![heat engine](https://upload.wikimedia.org/wikipedia/commons/a/a2/Heat_engine.png)
In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
and
engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
, a heat engine is a system that converts
heat
In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
to
mechanical energy
In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is ...
, which can then be used to do
mechanical work
In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...
. 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 higher temperature state. The working substance generates work in the
working body
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 ...
of the engine while
transferring heat
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
to the colder
sink
A sink is a bowl-shaped plumbing fixture for washing hands, dishwashing, and other purposes. Sinks have a tap (faucet) that supply hot and cold water and may include a spray feature to be used for faster rinsing. They also include a drain t ...
until it reaches a lower temperature state. During this process some of the thermal energy is converted into
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
by exploiting the properties of the working substance. The working substance can be any system with a non-zero
heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
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
An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy.
Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power ...
is any
machine that converts
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
to mechanical
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
. 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 reaction
In thermochemistry, an exothermic reaction is a "reaction for which the overall standard enthalpy change Δ''H''⚬ is negative." Exothermic reactions usually release heat. The term is often confused with exergonic reaction, which IUPAC defines ...
s (such as combustion),
nuclear fission,
absorption of light or energetic particles,
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of ...
,
dissipation
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
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.
Overview
In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
, heat engines are often modeled using a standard engineering model such as the
Otto cycle
An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
The Otto cycle is a description of what hap ...
. The theoretical model can be refined and augmented with actual data from an operating engine, using tools such as an
indicator diagram
An indicator diagram is a chart used to measure the thermal, or cylinder, performance of reciprocating steam and internal combustion engines and compressors. An indicator chart records the pressure in the cylinder versus the volume swept by the ...
. 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
In thermodynamics, the thermal efficiency (\eta_) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc.
For a ...
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
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
, 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
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic w ...
.
The efficiency of various heat engines proposed or used today has a large range:
*3% (97 percent waste heat using low quality heat) for the
ocean thermal energy conversion
Ocean Thermal Energy Conversion (OTEC) uses the ocean thermal gradient between cooler deep and warmer shallow or surface seawaters to run a heat engine and produce useful work, usually in the form of electricity. OTEC can operate with a very hi ...
(OTEC) ocean power proposal
*25% for most automotive gasoline engines
*49% for a
supercritical coal-fired power station such as the
Avedøre Power Station
The Avedøre Power Station ( da, Avedøreværket) is a combined heat and power station, located in Avedøre, Denmark, just south of Copenhagen, and is owned by Ørsted A/S. Avedøre Power Plant is a high-technology facility and one of the world's ...
*60% for a
combined cycle gas turbine
A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directio ...
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
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
John Ericsson (born Johan Ericsson; July 31, 1803 – March 8, 1889) was a Swedish-American inventor. He was active in England and the United States.
Ericsson collaborated on the design of the railroad steam locomotive ''Novelty'', which co ...
developed an external heated engine running on a cycle very much like the earlier
Diesel cycle
The Diesel cycle is a combustion process of a reciprocating internal combustion engine. In it, fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is then injected. This is in contrast to ign ...
. 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 engines and turbines.
Everyday examples
Everyday examples of heat engines include the
thermal power station
A thermal power station is a type of power station in which heat energy is converted to electrical energy. In a steam-generating cycle heat is used to boil water in a large pressure vessel to produce high-pressure steam, which drives a stea ...
,
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal c ...
,
firearms ,
refrigerators and
heat pump
A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
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 conditioners 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
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
Boyl ...
or the properties associated with 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.
A
Hadley cell
The Hadley cell, named after George Hadley, is a global-scale tropical atmospheric circulation that features air rising near the equator, flowing poleward at a height of 10 to 15 kilometers above the earth's surface, descending in the subtropics ...
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.
Phase-change cycles
In these cycles and engines, the
working fluid
For fluid power, a working fluid is a gas or liquid that primarily transfers force, motion, or mechanical energy. In hydraulics, water or hydraulic fluid transfers force between hydraulic components such as hydraulic pumps, hydraulic cylinders, ...
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
The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat sourc ...
(classical
steam engine)
*
Regenerative cycle (
steam engine more efficient than
Rankine cycle
The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat sourc ...
)
*
Organic Rankine cycle
In thermal engineering, the Organic Rankine Cycle (ORC) is a type of thermodynamic cycle. It is a variation of the Rankine cycle named for its use of an organic, high-molecular-mass fluid whose vaporization temperature is lower than that of wate ...
(Coolant changing phase in temperature ranges of ice and hot liquid water)
*Vapor to liquid cycle (
Drinking bird
Drinking birds, also known as insatiable birdies, dunking birds, drinky birds, water birds, dipping birds, and “Sippy Chickens” are toy heat engines that mimic the motions of a bird drinking from a water source. They are sometimes incorrectly ...
,
Injector
An injector is a system of ducting and nozzles used to direct the flow of a high-pressure fluid in such a way that a lower pressure fluid is entrained in the jet and carried through a duct to a region of higher pressure. It is a fluid-dynamic ...
,
Minto wheel)
*Liquid to solid cycle (
Frost heaving
Frost heaving (or a frost heave) is an upwards swelling of soil during freezing conditions caused by an increasing presence of ice as it grows towards the surface, upwards from the depth in the soil where freezing temperatures have penetrated in ...
– water changing from ice to liquid and back again can lift rock up to 60 cm.)
*Solid to gas cycle (
firearms – 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
A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynam ...
(
Carnot heat engine
A Carnot heat engine is a heat 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 1 ...
)
*
Ericsson cycle (Caloric Ship John Ericsson)
*
Stirling cycle (
Stirling engine
A Stirling engine is a heat engine that is operated by the cyclic compression and expansion of air or other gas (the ''working fluid'') between different temperatures, resulting in a net conversion of heat energy to mechanical work.
More specif ...
,
thermoacoustic devices)
*
Internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal c ...
(ICE):
**
Otto cycle
An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
The Otto cycle is a description of what hap ...
(e.g.
Gasoline/Petrol engine)
**
Diesel cycle
The Diesel cycle is a combustion process of a reciprocating internal combustion engine. In it, fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is then injected. This is in contrast to ign ...
(e.g.
Diesel engine
The diesel engine, named after Rudolf Diesel, is an internal combustion engine in which ignition of the fuel is caused by the elevated temperature of the air in the cylinder due to mechanical compression; thus, the diesel engine is a so-ca ...
)
**
Atkinson cycle
The Atkinson-cycle engine is a type of internal combustion engine invented by James Atkinson in 1882. The Atkinson cycle is designed to provide efficiency at the expense of power density.
A variation of this approach is used in some modern auto ...
(Atkinson engine)
**
Brayton cycle
The Brayton cycle is a thermodynamic cycle that describes the operation of certain heat engines that have air or some other gas as their working fluid. The original Brayton engines used a piston compressor and piston expander, but modern gas tu ...
or
Joule cycle
The Brayton cycle is a thermodynamic cycle that describes the operation of certain heat engines that have air or some other gas as their working fluid. The original Brayton engines used a piston compressor and piston expander, but modern gas tur ...
originally
Ericsson cycle (
gas turbine
A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directio ...
)
**
Lenoir cycle
The Lenoir cycle is an idealized thermodynamic cycle often used to model a pulse jet engine. It is based on the operation of an engine patented by Jean Joseph Etienne Lenoir in 1860. This engine is often thought of as the first commercially pr ...
(e.g.,
pulse jet engine
300px, Diagram of a pulsejet
A pulsejet engine (or pulse jet) is a type of jet engine in which combustion occurs in pulses. A pulsejet engine can be made with few or no moving parts, and is capable of running statically (i.e. it does not need ...
)
**
Miller cycle
In engineering, the Miller cycle is a thermodynamic cycle used in a type of internal combustion engine. The Miller cycle was patented by Ralph Miller, an American engineer, dated Dec 24, 1957. The engine may be two- or four-stroke and may be r ...
(Miller engine)
Liquid-only cycles
In these cycles and engines the working fluid are always like liquid:
*
Stirling cycle (
Malone engine
The Malone engine is a liquid-based engine invented by J.F.J Malone of Newcastle, England. The engine used high temperature water as its working fluid, and was therefore also referred to as the Hot Water Engine. A US patent, describing it with ...
)
*Heat Regenerative Cyclone
Electron cycles
*
Johnson thermoelectric energy converter
*Thermoelectric (
Peltier–Seebeck effect
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when ...
)
*
Thermogalvanic cell
*
Thermionic emission
Thermionic emission is the liberation of electrons from an electrode by virtue of its temperature (releasing of energy supplied by heat). This occurs because the thermal energy given to the charge carrier overcomes the work function of the mater ...
*
Thermotunnel cooling
Magnetic cycles
*
Thermo-magnetic motor
Thermomagnetic motors (also known as Curie wheels, Curie-motors and pyromagnetic motors) convert heat into kinetic energy using the thermomagnetic effect, i.e., the influence of temperature on the magnetic material magnetization.
Historical ...
(Tesla)
Cycles used for refrigeration
A domestic
refrigerator is an example of a
heat pump
A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
: 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
An air cycle machine (ACM) is the refrigeration unit of the environmental control system (ECS) used in pressurized gas turbine-powered aircraft. Normally an aircraft has two or three of these ACM. Each ACM and its components are often referred as ...
*
Gas-absorption refrigerator
An absorption refrigerator is a refrigerator that uses a heat source (e.g., solar energy, a fossil-fueled flame, waste heat from factories, or district heating systems) to provide the energy needed to drive the cooling process. The system uses t ...
*
Magnetic refrigeration
Magnetic refrigeration is a cooling technology based on the magnetocaloric effect. This technique can be used to attain extremely low temperatures, as well as the ranges used in common refrigerators.
A magnetocaloric material warms up when a ma ...
*
Stirling cryocooler
*
Vapor-compression refrigeration
Vapour-compression refrigeration or vapor-compression refrigeration system (VCRS), in which the refrigerant undergoes phase changes, is one of the many refrigeration cycles and is the most widely used method for air conditioning of buildings ...
*
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.
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
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
, after a completed cycle:
[.]
:
:and therefore
:
:where
:
is the net work extracted from the engine in one cycle. (It is negative, in the
IUPAC convention, since work is ''done by'' the engine.)
:
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.)
:
is the waste heat given off by the engine to the cold temperature heat sink. (It is negative
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
The coefficient of performance or COP (sometimes CP or CoP) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work (energy) required. Higher COPs equate to higher efficiency, lower energy ( ...
and it is ≥ 1.) In the case of an engine, one desires to extract work and has to put in heat
, for instance from
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combus ...
of a fuel, so the engine efficiency is reasonably defined as
:
The efficiency is less than 100% because of the waste heat
unavoidably lost to the cold sink (and corresponding compression work put in) during the required recompression at the cold temperature before the
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
A Carnot heat engine is a heat 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 1 ...
, although other engines using different cycles can also attain maximum efficiency. Mathematically, after a full cycle, the overall change of entropy is zero:
Note that
is positive because isothermal expansion in the power stroke increases the
multiplicity
Multiplicity may refer to: In science and the humanities
* Multiplicity (mathematics), the number of times an element is repeated in a multiset
* Multiplicity (philosophy), a philosophical concept
* Multiplicity (psychology), having or using mult ...
of the working fluid while
is negative since recompression decreases the multiplicity. If the engine is ideal and runs
reversibly,
and
, and thus
[.]
,
which gives
and thus the Carnot limit for heat-engine efficiency,
:
where
is the
absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic w ...
of the hot source and
that of the cold sink, usually measured in
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
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
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
. Since, by the
second law of thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
, 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.
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
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 derive ...
, where the system is broken into reversible subsystems, but with non reversible interactions between them. A classical example is the Curzon–Ahlborn engine,
[F. L. Curzon, B. Ahlborn (1975). "Efficiency of a Carnot Engine at Maximum Power Output". ''Am. J. Phys.'', Vol. 43, pp. 24.] very similar to a Carnot engine, but where the thermal reservoirs at temperature
and
are allowed to be different from the temperatures of the substance going through the reversible Carnot cycle:
and
. The heat transfers between the reservoirs and the substance are considered as conductive (and irreversible) in the form
. 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,
and the classical Carnot result is found
:
,
but at the price of a vanishing power output. If instead one choses to operate the engine at its maximum output power, the efficiency becomes
:
(Note: ''T'' in units of
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
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 derive ...
):
As shown, the Curzon–Ahlborn efficiency much more closely models that observed.
History
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
A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directio ...
s. Unfortunately, physical limits (such as the melting point of the materials used to build the engine) and environmental concerns regarding
NOx 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
x output . 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
The Kalina cycle, developed by Alexander Kalina, is a thermodynamic process for converting thermal energy into usable mechanical power.
It uses a solution of 2 fluids with different boiling points for its working fluid. Since the solution boil ...
, which uses a 70/30 mix of
ammonia
Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous wa ...
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 exploitation is the use of water above the critical point (
supercritical water). The behavior of fluids above their
critical point changes radically, and with materials such as water and
carbon dioxide
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is trans ...
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 CO2.
SO2 and
xenon
Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...
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
Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, ...
cross section of almost all
isotopes of xenon
Naturally occurring xenon (54Xe) consists of seven stable isotopes and two very long-lived isotopes. Double electron capture has been observed in 124Xe (half-life ) and double beta decay in 136Xe (half-life ), which are among the longest measured ...
, whereas carbon dioxide and water can also double as a
neutron moderator for a thermal spectrum reactor.
#Exploit the
chemical properties
A chemical property is any of a material's properties that becomes evident during, or after, a chemical reaction; that is, any quality that can be established only by changing a substance's chemical identity.William L. Masterton, Cecile N. Hurley, ...
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
Nitrogen dioxide is a chemical compound with the formula . It is one of several nitrogen oxides. is an intermediate in the industrial synthesis of nitric acid, millions of tons of which are produced each year for use primarily in the productio ...
(NO
2), a toxic component of smog, which has a natural
dimer
Dimer may refer to:
* Dimer (chemistry), a chemical structure formed from two similar sub-units
** Protein dimer, a protein quaternary structure
** d-dimer
* Dimer model, an item in statistical mechanics, based on ''domino tiling''
* Julius Dimer ...
as di-nitrogen tetraoxide (N
2O
4). At low temperature, the N
2O
4 is compressed and then heated. The increasing temperature causes each N
2O
4 to break apart into two NO
2 molecules. This lowers the molecular weight of the working fluid, which drastically increases the efficiency of the cycle. Once the NO
2 has expanded through the turbine, it is cooled by the
heat sink
A heat sink (also commonly spelled heatsink) is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, th ...
, which makes it recombine into N
2O
4. This is then fed back by the compressor for another cycle. Such species as
aluminium bromide
Aluminium bromide is any chemical compound with the empirical formula AlBrx. Aluminium tribromide is the most common form of aluminium bromide. It is a colorless, sublimable hygroscopic solid; hence old samples tend to be hydrated, mostly as al ...
(Al
2Br
6), NOCl, and Ga
2I
6 have all been investigated for such uses. To date, their drawbacks have not warranted their use, despite the efficiency gains that can be realized.
Heat engine processes
Each process is one of the following:
*
isothermal
In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...
(at constant temperature, maintained with heat added or removed from a heat source or sink)
*
isobaric
Isobar may refer to:
* Isobar (meteorology), a line connecting points of equal atmospheric pressure reduced to sea level on the maps.
* Isobaric process
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pr ...
(at constant pressure)
*
isometric/isochoric (at constant volume), also referred to as iso-volumetric
*
adiabatic (no heat is added or removed from the system during adiabatic process)
*
isentropic
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 net transfer of heat or matter. Such an idealized process ...
(reversible adiabatic process, no heat is added or removed during isentropic process)
See also
*
Einstein refrigerator
The Einstein–Szilard or Einstein refrigerator is an absorption refrigerator which has no moving parts, operates at constant pressure, and requires only a heat source to operate. It was jointly invented in 1926 by Albert Einstein and his form ...
*
Heat pump
A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
*
Reciprocating engine
A reciprocating engine, also often known as a piston engine, is typically a heat engine that uses one or more reciprocating pistons to convert high temperature and high pressure into a rotating motion. This article describes the common fea ...
for a general description of the mechanics of piston engines
*
Thermosynthesis Thermosynthesis is a theoretical mechanism proposed by Anthonie Muller for biological use of the free energy in a temperature gradient to drive energetically uphill anabolic reactions. It makes use of this thermal gradient, or the dissipative struc ...
*
Timeline of heat engine technology
A timeline is a display of a list of events in chronological order. It is typically a graphic design showing a long bar labelled with dates paralleling it, and usually contemporaneous events.
Timelines can use any suitable scale representi ...
References
*
*
*
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