexions was to bring to public notice the potential of the steam engine for improving the standard of living in France".
The first useful steam engines were developed in Britain and were typically employed for pumping water out of coal mines. Since an engine could burn the mine's own coal (including waste coal, which had no commercial value)Small coals were not popular in the market and might not pay the cost of carriage to consumer. Where this was so they were often screened out and burned on the mine's waste-heap: William Stanley Jevons estimated that at least 5 million tons of small coals were burned annually upon the colliery waste-heaps of England, the true amounts being incalculable: . fuel economy was of little concern.Carr and Cowart of the U.S. Naval Academy calculated that a Newcomen atmospheric engine at Parkgate, Yorkshire, had a thermal efficiency of only 2.7%. Yet it was purchased in preference to a more efficient but more costly Watt engine since fuel economy did not matter: it burned waste coal. It was not finally retired until 1934, after doing more than 100 years service. Well over a thousand Newcomen engines were built. .Despite its higher fuel consumption, the Newcomen atmospheric engine was competitive with the more efficient Watt engine wherever coal was cheap enough. "The presence of Watt engines during the last quarter of the [18th] century not only failed to stop the adoption of Newcomen engines, but, in fact, their diffusion accelerated compared to the pre-Watt era": . The incentive to have efficient engines arose in parts of the country where fuel was costly, such as Cornwall.
The mines of Cornwall produced useful metals like tin; but not coal. The fuel to power their pumping engines had to be imported by sea and was expensive; users were keenly aware that "heat cost money". They sought the engine that did the best "duty'", measured in millions of pounds of water lifted one foot high per bushel of coal burnt. A practical business measure, it was a crude indication of the thermodynamic efficiency of an engine.
Cornish engineers were famous for the efficiency of their engines and their achievements were studied avidly, not least in France, where coal was expensive too. Sadi Carnot's book mentioned three of them by name, Richard Trevithick, Arthur Woolf and Jonathan Hornblower. Such men developed the Cornish engine in which high pressure steam was cut off early when the piston was at the beginning of its stroke, letting the steam's expansion complete the stroke by itself. Today it might be called adiabatic expansion.
Their ideas were enthusiastically taken up in France,"[In France], especially after 1815, the news of the successful design of high pressure expansive engines by Trevithick and Woolf in Cornwall and of their staggering improvements in fuel-efficiency was received with enthusiasm": . where additionally, scientists and engineers were interested in the theory of steam and other engines.
Significance
Importance Carnot's innovation has been described as "real genius" and "one of the greatest intellectual achievements of the human mind". For Nobel laureate Richard Feynman In particular it led to the discovery of the Second Law, of which it has been claimed that "Not knowing the Second Law of Thermodynamics is equivalent to never having read a work by Shakespeare".The claim was originally made by the novelist and scientist C.P. Snow in his influential 1959 lecture The Two Cultures: .
Clarity Sadi Carnot died young and published only one work: Reflections on the Motive Power of Fire (1824). A short book addressed to practical engineers in popular language, it has been described as "remarkably accessible to modern readers"; "very clearly written ... [the] mathematical arguments are consigned to footnotes". It is known that Carnot was anxious to be understood by non-specialists.His brother later recalled: "Anxious to be perfectly clear, Sadi made me read some passages of his manuscript in order to convince himself that it would be understood by persons occupied with other studies": . Yet, in many university courses the Carnot cycle it is introduced in such an abstract way that students have trouble intuiting his ideas, and their implications."There is, perhaps, no proposition in the range of Physics that is more difficult of comprehension by the average student than that embodied in the so-called Carnot Engine and Carnot Cycle":
Not all approve of his popular exposition. In The Tragicomical History of Thermodynamics 1822-1854 Clifford Truesdell strongly criticised Carnot for his lack of mathematical rigour, which (he said) has affected the discipline ever since.
Flaw in theory, and rescue Carnot's theory as published contains a serious flaw, which he increasingly came to suspect himself. Like many scientists of his time he had assumed heat was an actual substance (they called it caloric). This is an intuitive way to think about heat and it has been shown that children think similarly.
After Carnot's death new data led to a fundamental shift in scientific thinking. Heat is now usuallyBut not invariably. The Karlsruhe Physics Course is a German and English high school textbook that introduces the concept of heat as equivalent to entropy, measured units in called Carnots; only later is the concept of energy introduced. . described as a form of energy, which can be converted into mechanical work, and vice versa. Carnot's theory was eventually rescued by Rudolf Clausius and (independently) William Thomson (Lord Kelvin), who made the necessary corrections.See also ; . Today most students are taught not Carnot's theory but the rescued version. If Carnot's version is taught first it is easier to understand. This detail will be explained later.
Context and motivation Carnot's motivation was practical. "The purpose of Reflexions was to bring to public notice the potential of the steam engine for improving the standard of living in France".
The first useful steam engines were developed in Britain and were typically employed for pumping water out of coal mines. Since an engine could burn the mine's own coal (including waste coal, which had no commercial value) fuel economy was of little concern. The incentive to have efficient engines arose in parts of the country where fuel was costly, such as Cornwall.
The mines of Cornwall produced useful metals like tin; but not coal. The fuel to power their pumping engines had to be imported by sea and was expensive; users were keenly aware that "heat cost money". They sought the engine that did the best "duty'", measured in millions of pounds of water lifted one foot high per bushel of coal burnt. A practical business measure, it was a crude indication of the thermodynamic efficiency of an engine.
Cornish engineers were famous for the efficiency of their engines and their achievements were studied avidly, not least in France, where coal was expensive too. Sadi Carnot's book mentioned three of them by name, Richard Trevithick, Arthur Woolf and Jonathan Hornblower. Such men developed the Cornish engine in which high pressure steam was cut off early when the piston was at the beginning of its stroke, letting the steam's expansion complete the stroke by itself. Today it might be called adiabatic expansion.
Their ideas were enthusiastically taken up in France, where additionally, scientists and engineers were interested in the theory of steam and other engines.
Carnot's aim
"Every one knows that heat can produce motion", began Carnot. Typically it was done by steam engines. Important to the Industrial Revolution, they had been vastly improved by practical British engineers, said Carnot,"There is almost as great a distance between the first apparatus in which the expansive force of steam was displayed and the existing machine, as between the first raft that man ever made and the modern vessel.If the honor of a discovery belongs to the nation in which it has acquired its growth and all its developments, this honor cannot be here refused to England. Savery, Newcomen, Smeaton, the famous Watt, Woolf, Trevithick, and some other English engineers, are the veritable creators of the steam-engine. It has acquired at their hands all its successive degrees of improvement": . but without really understanding the theory of what they were doing.
Because of the remarkable improvements that had already been made in fuel efficiency - a ten-fold increase since 1775 - it was asked whether it would go on for ever. Or would engineers run up against a fundamental limit, impossible to exceed? Matters such as these had attracted some of the ablest mathematicians and physicists in France.
Engineers also wondered if there could be a better working substance than steam. In principle, anything that exerted a force when heated and cooled might work, even a solid metallic bar. Many substances were tried or considered, for example the Stirling engine used air. Others included alcohol, ammonia, even mercury; there were hundreds of such exotic proposals, some dangerous: there were ships and factories powered by engines that worked by boiling ether, a highly flammable liquid.
To answer questions such as these, said Carnot, one needed to think generally, to go beyond the details of this or that engine.
For historian of science John D. Norton "it is important to realize just how audacious it was of Sadi to seek such a simple general theory, let alone to find it", for the practical engines of his day were already very complicated devices.
Reasoning Edwin Thompson Jaynes wrote: