Heat engine
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{{Portal|Energy}}
A '''heat engine''' is a physical or theoretical device that converts [[thermal energy]] to mechanical output. The mechanical output is called [[Mechanical work|work]], and the thermal energy input is called [[heat]]. Heat engines typically run on a specific [[thermodynamic cycle]]. Heat engines are often named after the thermodynamic cycle they are modeled by. They often pick up alternate names, such as gasoline/petrol, turbine, or steam engines. Heat engines can generate heat inside the engine itself or it can absorb heat from an external source. Heat engines can be open to the atmospheric air or sealed and closed off to the outside (Open or closed cycle).
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 "[[Heat sink|sink]]". Heat is [[heat transfer|transferred]] from the source, through the "[[working body]]" of the engine, to the sink, and in this process some of the heat is converted into [[energy|work]] by exploiting the properties of a working substance (usually a gas or liquid).
[[Image:Carnot_heat_engine_2.svg|500px|thumb|right|Figure 1: '''Heat engine diagram''']]
==Overview==
Heat engines are often confused with the cycles they attempt to mimic. Typically when describing the physical device the term 'engine' is used. When describing the model the term 'cycle' is used.
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 gaining a good understanding of the (possibly simplified or idealized) 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 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 obtains) is equal to the temperature difference between the hot and cold ends divided by the temperature at the hot end, all expressed in [[absolute temperature]] or [[kelvin|kelvins]].
The efficiency of various heat engines proposed or used today ranges from 3 percent <ref>[[Ocean_thermal_energy_conversion]]</ref>(97 percent waste heat) for the [[Ocean thermal energy conversion|OTEC]] ocean power proposal through 25 percent for most automotive engines, to 45 percent for a [[super critical]] [[Fossil fuel power plant|coal plant]], to about 60 percent for a steam-cooled [[combined cycle]] [[gas turbine]]. All of these processes gain their efficiency (or lack thereof) due to the temperature drop across them.
OTEC uses the temperature difference of ocean water on the surface and ocean water from the depths, a small difference of perhaps 25 degrees Celsius, and so the efficiency must be low. The combined cycle gas turbines use natural-gas fired burners to heat air to near 1530 degrees Celsius, a difference of a large 1500 degrees Celsius, and so the efficiency can be large when the steam-cooling cycle is added in. <ref>[http://www.fe.doe.gov/programs/powersystems/publications/Brochures/Advancedturbinesystems.pdf U.S. Department of Energy • Office of Fossil Energy, National Energy Technology Laborator: Advanced Turbine Systems. Advancing The Gas Turbine Power Industry]</ref>
==Everyday examples==
Examples of everyday heat engines include: the [[steam engine]], the [[diesel engine]], and the [[internal_combustion_engine|gasoline (petrol) engine]] in an [[automobile]].
A common toy that is also a heat engine is a [[drinking bird]].
All of these familiar heat engines are powered by the expansion of heated gases.
The general surroundings are the heat sink, providing relatively cool gases which, when heated, expand rapidly to drive the mechanical motion of the engine.
==Examples of heat engines==
It is important to note that although some cycles have a typical combustion location (internal external), they often can be implemented as the other combustion cycle. For example, [[John Ericsson]] developed an external heated engine running on a cycle very much like the earlier [[Diesel cycle]]. In addition, the externally heated engines can often be implemented in open or closed cycles.
What this boils down to is there are thermodynamic cycles and a large number of ways of implementing them with mechanical devices called engines.
=== Phase change cycles ===
In these cycles and engines, the working fluids are gases and liquids. The engine converts the working fluid from a gas to a liquid.
* [[Rankine cycle]] (classical [[steam engine]])
* [[Regenerative cycle]] ([[steam engine]] more efficient than [[Rankine cycle]])
* Vapor to liquid cycle ([[Drinking bird]], [[Injector]])
* Liquid to solid cycle ([[Frost heaving]] — water changing from ice to liquid and back again can lift rock up to 60 m.)
* Solid to gas cycle ([[Dry ice cannon]] — Dry ice sublimes to gas.)
=== Gas only cycles ===
In these cycles and engines the working fluid is always a gas (ie, there is no phase change):
* [[Carnot cycle]] ([[Carnot heat engine]])
* [[Ericsson Cycle]] ([[Caloric Ship John Ericsson]])
* [[Stirling cycle]] ([[Stirling engine]], [[Thermoacoustic refrigeration|thermoacoustic]] devices)
* [[Internal combustion engine]] (ICE):
** [[Otto cycle]] (eg. [[Gasoline/Petrol engine]], [[high-speed diesel engine]])
** [[Diesel cycle]] (eg. low-speed [[diesel engine]])
** [[Atkinson Cycle]] ([[Atkinson Engine]])
** [[Brayton cycle]] or [[Joule cycle]] originally [[Ericsson Cycle]] ([[gas turbine]])
** [[Lenoir cycle]] (e.g., [[pulse jet engine]])
** [[Miller cycle]]
=== Liquid only cycles ===
In these cycles and engines the working fluid are always like liquid:
* [[Stirling Cycle]] ([[Malone engine]])
=== Electron cycles ===
* Thermoelectric ([[Peltier-Seebeck effect]])
* [[Thermionic emission]]
* [[Thermotunnel cooling]]
=== Magnetic cycles ===
* [[Thermo-magnetic motor]] (Tesla)
=== Cycles used for refrigeration ===
A [[refrigerator]] is 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.
* [[Vapor-compression refrigeration]]
* [[Stirling engine#Stirling cryocoolers|Stirling cryocooler]]
* [[Gas-absorption refrigerator]]
* [[Air cycle machine]]
* [[Vuilleumier refrigeration]]
=== Evaporative Heat Engines ===
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.
==Efficiency==
The efficiency of a heat engine relates how much useful power is output for a given amount of heat energy input.
From the laws of [[thermodynamics]]:
::<math> dW \ = \ dQ_c \ - \ (-dQ_h) </math>
:where
::<math> dW = -PdV </math> is the work extracted from the engine. (It is negative since work is ''done by'' the engine.)
::<math> dQ_h = T_hdS_h </math> is the heat energy taken from the high temperature system. (It is negative since heat is extracted from the source, hence <math>(-dQ_h)</math> is positive.)
::<math> dQ_c = T_cdS_c </math> is the heat energy delivered to the cold temperature system. (It is positive since heat is added to the sink.)
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 you get out" to "what you put in."
In the case of an engine, one desires to extract work and puts in a heat transfer.
::<math>\eta = \frac{-dW}{-dQ_h} = \frac{-dQ_h - dQ_c}{-dQ_h} = 1 - \frac{dQ_c}{-dQ_h}</math>
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 [[Thermodynamic reversibility|reversible]] processes, the change in [[entropy]] of the cold reservoir is the negative of that of the hot reservoir (i.e., <math>dS_c = -dS_h</math>), keeping the overall change of entropy zero. Thus:
::<math>\eta_\text{max} = 1 - \frac{T_cdS_c}{-T_hdS_h} = 1 - \frac{T_c}{T_h}</math>
where <math>T_h</math> is the [[absolute temperature]] of the hot source and <math>T_c</math> that of the cold sink, usually measured in [[kelvin]]. Note that <math>dS_c</math> is positive while <math>dS_h</math> 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 forbidden, the Carnot efficiency is a theoretical upper bound on the efficiency of ''any'' process.
Empirically, no engine has ever been shown to run at a greater efficiency than a Carnot cycle heat engine.
[[Image:GFImg3.png|thumb|right|325px|Figure 2: '''Carnot cycle efficiency''']]
[[Image:GFImg4.png|thumb|right|325px|Figure 3: '''Carnot cycle efficiency''']]
Here are two plots, Figure 2 and Figure 3, for the Carnot cycle efficiency. One plot indicates how the cycle efficiency changes with an increase in the heat addition temperature for a constant compressor inlet temperature, while the other indicates how the cycle efficiency changes with an increase in the heat rejection temperature for a constant turbine inlet temperature.
==Other criteria of heat engine performance==
One problem with the ideal Carnot efficiency as a criterion of heat engine performance is the fact that 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 at differing temperatures is irreversible, and therefore the Carnot efficiency expression only applies in the infinitesimal limit. The major problem with that is that the object of most heat engines is to output some sort of power, and infinitesimal power is usually not what is being sought.
A different measure of heat engine efficiency is given by the '''[[endoreversible]] process''', which is identical to the Carnot cycle except in that the two processes of heat transfer are ''not'' reversible. As derived in Callen (1985), the efficiency for such a process is given by:
::<math>\eta = 1 - \sqrt{\frac{T_c}{T_h}}</math> (Note: Units [[kelvin|K]] or [[degree Rankine|°R]])
(Note: This equation is quite frequently traced to a paper by F.L. Curzon and B. Ahlborn, American Journal of Physics, vol. 43, pp. 22-24 (1975). The book by [[Herbert Callen]] probably copied from this paper. In a 1996 review paper by [[Adrian Bejan]] (J. Appl. Phys., vol. 79, pp. 1191-1218, 1 Feb. 1996), [[Adrian Bejan]] pointed out that this equation was also derived by P. Chambadal and I.I. Novikov earlier than Curzon and Ahlborn in the 1950s. Probably, this equation was just re-discovered by Curzon and Ahlborn in 1975. Therefore, some scientists call this efficiency the Chambadal-Novikov-Curzon-Ahlborn efficiency.)
This model does a better job of predicting how well real-world heat engines can do, as can be seen in the following table (Callen):
(Note: This table appeared in the paper by F.L. Curzon and B. Ahlborn, American Journal of Physics, vol. 43, pp. 22-24 (1975). The book by [[Herbert Callen]] probably copied from this paper.)
{| class="wikitable"
|+'''Efficiencies of Power Plants'''
|-
! ''Power Plant'' !! <math>T_c</math> (°C) !! <math>T_h</math> (°C) !! <math>\eta</math> (Carnot) !! <math>\eta</math> (Endoreversible) !! <math>\eta</math> (Observed)
|-
! [[West Thurrock]] ([[United Kingdom|UK]]) [[Fossil fuel power plant|coal-fired power plant]]
| 25 || 565 || 0.64 || 0.40 || 0.36
|-
! [[CANDU reactor|CANDU]] ([[Canada]]) [[nuclear power plant]]
| 25 || 300 || 0.48 || 0.28 || 0.30
|-
! [[Larderello]] ([[Italy]]) [[Geothermal power|geothermal power plant]]
| 80 || 250 || 0.33 || 0.178 || 0.16
|}
As shown, the endoreversible efficiency much more closely models the observed data.
==Heat engine enhancements==
Engineers have studied the various heat engine cycles extensively in an effort 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 worked out at least two ways to possibly go around that limit, and one way to get better efficiency without bending any rules.
# Increase the [[temperature]] difference in the heat engine. The simplest way to do this is to increase the hot side temperature, and is the approach used in modern combined-cycle [[gas turbine]]s. Unfortunately, [[NOx|NO<sub>x</sub>]] production and material limits (melting the turbine blades) place a hard limit to how hot you can make a workable heat engine. Modern gas turbines are about as hot as they can become and still maintain acceptable NO<sub>x</sub> pollution levels. Another way of increasing efficiency is to lower the output temperature. One new method of doing so is to use mixed chemical working fluids, and then exploit the changing behavior of the mixtures. One of the most famous is the so-called [[Kalina cycle]], which uses a 70/30 mix of [[ammonia]] and water as its working fluid. This mixture allows the cycle to generate useful power at considerably lower temperatures than most other processes.
# Exploit the physical properties of the working fluid. The most common such exploit is the use of water above the so-called critical point, or so-called supercritical steam. The behavior of fluids above their critical point changes radically, and with materials such as water and [[carbon dioxide]] it is possible to exploit those changes in behavior to extract greater thermodynamic efficiency from the heat engine, even if it is using a fairly conventional Brayton or Rankine cycle. A newer and very promising material for such applications is CO<sub>2</sub>. SO<sub>2</sub> and [[xenon]] have also been considered for such applications, although SO<sub>2</sub> is a little toxic for most.
# Exploit the chemical properties of the working fluid. A fairly new and novel exploit is to use exotic working fluids with advantageous chemical properties. One such is [[nitrogen dioxide]] (NO<sub>2</sub>), a toxic component of [[smog]], which has a natural [[dimer]] as di-nitrogen tetraoxide (N<sub>2</sub>O<sub>4</sub>). At low temperature, the N<sub>2</sub>O<sub>4</sub> is compressed and then heated. The increasing temperature causes each N<sub>2</sub>O<sub>4</sub> to break apart into two NO<sub>2</sub> molecules. This lowers the molecular weight of the working fluid, which drastically increases the efficiency of the cycle. Once the NO<sub>2</sub> has expanded through the turbine, it is cooled by the [[heat sink]], which causes it to recombine into N<sub>2</sub>O<sub>4</sub>. This is then fed back to the compressor for another cycle. Such species as [[aluminium bromide]] (Al<sub>2</sub>Br<sub>6</sub>), NOCl, and Ga<sub>2</sub>I<sub>6</sub> have all been investigated for such uses. To date, their drawbacks have not warranted their use, despite the efficiency gains that can be realized. <ref>[https://netfiles.uiuc.edu/mragheb/www/NPRE%20402%20ME%20405%20Nuclear%20Power%20Engineering/Nuclear%20Reactors%20Concepts%20and%20Thermodynamic%20Cycles.pdf Nuclear Reactors Concepts and Thermodynamic Cycles]</ref>
==Heat engine processes==
{| class="wikitable"
|+<!-- no title, because it starts a section.-->
|-
! Cycle/Process !! Compression !! Heat Addition !! Expansion !! Heat Rejection
|-
|colspan="5" align="center" | Power cycles normally with [[external combustion]]
|-
! [[Carnot cycle|Carnot]]
| adiabatic || isothermal || adiabatic || isothermal
|-
! [[Stirling cycle|Stirling]]
| isothermal || isometric || isothermal || isometric
|-
! [[Ericsson cycle|Ericsson]]
| isothermal || isobaric || isothermal || isobaric
|-
! [[Rankine cycle|Rankine (Steam)]]
| adiabatic || isobaric || adiabatic || isobaric
|-
! [[Stoddard cycle|Stoddard]]
| adiabatic || isobaric || adiabatic || isobaric
|-
|colspan="5" align="center" | Power cycles normally with [[internal combustion]]
|-
! [[Otto cycle|Otto (Petrol)]]
| adiabatic ||isometric || adiabatic || isometric
|-
! [[Diesel cycle|Diesel]]
| adiabatic || isobaric || adiabatic || isometric
|-
! [[Brayton cycle|Brayton (Jet)]]
| adiabatic || isobaric || adiabatic || isobaric
|}
Each process is one of the following:
* [[isothermal process|isothermal]] (at constant temperature, maintained with heat added or removed from a heat source or sink)
* [[isobaric process|isobaric]] (at constant pressure)
* [[isochoric process|isometric/isochoric]] (at constant volume)
* [[adiabatic process|adiabatic]] (no heat is added or removed from the system during adiabatic process which is equivalent to saying that the entropy remains constant)
==References==
<References/>
* {{cite book | last = Kroemer | first = Herbert | coauthors = Kittel, Charles | title = Thermal Physics | edition = 2nd ed. | publisher = W. H. Freeman Company | year = 1980 | id = ISBN 0-7167-1088-9 }}
* {{cite book | last = Callen | first = Herbert B. | title = Thermodynamics and an Introduction to Thermostatistics | edition = 2nd ed. | publisher = John Wiley & Sons, Inc. | year = 1985 | id = ISBN 0-471-86256-8 }}
==See also==
*[[Reciprocating engine]] for a general description of the mechanics of piston engines
*[[Heat pump]]
*[[Carnot heat engine]]
*[[Timeline of heat engine technology]]
*[[Heat engine classifications]]
{{Thermodynamic cycles|state=uncollapsed}}
{{Machine configurations|state=uncollapsed}}
==External links==
*[http://www.icefoundry.org/how-stirling-engine-works.php Video of Stirling engine running on dry ice]
*[http://www.taftan.com/thermodynamics/HENGINE.HTM Heat Engine]
*[http://web.archive.org/web/20030123072140/www.uq.edu.au/~e4nsrdja/teaching/e4213/Related/Cycles/Refrig.htm Webarchive backup: Refrigeration Cycle] Citat: "...The refrigeration cycle is basically the Rankine cycle run in reverse..."
*[http://www.redrok.com/engine.htm Red Rock Energy Solar Heliostats: Heat Engine Projects] Citat: "...Choosing a Heat Engine..."
*[http://www.stanford.edu/class/ee293a/FEP4_Text_X.pdf Overview of heat engine types]
*[http://www.treefinder.de/ideas.html#1 The rotary piston array machine]
*[http://www.bingo-ev.de/~rd2553 The gyroscope combustion motor]
*[http://www.stirlingengines.org.uk/index.html The external combustion air engine]
*[http://www.ernsblog.com/engineeff.html Super-efficient Atkinson-Diesel Cycle]
[[Category:Fundamental physics concepts]]
[[Category:Heat]]
[[Category:Energy conversion]]
[[Category:HVAC]]
[[Category:Thermodynamics]]
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