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 the 1824. The Carnot engine model was graphically expanded upon by Benoit Paul Émile Clapeyron in 1834 and mathematically elaborated upon by Rudolf Clausius in the 1850s and 60s from which the concept of entropy emerged. A heat engine is an engine that uses heat to produce mechanical work by carrying a working substance through a cyclic process. ... Sadi Carnot Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French mathematician and engineer who gave the first successful theoretical account of heat engines, the Carnot cycle, and laid the foundations of the second law of thermodynamics. ... 1824 was a leap year starting on Thursday (see link for calendar). ... Emile_Clapeyron Benoit Paul Émile Clapeyron (February 26, 1799 - January 28, 1864) was an French engineer and physicist, considered as one of the founders of thermodynamics. ... 1834 was a common year starting on Wednesday (see link for calendar). ... Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... // Events and Trends Technology Production of steel revolutionised by invention of the Bessemer process Benjamin Silliman fractionates petroleum by distillation for the first time First transatlantic telegraph cable laid First safety elevator installed by Elisha Otis Science Charles Darwin publishes The Origin of Species, putting forward the theory of evolution... // Events and trends Technology The First Transcontinental Railroad in the United States is built in the six year period between 1863 and 1869. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ...

Carnot engine diagram (original)

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. Image File history File links Download high-resolution version (365x793, 62 KB) Summary Sadi Carnots pison-and-cylinder diagram from 1824 Licensing The two-dimensional work of art depicted in this image is in the public domain in the United States and in those countries with a copyright term... Image File history File links Download high-resolution version (365x793, 62 KB) Summary Sadi Carnots pison-and-cylinder diagram from 1824 Licensing The two-dimensional work of art depicted in this image is in the public domain in the United States and in those countries with a copyright term... This article needs to be cleaned up to conform to a higher standard of quality. ... A thermodynamic cycle is a series of thermodynamic processes which returns a system to its initial state. ... Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ... In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot source and a cold sink. Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. ...

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 rather than a heat engine. Work (abbreviated W) is defined as the line integral of a scalar product of force and displacement vectors (see below). ... It has been suggested that Refrigerator be merged into this article or section. ...

In the adjacent diagram, from the original 1824 paper by Sadi Carnot entitled On the Motive Power of Fire, we are told to “imagine two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies, to which we can give or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of caloric. We shall call the first the furnace and the second the refrigerator.” Carnot then explains how we can obtain motive power, i.e. “work”, by carrying a certain quantity of heat from the body A to the body B. While phlogiston theory was widely accepted, phlogiston was thought to be the matter of heat. ... A furnace is a device for heating air or any other fluid. ... In thermodynamics, motive power is an agency, as water or steam, used to impart motion. ...

Modern diagram

Above, we see the original piston-and-cylinder diagram used by Carnot in discussing his ideal engine; below, we see the Carnot engine as is typically modeled in current use:

Carnot engine diagram (modern)

In the diagram shown, the “working body” (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which heat Q can be introduced or transmitted through to produce work. Carnot had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, or air, etc. Although, in these early years, engines came in a number of configurations, typically Q_H was supplied by a boiler, wherein water was boiled over a furnace; Q_C was typically a stream of cold flowing water in the form of a condenser located on a separate part of the engine. The output work W here is the movement of the piston as it is used to turn a crank-arm, which was then typically used to turn a pulley so to lift water out of flooded salt mines. Carnot defined work as “weight lifted through a height”. Image File history File links Carnot-engine. ... Image File history File links Carnot-engine. ... In physics, heat, symbolized by Q, is defined as energy in transit. ... Look up work in Wiktionary, the free dictionary. ... The term condenser has the following meanings: In electronics, it is another (old-fashioned) word for capacitor. ...

Carnot's theorem

It can be seen from the above diagram, that for any cycle operating between temperatures T_H and T_C, none can exceed the efficiency of a Carnot cycle. A heat engine is an engine that uses heat to produce mechanical work by carrying a working substance through a cyclic process. ...

A real engine (left) compared to the Carnot cycle (right). The entropy of a real material changes with temperature. This change is indicated by the curve on a T-S diagram. For this figure, the curve indicates a vapor-liquid equilibrium (See Rankine cycle). Irreversible systems and losses of heat (for example, due to friction) prevent the ideal from taking place at every step.

Carnot's theorem is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs. Thus, Equation 3 gives the maximum efficiency possible for any engine using the corresponding temperatures. A corollary to Carnot's theorem states that: All reversible engines operating between the same heat reservoirs are equally efficient. Image File history File linksMetadata Download high-resolution version (911x332, 44 KB) Real process cycle compared with Carnot cycle. ... Image File history File linksMetadata Download high-resolution version (911x332, 44 KB) Real process cycle compared with Carnot cycle. ... The Rankine cycle is a thermodynamic cycle. ...

In other words, maximum efficiency is achieved if and only if no new entropy is created in the cycle. Otherwise, since entropy is a state function, the required dumping of heat into the environment to dispose of excess entropy leads to a reduction in efficiency. So Equation 3 gives the efficiency of any reversible heat engine. In thermodynamics, a state function (or state quantity) is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. ... In thermodynamics, a reversible process (or reversible cycle if the process is cyclic) is a process that can be reversed by means of infinitesimal changes in some property of the system. ... In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot source and a cold sink. Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. ...

Efficiency of real heat engines

Carnot realised that in reality it is not possible to build a thermodynamically reversible engine, so real heat engines are less efficient than indicated by Equation 3. Nevertheless, Equation 3 is extremely useful for determining the maximum efficiency that could ever be expected for a given set of thermal reservoirs. A reversible process (or reversible cycle if the process is cyclic) , in thermodynamics, is a process that can be reversed by means of infinitesimal changes in some property of the system (Sears and Salinger, 1986). ...

Although Carnot's cycle is an idealisation, the expression of Carnot efficiency is still useful. Consider the average temperatures, In mathematics, there are numerous methods for calculating the average or central tendency of a list of n numbers. ...

at which heat is input and output, respectively. Replace T_H and T_C in Equation (3) by <T_H> and <T_C> respectively.

For the Carnot cycle, or its equivalent, <T_H> is the highest temperature available and <T_C> the lowest. For other less efficient cycles, <T_H> will be lower than T_H , and <T_C> will be higher than T_C. This can help illustrate, for example, why a reheater or a regenerator can improve thermal efficiency. SR-71 in flight with J58 on full afterburner An afterburner is an additional component added to some jet engines, primarily those on military aircraft. ... A Stirling engine and generator set with 55 kW electrical output, for combined heat and power applications. ...

See also: Heat Engine (efficiency and other performance criteria)

In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot source and a cold sink. Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. ... In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot source and a cold sink. Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. ...

References

• Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics, 2nd ed., W. H. Freeman Company. ISBN 0-7167-1088-9.

See also

• Carnot cycle