Heat engine

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Figure 1: Heat engine diagram Heat engine.png
Figure 1: Heat engine diagram

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. [1] [2] 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. [3] 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 Ericsson [7] 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.

Everyday examples

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 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. [8]

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. [9]

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, from liquid to gas, or both, generating work from the fluid expansion or compression.

Gas-only cycles

In these cycles and engines the working fluid is always a gas (i.e., there is no phase change):

Liquid-only cycles

In these cycles and engines the working fluid are always like liquid:

Electron cycles

Magnetic cycles

Cycles used for 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:

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. [12] 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:

is the work extracted from the engine. (It is negative since work is done by the engine.)
is the heat energy taken from the high temperature system. (It is negative since heat is extracted from the source, hence is positive.)
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 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.

Figure 2: Carnot cycle efficiency with changing heat addition temperature. Carnot Efficiency.svg
Figure 2: Carnot cycle efficiency with changing heat addition temperature.
Figure 3: Carnot cycle efficiency with changing heat rejection temperature. Carnot Efficiency2.svg
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 cycle is identical to the Carnot cycle except that the two processes of heat transfer are not reversible (Callen 1985):

(Note: Units K or °R)

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

Efficiencies of power stations [13]
Power station (°C) (°C) (Carnot) (Endoreversible) (Observed)
West Thurrock (UK) coal-fired power station 255650.640.400.36
CANDU (Canada) nuclear power station 253000.480.280.30
Larderello (Italy) geothermal power station 802500.330.1780.16

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:

  1. 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 turbines. Unfortunately, physical limits (such as the melting point of the materials used to build the engine) and environmental concerns regarding NOx production 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 NOx output [ citation needed ]. 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.
  2. Exploit the physical properties of the working fluid. The most common such exploitation is the use of water above the critical point, or 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 CO2. SO2 and xenon have also been considered for such applications, although SO2 is toxic.
  3. 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 (NO2), a toxic component of smog, which has a natural dimer as di-nitrogen tetraoxide (N2O4). At low temperature, the N2O4 is compressed and then heated. The increasing temperature causes each N2O4 to break apart into two NO2 molecules. This lowers the molecular weight of the working fluid, which drastically increases the efficiency of the cycle. Once the NO2 has expanded through the turbine, it is cooled by the heat sink, which makes it recombine into N2O4. This is then fed back by the compressor for another cycle. Such species as aluminium bromide (Al2Br6), NOCl, and Ga2I6 have all been investigated for such uses. To date, their drawbacks have not warranted their use, despite the efficiency gains that can be realized. [14]

Heat engine processes

CycleCompression, 1→2Heat addition, 2→3Expansion, 3→4Heat rejection, 4→1Notes
Power cycles normally with external combustion - or heat pump cycles:
Bell Coleman adiabaticisobaricadiabaticisobaricA reversed Brayton cycle
Carnot isentropicisothermalisentropicisothermal Carnot heat engine
Ericsson isothermalisobaricisothermalisobaricThe second Ericsson cycle from 1853
Rankine adiabaticisobaricadiabaticisobaric Steam engine
Hygroscopic adiabaticisobaricadiabaticisobaric Hygroscopic cycle
Scuderi adiabaticvariable pressure
and volume
Stirling isothermalisochoricisothermalisochoric Stirling engine
Manson isothermalisochoricisothermalisochoric then adiabatic Manson-Guise Engine
Stoddard adiabaticisobaricadiabaticisobaric
Power cycles normally with internal combustion:
Brayton adiabaticisobaricadiabaticisobaric Jet engine. The external combustion version of this cycle is known as first Ericsson cycle from 1833.
Diesel adiabaticisobaricadiabaticisochoric Diesel engine
Lenoir isochoricadiabaticisobaric Pulse jets. Note, 1→2 accomplishes both the heat rejection and the compression.
Otto isentropicisochoricisentropicisochoric Gasoline / petrol engines

Each process is one of the following:

See also

Related Research Articles

Carnot heat engine heat engine is a engine that operates based on carnot cycle. the basic model was introduced by nicolas léonard sardi carnot

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.

Entropy physical property of the state of a system, measure of disorder

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,

Nicolas Léonard Sadi Carnot French physicist, the "father of thermodynamics" (1796–1832)

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.

Second law of thermodynamics Law of physics

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.

Carnots theorem (thermodynamics) Principle that specifies limits on the maximum efficiency any heat engine can obtain

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.

Isentropic process Thermodynamic process that is reversible and adiabatic

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.

Thermodynamic system Precisely specified macroscopic region of the universe, defined by boundaries

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.

Rankine cycle Model that is used to predict the performance of steam turbine systems

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.

Laws of thermodynamics law that defines fundamental physical quantities that characterize thermodynamic systems and their behavior

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.

Thermodynamic cycle 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

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.

Thermal efficiency performance measure of a device that uses thermal energy

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.

Clausius theorem

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.

Carnot cycle Theoretical thermodynamic cycle proposed by Nicolas Leonard Sadi Carnot in 1824

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.

Heat pump and refrigeration cycle Mathematical models of heat pumps and refrigeration

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.

Heat energy transfer process, or its amount (and direction), that is associated with a temperature difference

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 Physical quantity that expresses hot and cold

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

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.


  1. 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 a thermodynamic cycle and does a certain amount of net positive work as a result of heat transfer from a high-temperature body and 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."
  2. Mechanical efficiency of heat engines, p. 1 (2007) by James R. Senf: "Heat engines are made to provide mechanical energy from thermal energy."
  3. 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 ), "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!"
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