Editing Heat engine

{{Short description|System that converts heat or thermal energy to mechanical work}}
{{See also|Thermodynamic cycle}}
[[File:heat engine.png|thumb|upright=1.0|Figure 1: Heat engine diagram]]
{{Use dmy dates|date=April 2022}}
{{Thermodynamics sidebar|cTopic=[[Thermodynamic system|Systems]]}}

A '''heat engine''' is a system that transfers [[thermal energy]] to do [[work (physics)|mechanical]] or [[voltage#Definition|electrical work]].<ref>''Fundamentals of Classical Thermodynamics'', 3rd ed. p. 159, (1985) by G. J. Van Wylen and R. E. Sonntag: "A heat engine may be defined as a device that operates in thermodynamic cycle and does a certain amount of net positive work as a result of heat transfer from a high-[[temperature]] body to a low-temperature body. Often the term heat engine is used in a broader sense to include all devices that produce work, either through heat transfer or combustion, even though the device does not operate in a thermodynamic cycle. The internal-combustion engine and the gas turbine are examples of such devices, and calling these heat engines is an acceptable use of the term."</ref><ref>''Mechanical efficiency of heat engines'', p. 1 (2007) by James R. Senf: "Heat engines are made to provide mechanical energy from thermal energy."</ref> While originally conceived in the context of mechanical energy, the concept of the heat [[engine]] has been applied to various other kinds of energy, particularly [[electrical energy|electrical]], since at least the late 19th century.<ref>{{cite journal |last1=Kenelly |first1=A.E. |author1-link=Arthur E. Kennelly |title=Discussion of 'Thermo-electric and galvanic actions compared' |journal=Journal of the Franklin Society |date=Dec 1898 |volume=CXLVI |page=442 |url=https://books.google.com/books?id=nXooAQAAIAAJ&pg=PA442}}</ref><ref>{{cite journal |last1=Laurie |first1=Arthur Pillans |author1-link=Arthur Pillans Laurie |title=Faraday society |journal=The Electrical Review |date=17 Jan 1914 |volume=72 |issue=1834 |page=90 |url=https://books.google.com/books?id=fko1AQAAMAAJ&pg=PA90 |access-date=11 February 2023}}</ref> The heat engine 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 higher temperature state. The working substance generates work in the [[thermodynamic system|working body]] of the engine while [[heat transfer|transferring heat]] to the colder [[thermal reservoir|sink]] until it reaches a lower temperature state. During this process some of the thermal energy is converted into [[energy|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 (physics)|drag]].

In general, an engine is any [[machine]] that converts [[energy]] to mechanical [[work (physics)|work]]. Heat engines distinguish themselves from other types of engines by the fact that their efficiency is fundamentally limited by [[Carnot's theorem (thermodynamics)|Carnot's theorem]] of [[thermodynamics]].<ref>''Thermal physics: entropy and free energies'', by Joon Chang Lee (2002), Appendix A, p. 183: "A heat engine absorbs energy from a heat source and then converts it into work for us.... When the engine absorbs heat energy, the absorbed heat energy comes with entropy." (heat energy <math>\Delta Q=T \Delta S</math>), "When the engine performs work, on the other hand, no entropy leaves the engine. This is problematic. We would like the engine to repeat the process again and again to provide us with a steady work source. ... to do so, the working substance inside the engine must return to its initial thermodynamic condition after a cycle, which requires to remove the remaining entropy. The engine can do this only in one way. It must let part of the absorbed heat energy leave without converting it into work. Therefore the engine cannot convert all of the input energy into work!"</ref> 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 reaction]]s (such as combustion), [[nuclear power|nuclear fission]], [[absorption (electromagnetic radiation)|absorption]] of light or energetic particles, [[friction]], [[dissipation]] and [[electrical resistance|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.

== Overview ==
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]].

The efficiency of various heat engines proposed or used today has a large range:
*3%<ref>{{cite journal |url=https://www.researchgate.net/publication/237251713 |title=Experimental Investigations on a Standing-Wave Thermoacoustic Engine |last=Eman |first=Mahmod Mohamed |date=June 2013 |access-date=21 January 2018 |publisher=[[Cairo University]] |journal=[[ResearchGate]] |location=Giza, Egypt}}</ref> (97 percent waste heat using low quality heat) for the [[ocean thermal energy conversion]] (OTEC) ocean power proposal
*25% for most automotive gasoline engines<ref>[https://www.fueleconomy.gov/feg/atv.shtml Where the Energy Goes: Gasoline Vehicles], US Dept of Energy</ref>
*49% for a [[supercritical steam generator|supercritical]] [[coal-fired power station]] such as the [[Avedøre Power Station]]
*50%+ for [[long stroke marine Diesel engines]] [https://www.mhi.co.jp/technology/review/pdf/e451/e451021.pdf]
*60% for a [[combined cycle]] [[gas turbine]]<ref>{{cite web |title=Efficiency by the Numbers |url=https://memagazineblog.org/2012/07/01/efficiency-by-the-numbers/ |archive-url=https://web.archive.org/web/20090616132320/http://memagazine.asme.org/Web/Efficiency_by_Numbers.cfm |archive-date=16 June 2009 |last1=Langston |first1=Lee S. |publisher=ASME |url-status=live}}</ref>

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.

== Examples ==
Although some cycles have a typical combustion location (internal or external), they can often be implemented with the other. For example, [[John Ericsson]]<ref name="hae-ericsson1833">{{cite web|url=http://hotairengines.org/closed-cycle-engine/ericsson-1833|title=Ericsson's 1833 caloric engine|work=hotairengines.org}}</ref> developed 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. In a closed cycle the working fluid is retained within the engine at the completion of the cycle whereas is an open cycle the working fluid is either exchanged with the environment together with the products of combustion in the case of the internal combustion engine or simply vented to the environment in the case of external combustion engines like [[steam engine]]s and [[Steam turbine|turbines]].

=== Everyday examples ===
Everyday examples of heat engines include the [[thermal power station]], [[internal combustion engine]], [[firearm]]s, [[refrigerator]]s and [[heat pump]]s. Power stations are examples of heat engines run in a forward direction in which heat flows from a hot reservoir and flows into a cool reservoir to produce work as the desired product. Refrigerators, [[air conditioner]]s and heat pumps are examples of heat engines that are run in reverse, i.e. they use work to take heat energy at a low temperature and raise its temperature in a more efficient way than the simple conversion of work into heat (either through friction or electrical resistance). Refrigerators remove heat from within a thermally sealed chamber at low temperature and vent waste heat at a higher temperature to the environment and heat pumps take heat from the low temperature environment and 'vent' it into a thermally sealed chamber (a house) at higher temperature.

In general heat engines exploit the thermal properties associated with the expansion and compression of gases according to the [[gas laws]] or the properties associated with [[phase transition|phase changes]] between gas and liquid states.

=== Earth's heat engine ===
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.<ref name="Lindsey 2009">{{cite journal
|last=Lindsey
|first=Rebecca
|year=2009
|title=Climate and Earth's Energy Budget
|journal=NASA Earth Observatory
|url=http://earthobservatory.nasa.gov/Features/EnergyBalance/
}}</ref>

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.<ref>{{cite journal |author=Junling Huang and Michael B. McElroy|title=Contributions of the Hadley and Ferrel Circulations to the Energetics of the Atmosphere over the Past 32 Years|journal=Journal of Climate |issue=7 |volume=27 |pages=2656–2666 |year=2014 |doi=10.1175/jcli-d-13-00538.1|bibcode=2014JCli...27.2656H|s2cid=131132431 |doi-access=free }}</ref>

=== Phase-change cycles ===
In [[phase transition|phase change]] cycles and engines, the [[working fluid]]s 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.
*[[Rankine cycle]] (classical [[steam engine]])
*[[Regenerative cycle]] ([[steam engine]] more efficient than [[Rankine cycle]])
*[[Organic Rankine cycle]] (Coolant changing phase in temperature ranges of ice and hot liquid water)
*Vapor to liquid cycle ([[drinking bird]], [[injector]], [[Minto wheel]])
*Liquid to solid cycle ([[frost heaving]] – water changing from ice to liquid and back again can lift rock up to 60&nbsp;cm.)
*Solid to gas cycle ([[firearm]]s  – solid propellants combust to hot gases.)

=== Gas-only cycles ===
In these cycles and engines the working fluid is always a gas (i.e., there is no phase change):
*[[Carnot cycle]] ([[Carnot heat engine]])
*[[Ericsson cycle]] (Caloric Ship John Ericsson)
*[[Stirling cycle]] ([[Stirling engine]],<ref name="hae-stirling1842">{{cite web|url=http://hotairengines.org/closed-cycle-engine/stirling-1827/stirling-dundee-engine|title=Stirling's Dundee engine of 1841|work=hotairengines.org}}</ref> [[thermoacoustic refrigeration|thermoacoustic]] devices)
*[[Internal combustion engine]] (ICE):
**[[Otto cycle]] (e.g. [[petrol engine|gasoline/petrol engine]])
**[[Diesel cycle]] (e.g. [[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]] (Miller engine)

=== Liquid-only cycles ===
In these cycles and engines the working fluid are always like liquid:
*[[Stirling cycle]] ([[Malone engine]])

=== Electron cycles ===
*[[Johnson thermoelectric energy converter]]
*Thermoelectric ([[Peltier–Seebeck effect]])
*[[Thermogalvanic cell]]
*[[Thermionic emission]]
*[[Thermotunnel cooling]]

=== Magnetic cycles ===
*[[Thermo-magnetic motor]] (Tesla)

=== Cycles used for refrigeration ===
{{Main|Refrigeration}}
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:
*[[Air cycle machine]]
*[[Gas-absorption refrigerator]]
*[[Magnetic refrigeration]]
*[[Stirling engine#Stirling cryocoolers|Stirling cryocooler]]
*[[Vapor-compression refrigeration]]
*[[Vuilleumier cycle]]

=== 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.

=== Mesoscopic heat engines ===
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.<ref name='sinitsyn-11jpa'>{{cite journal|title=Fluctuation Relation for Heat Engines|author=N. A. Sinitsyn |journal=J. Phys. A: Math. Theor.|volume=44|year=2011|issue=40 |page=405001|doi=10.1088/1751-8113/44/40/405001|arxiv=1111.7014 |bibcode=2011JPhA...44N5001S|s2cid=119261929 }}</ref> <!-- N.A. Sinitsyn 2011 JPA ''44''' 405001 --> This relation transforms the Carnot's inequality into exact equality. This relation is also a Carnot cycle equality

== Efficiency ==
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:<ref name="PlanckBook">{{cite book |last=Planck |first=M. |title=Treatise on Thermodynamics |page=§&nbsp;90 & §&nbsp;137 |quote=eqs.(39), (40), & (65) |publisher=Dover Publications |year=1945}}.</ref>
:<math> W + Q = \Delta_{cycle}U = 0 </math>
:and therefore
:<math> W = -Q = - (Q_c + Q_h) </math>
:where
:<math> W = -\oint PdV </math> is the net work extracted from the engine in one cycle. (It is negative, in the [[Work (thermodynamics)#Sign convention|IUPAC convention]], since work is ''done by'' the engine.)
:<math> Q_h > 0 </math> is the heat energy taken from the high temperature heat source in the surroundings in one cycle. (It is positive since heat energy is ''added'' to the engine.)
:<math> Q_c = -|Q_c|<0 </math> is the waste heat given off by the engine to the cold temperature heat sink. (It is negative<ref name="PlanckBook" /> since heat is ''lost'' by the engine 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 giving off the rest as waste heat to the cold temperature heat sink.

In general, the efficiency of a given heat transfer process is defined by the ratio of "what is taken out" to "what is put in". (For a refrigerator or heat pump, which can be considered as a heat engine run in reverse, this is the [[coefficient of performance]] and it is ≥ 1.) In the case of an engine, one desires to extract work and has to put in heat <math> Q_h  </math>, for instance from [[combustion]] of a fuel, so the engine efficiency is reasonably defined as
:<math>\eta = \frac{|W|}{Q_h} = \frac{Q_h + Q_c}{Q_h} = 1 + \frac{Q_c}{Q_h} = 1 - \frac{|Q_c|}{Q_h}</math>

The efficiency is less than 100% because of the waste heat <math> Q_c<0  </math> unavoidably lost to the cold sink (and corresponding compression work put in) during the required recompression at the cold temperature before the [[Power stroke (engine)|power stroke]] of the engine can occur again.

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, after a full cycle, the overall change of entropy is zero:

<math>\ \ \ \Delta S_h + \Delta S_c = \Delta_{cycle} S = 0</math>

Note that <math>\Delta S_h</math> is positive because isothermal expansion in the power stroke increases the [[Multiplicity (statistical mechanics)|multiplicity]] of the working fluid while <math>\Delta S_c</math> is negative since recompression decreases the multiplicity. If the engine is ideal and runs [[Reversible process (thermodynamics)|reversibly]], <math> Q_h = T_h\Delta S_h  </math> and <math> Q_c = T_c\Delta S_c  </math>, and thus<ref name="FermiBook">{{cite book |last=Fermi |first=E. |title=Thermodynamics |page=48 |quote= eq.(64) |publisher=Dover Publications (still in print) |year=1956}}.</ref><ref name="PlanckBook" />

<math> Q_h / T_h + Q_c / T_c = 0 </math>,

which gives <math> Q_c /Q_h = -T_c / T_h  </math> and thus the Carnot limit for heat-engine efficiency,
:<math>\eta_\text{max} = 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]]s.

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 with temperature. 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.

{| cellpadding="2" style="border:1px solid darkgrey; margin:auto;" class=skin-invert-image
|-
|[[File:Carnot Efficiency.svg|none|thumb|385x385px|Figure 2: Carnot cycle efficiency with changing heat addition temperature.]]
|[[File:Carnot Efficiency2.svg|none|thumb|450x450px|Figure 3: Carnot cycle efficiency with changing heat rejection temperature.]]
|}

=== Endo-reversible heat-engines ===
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 system is broken into reversible subsystems, but with non reversible interactions between them. A classical example is the Curzon–Ahlborn engine,<ref name=CurzonAhlborn1975>F. L. Curzon, B. Ahlborn (1975). "Efficiency of a Carnot Engine at Maximum Power Output". ''Am. J. Phys.'', Vol. 43, pp. 24.</ref> very similar to a Carnot engine, but where the thermal reservoirs at temperature <math>T_h</math> and <math>T_c</math> are allowed to be different from the temperatures of the substance going through the reversible Carnot cycle: <math>T'_h</math> and <math>T'_c</math>. The heat transfers between the reservoirs and the substance are considered as conductive (and irreversible) in the form <math>dQ_{h,c}/dt = \alpha (T_{h,c}-T'_{h,c})</math>. In this case, a tradeoff has to be made between power output and efficiency. If the engine is operated very slowly, the heat flux is low, <math>T\approx T'</math> and the classical Carnot result is found
:<math>\eta = 1 - \frac{T_c}{T_h}</math>,
but at the price of a vanishing power output. If instead one chooses to operate the engine at its maximum output power, the efficiency becomes
:<math>\eta = 1 - \sqrt{\frac{T_c}{T_h}}</math> (Note: ''T'' in units of [[kelvin|K]] or [[Rankine scale|°R]])

This model does a better job of predicting how well real-world heat-engines can do (Callen 1985, see also [[endoreversible thermodynamics]]):

{| class="wikitable"
|+'''Efficiencies of power stations'''<ref name=CurzonAhlborn1975 />
|-
! ''Power station'' !! <math>T_c</math> (°C) !! <math>T_h</math> (°C) !! <math>\eta</math> (Carnot) !! <math>\eta</math> (Endoreversible) !! <math>\eta</math> (Observed)
|-
! [[West Thurrock]] (UK) [[coal-fired power station]]
| 25 || 565 || 0.64 || 0.40 || 0.36
|-
! [[CANDU reactor|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 Curzon–Ahlborn efficiency much more closely models that observed.

== History ==
{{Main|Timeline of heat engine technology}}
{{See also|History of the internal combustion engine|History of thermodynamics}}

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.

== Enhancements ==
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:
#Increase the temperature difference in the heat engine. The simplest way to do this is to increase the hot side temperature, which is the approach used in modern combined-cycle [[gas turbine]]s. Unfortunately, physical limits (such as the melting point of the materials used to build the engine) and environmental concerns regarding [[NOx|NO<sub>x</sub>]] production (if the heat source is combustion with ambient air) restrict the maximum temperature on workable heat-engines. Modern gas turbines run at temperatures as high as possible within the range of temperatures necessary to maintain acceptable NO<sub>x</sub> output {{Citation needed|date=January 2010}}. Another way of increasing efficiency is to lower the output temperature. One new method of doing so is to use mixed chemical working fluids, 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 property|physical properties]] of the working fluid. The most common such exploitation is the use of water above the critical point ([[supercritical water]]). The behavior of fluids above their [[critical point (thermodynamics)|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 [[supercritical carbon dioxide|supercritical CO<sub>2</sub>]]. [[Sulfur dioxide|SO<sub>2</sub>]] and [[xenon]] have also been considered for such applications. Downsides include issues of corrosion and erosion, the different chemical behavior above and below the critical point, the needed high pressures and – in the case of sulfur dioxide and to a lesser extent carbon dioxide – toxicity. Among the mentioned compounds xenon is least suitable for use in a nuclear reactor due to the high [[neutron absorption]] cross section of almost all [[isotopes of xenon]], whereas carbon dioxide and water can also double as a [[neutron moderator]] for a thermal spectrum reactor.
#Exploit the [[chemical property|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 (chemistry)|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 [[Thermal reservoir|heat sink]], which makes it recombine into N<sub>2</sub>O<sub>4</sub>. This is then fed back by 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>{{cite web |url=https://netfiles.uiuc.edu/mragheb/www/NPRE%20402%20ME%20405%20Nuclear%20Power%20Engineering/Nuclear%20Reactors%20Concepts%20and%20Thermodynamic%20Cycles.pdf |title=Nuclear Reactors Concepts and Thermodynamic Cycles |access-date=2012-03-22 |url-status=dead |archive-url=https://web.archive.org/web/20090318233007/https://netfiles.uiuc.edu/mragheb/www/NPRE%20402%20ME%20405%20Nuclear%20Power%20Engineering/Nuclear%20Reactors%20Concepts%20and%20Thermodynamic%20Cycles.pdf |archive-date=18 March 2009}}</ref>

== Heat engine processes ==
{{Table of thermodynamic cycles}}

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), also referred to as iso-volumetric
*[[adiabatic process|adiabatic]] (no heat is added or removed from the system during adiabatic process)
*[[isentropic process|isentropic]] (reversible adiabatic process, no heat is added or removed during isentropic process)

== See also ==
{{Portal|Energy}}
*[[Carnot heat engine]]
*[[Cogeneration]]
*[[Einstein refrigerator]]
*[[Heat pump]]
*[[Reciprocating engine]] for a general description of the mechanics of piston engines
*[[Stirling engine]]
*[[Thermosynthesis]]
*[[Timeline of heat engine technology]]

== References ==
{{Commons category|Heat engines}}
{{Reflist}}
*{{cite book |last=Kroemer |first=Herbert |author2=Kittel, Charles |title=Thermal Physics |edition=2nd |publisher=W. H. Freeman Company |year=1980 |isbn=0-7167-1088-9}}
*{{cite book |last=Callen |first=Herbert B. |title=Thermodynamics and an Introduction to Thermostatistics |edition=2nd |publisher=[[John Wiley & Sons, Inc.]] |year=1985 |isbn=0-471-86256-8}}
*{{cite book |last=Robinson |first=Clark |title=The Thermodynamics of Firearms  |publisher=MaGraw-Hill Book Company Inc. |year=1943}}

{{Heat engines|state=uncollapsed}}
{{Thermodynamic cycles}}

{{Authority control}}

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