The classical Carnot heat engine
In thermodynamics and engineering, a heat engine is a system that converts heat or thermal energy—and chemical energy—to mechanical energy, which can then be used to do mechanical work.It does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag.
In general an engine converts energy to mechanical work. Heat engines distinguish themselves from other types of engines by the fact that their efficiency is fundamentally limited by Carnot's theorem.Although this efficiency limitation can be a drawback, an advantage of heat engines is that most forms of energy can be easily converted to heat by processes like exothermic reactions (such as combustion), absorption of light or energetic particles, friction, dissipation and resistance. Since the heat source that supplies thermal energy to the engine can thus be powered by virtually any kind of energy, heat engines cover a wide range of applications.
Heat engines are often confused with the cycles they attempt to implement. Typically, the term "engine" is used for a physical device and "cycle" for the models.
In thermodynamics, heat engines are often modeled using a standard engineering model such as the Otto cycle. The theoretical model can be refined and augmented with actual data from an operating engine, using tools such as an indicator diagram. Since very few actual implementations of heat engines exactly match their underlying thermodynamic cycles, one could say that a thermodynamic cycle is an ideal case of a mechanical engine. In any case, fully understanding an engine and its efficiency requires a good understanding of the (possibly simplified or idealised) theoretical model, the practical nuances of an actual mechanical engine and the discrepancies between the two.
In general terms, the larger the difference in temperature between the hot source and the cold sink, the larger is the potential thermal efficiency of the cycle. On Earth, the cold side of any heat engine is limited to being close to the ambient temperature of the environment, or not much lower than 300 Kelvin, so most efforts to improve the thermodynamic efficiencies of various heat engines focus on increasing the temperature of the source, within material limits. The maximum theoretical efficiency of a heat engine (which no engine ever attains) is equal to the temperature difference between the hot and cold ends divided by the temperature at the hot end, each expressed in absolute temperature (Kelvin).
The efficiency of various heat engines proposed or used today has a large range:
The efficiency of these processes is roughly proportional to the temperature drop across them. Significant energy may be consumed by auxiliary equipment, such as pumps, which effectively reduces efficiency.
It is important to note that although some cycles have a typical combustion location (internal or external), they often can be implemented with the other. For example, John Ericssondeveloped an external heated engine running on a cycle very much like the earlier Diesel cycle. In addition, externally heated engines can often be implemented in open or closed cycles.
Everyday examples of heat engines include the thermal power station, internal combustion engine and steam locomotive. All of these heat engines are powered by the expansion of heated gases.
Earth's atmosphere and hydrosphere—Earth’s heat engine—are coupled processes that constantly even out solar heating imbalances through evaporation of surface water, convection, rainfall, winds and ocean circulation, when distributing heat around the globe.
A Hadley cell is an example of a heat engine. It involves the rising of warm and moist air in the earth's equatorial region and the descent of colder air in the subtropics creating a thermally driven direct circulation, with consequent net production of kinetic energy.
In these cycles and engines, the working fluids are gases and liquids. The engine converts the working fluid from a gas to a liquid, from liquid to gas, or both, generating work from the fluid expansion or compression.
In these cycles and engines the working fluid is always a gas (i.e., there is no phase change):
In these cycles and engines the working fluid are always like liquid:
A domestic refrigerator is an example of a heat pump: a heat engine in reverse. Work is used to create a heat differential. Many cycles can run in reverse to move heat from the cold side to the hot side, making the cold side cooler and the hot side hotter. Internal combustion engine versions of these cycles are, by their nature, not reversible.
Refrigeration cycles include:
The Barton evaporation engine is a heat engine based on a cycle producing power and cooled moist air from the evaporation of water into hot dry air.
Mesoscopic heat engines are nanoscale devices that may serve the goal of processing heat fluxes and perform useful work at small scales. Potential applications include e.g. electric cooling devices. In such mesoscopic heat engines, work per cycle of operation fluctuates due to thermal noise. There is exact equality that relates average of exponents of work performed by any heat engine and the heat transfer from the hotter heat bath.This relation transforms the Carnot's inequality into exact equality. This relation is also a Carnot cycle equality
The efficiency of a heat engine relates how much useful work is output for a given amount of heat energy input.
From the laws of thermodynamics, after a completed cycle:
In other words, a heat engine absorbs heat energy from the high temperature heat source, converting part of it to useful work and delivering the rest to the cold temperature heat sink.
In general, the efficiency of a given heat transfer process (whether it be a refrigerator, a heat pump or an engine) is defined informally by the ratio of "what is taken out" to "what is put in".
In the case of an engine, one desires to extract work and puts in a heat transfer.
The theoretical maximum efficiency of any heat engine depends only on the temperatures it operates between. This efficiency is usually derived using an ideal imaginary heat engine such as the Carnot heat engine, although other engines using different cycles can also attain maximum efficiency. Mathematically, this is because in reversible processes, the change in entropy of the cold reservoir is the negative of that of the hot reservoir (i.e., ), keeping the overall change of entropy zero. Thus:
where is the absolute temperature of the hot source and that of the cold sink, usually measured in kelvins. Note that is positive while is negative; in any reversible work-extracting process, entropy is overall not increased, but rather is moved from a hot (high-entropy) system to a cold (low-entropy one), decreasing the entropy of the heat source and increasing that of the heat sink.
The reasoning behind this being the maximal efficiency goes as follows. It is first assumed that if a more efficient heat engine than a Carnot engine is possible, then it could be driven in reverse as a heat pump. Mathematical analysis can be used to show that this assumed combination would result in a net decrease in entropy. Since, by the second law of thermodynamics, this is statistically improbable to the point of exclusion, the Carnot efficiency is a theoretical upper bound on the reliable efficiency of any thermodynamic cycle.
Empirically, no heat engine has ever been shown to run at a greater efficiency than a Carnot cycle heat engine.
Figure 2 and Figure 3 show variations on Carnot cycle efficiency. Figure 2 indicates how efficiency changes with an increase in the heat addition temperature for a constant compressor inlet temperature. Figure 3 indicates how the efficiency changes with an increase in the heat rejection temperature for a constant turbine inlet temperature.
By its nature, any maximally efficient Carnot cycle must operate at an infinitesimal temperature gradient; this is because any transfer of heat between two bodies of differing temperatures is irreversible, therefore the Carnot efficiency expression applies only to the infinitesimal limit. The major problem is that the objective of most heat-engines is to output power, and infinitesimal power is seldom desired.
A different measure of ideal heat-engine efficiency is given by considerations of endoreversible thermodynamics, where the cycle is identical to the Carnot cycle except that the two processes of heat transfer are not reversible (Callen 1985):
This model does a better job of predicting how well real-world heat-engines can do (Callen 1985, see also endoreversible thermodynamics):
|West Thurrock (UK) coal-fired power station||25||565||0.64||0.40||0.36|
|CANDU (Canada) nuclear power station||25||300||0.48||0.28||0.30|
|Larderello (Italy) geothermal power station||80||250||0.33||0.178||0.16|
As shown, the endo-reversible efficiency much more closely models that observed.
Heat engines have been known since antiquity but were only made into useful devices at the time of the industrial revolution in the 18th century. They continue to be developed today.
Engineers have studied the various heat-engine cycles to improve the amount of usable work they could extract from a given power source. The Carnot cycle limit cannot be reached with any gas-based cycle, but engineers have found at least two ways to bypass that limit and one way to get better efficiency without bending any rules:
|Cycle||Compression, 1→2||Heat addition, 2→3||Expansion, 3→4||Heat rejection, 4→1||Notes|
|Power cycles normally with external combustion - or heat pump cycles:|
|Bell Coleman||adiabatic||isobaric||adiabatic||isobaric||A reversed Brayton cycle|
|Carnot||isentropic||isothermal||isentropic||isothermal||Carnot heat engine|
|Ericsson||isothermal||isobaric||isothermal||isobaric||The second Ericsson cycle from 1853|
|Manson||isothermal||isochoric||isothermal||isochoric then adiabatic||Manson-Guise Engine|
|Power cycles normally with internal combustion:|
|Brayton||adiabatic||isobaric||adiabatic||isobaric||Jet engine. The external combustion version of this cycle is known as first Ericsson cycle from 1833.|
|Lenoir||isochoric||adiabatic||isobaric||Pulse jets. Note, 1→2 accomplishes both the heat rejection and the compression.|
|Otto||isentropic||isochoric||isentropic||isochoric||Gasoline / petrol engines|
Each process is one of the following:
A Carnot heat engine is a theoretical engine that operates on the Carnot cycle. The basic model for this engine was developed by 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 from which the concept of entropy emerged.
In statistical mechanics, entropy is an extensive property of a thermodynamic system. It quantifies the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system. Under the assumption that each microstate is equally probable, the entropy is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally,
Sous-lieutenantNicolas Léonard Sadi Carnot was a French mechanical engineer in the French Army, military scientist and physicist, often described as the "father of thermodynamics." Like Copernicus, he published only one book, the Reflections on the Motive Power of Fire, in which he expressed, at the age of 27 years, the first successful theory of the maximum efficiency of heat engines. In this work he laid the foundations of an entirely new discipline, thermodynamics. Carnot's work attracted little attention during his lifetime, but it was later used by Rudolf Clausius and Lord Kelvin to formalize the second law of thermodynamics and define the concept of entropy.
The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.
Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also called Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain. The efficiency of a Carnot engine depends solely on the temperatures of the hot and cold reservoirs.
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes.
A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are not thermodynamic systems. A wall of a thermodynamic system may be purely notional, when it is described as being 'permeable' to all matter, all radiation, and all forces.
The Rankine cycle is a model used to predict the performance of steam turbine systems. It was also used to study the performance of reciprocating steam engines. The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work while undergoing phase change. It is an idealized cycle in which friction losses in each of the four components are neglected. The heat is supplied externally to a closed loop, which usually uses water as the working fluid. It is named after William John Macquorn Rankine, a Scottish polymath and Glasgow University professor.
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.
A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. At every point in the cycle, the system is in thermodynamic equilibrium, so the cycle is reversible.
In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine, a boiler, furnace, or a refrigerator for example. For a heat engine, thermal efficiency is the fraction of the energy added by heat that is converted to net work output. In the case of a refrigeration or heat pump cycle, thermal efficiency is the ratio of net heat output for heating, or removal for cooling, to energy input.
The Clausius theorem (1855) states that a system exchanging heat with external reservoirs and undergoing a cyclic process, is one that ultimately returns a system to its original state,
The concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work. Early heat-powered engines such as Thomas Savery's (1698), the Newcomen engine (1712) and the Cugnot steam tricycle (1769) were inefficient, converting less than two percent of the input energy into useful work output; a great deal of useful energy was dissipated or lost. Over the next two centuries, physicists investigated this puzzle of lost energy; the result was the concept of entropy.
Entropy is a property of thermodynamical systems. The term entropy was introduced by Rudolf Clausius who named it from the Greek word τρoπή, "transformation". He considered transfers of energy as heat and work between bodies of matter, taking temperature into account. Bodies of radiation are also covered by the same kind of reasoning.
The Carnot cycle is a theoretical ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. It is not an actual thermodynamic cycle but is a theoretical construct.
Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pumps and refrigerators. A heat pump is a mechanical system that allows for the transference of heat from one location at a lower temperature to another location at a higher temperature. Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink, or a "refrigerator" if the objective is to cool the heat source. In either case, the operating principles are identical. Heat is moved from a cold place to a warm place.
In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. The various mechanisms of energy transfer that define heat are stated in the next section of this article.
Temperature is a physical property of matter that quantitatively expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder.
Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer than are typically made in reversible thermodynamics. It gives an upper bound on the energy that can be derived from a real process that is lower than that predicted by Carnot for a Carnot cycle, and accommodates the exergy destruction occurring as heat is transferred irreversibly.
A quantum heat engine is a device that generates power from the heat flow between hot and cold reservoirs. The operation mechanism of the engine can be described by the laws of quantum mechanics. The first realization of a quantum heat engine was pointed out by Scovil and Schulz-DuBois in 1959, showing the connection of efficiency of the Carnot engine and the 3-level maser. Quantum refrigerators share the structure of quantum heat engines with the purpose of pumping heat from a cold to a hot bath consuming power first suggested by Geusic, Schulz-DuBois, De Grasse and Scovil. When the power is supplied by a laser the process is termed optical pumping or laser cooling, suggested by Weinland and Hench. Surprisingly heat engines and refrigerators can operate up to the scale of a single particle thus justifying the need for a quantum theory termed quantum thermodynamics.
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