Heat engine

# Heat engine

Overview
In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, a heat engine is a system that performs the conversion of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

or thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....

to mechanical work
Mechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...

. It does this by bringing a working substance from a high temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance in the high temperature state. The working substance generates work in the "working body
Thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....

" of the engine while transferring heat
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

to the colder "sink
Heat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...

" until it reaches a low temperature state. During this process some of the thermal energy is converted into work
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

, but it usually is a gas or liquid.
Discussion
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Encyclopedia
In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, a heat engine is a system that performs the conversion of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

or thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....

to mechanical work
Mechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...

. It does this by bringing a working substance from a high temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance in the high temperature state. The working substance generates work in the "working body
Thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....

" of the engine while transferring heat
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

to the colder "sink
Heat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...

" until it reaches a low temperature state. During this process some of the thermal energy is converted into work
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

, but it usually is a gas or liquid.

In general an engine
Engine
An engine or motor is a machine designed to convert energy into useful mechanical motion. Heat engines, including internal combustion engines and external combustion engines burn a fuel to create heat which is then used to create motion...

converts energy to mechanical work. Heat engines distinguish themselves from other types of engines by the fact that their efficiency is fundamentally limited by Carnot's theorem. Although this efficiency limitation can be a drawback, an advantage of heat engines is that most forms of energy can be easily converted to heat by processes like exothermic reaction
Exothermic reaction
An exothermic reaction is a chemical reaction that releases energy in the form of light or heat. It is the opposite of an endothermic reaction. Expressed in a chemical equation:-Overview:...

s (such as combustion), absorption
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

of light or energetic particles, friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

, dissipation
Dissipation
In physics, dissipation embodies the concept of a dynamical system where important mechanical models, such as waves or oscillations, lose energy over time, typically from friction or turbulence. The lost energy converts into heat, which raises the temperature of the system. Such systems are called...

and resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

. Since the heat source that supplies thermal energy to the engine can thus be powered by virtually any kind of energy, heat engines are very versatile and have a wide range of applicability.

Heat engines are often confused with the cycles they attempt to mimic. Typically when describing the physical device the term 'engine' is used. When describing the model the term 'cycle' is used.

## Overview

In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, heat engines are often modeled using a standard engineering model such as the Otto cycle
Otto cycle
An Otto cycle is an idealized thermodynamic cycle which describes the functioning of a typical reciprocating piston engine, the thermodynamic cycle most commonly found in automobile engines....

. The theoretical model can be refined and augmented with actual data from an operating engine, using tools such as an indicator diagram. Since very few actual implementations of heat engines exactly match their underlying thermodynamic cycles, one could say that a thermodynamic cycle is an ideal case of a mechanical engine. In any case, fully understanding an engine and its efficiency requires gaining a good understanding of the (possibly simplified or idealized) theoretical model, the practical nuances of an actual mechanical engine, and the discrepancies between the two.

In general terms, the larger the difference in temperature between the hot source and the cold sink, the larger is the potential thermal efficiency
Thermal efficiency
In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a boiler, a furnace, or a refrigerator for example.-Overview:...

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
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

, so most efforts to improve the thermodynamic efficiencies of various heat engines focus on increasing the temperature of the source, within material limits. The maximum theoretical efficiency of a heat engine (which no engine ever obtains) is equal to the temperature difference between the hot and cold ends divided by the temperature at the hot end, all expressed in absolute temperature or kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

s.

The efficiency of various heat engines proposed or used today ranges from 3 percent (97 percent waste heat) for the OTEC
Ocean thermal energy conversion
Ocean Thermal Energy Conversion uses the difference between cooler deep and warmer shallow or surface ocean waters to run a heat engine and produce useful work, usually in the form of electricity....

ocean power proposal through 25 percent for most automotive engines , to 45 percent for a supercritical coal plant, to about 60 percent for a steam-cooled combined cycle
Combined cycle
In electric power generation a combined cycle is an assembly of heat engines that work in tandem off the same source of heat, converting it into mechanical energy, which in turn usually drives electrical generators...

gas turbine
Gas turbine
A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....

.

All of these processes gain their efficiency (or lack thereof) due to the temperature drop across them.

### Power

Heat engines can be characterized by their specific power
Specific power
In physics and engineering, surface power density or sometimes simply specific power is power per unit area.-Applications:* The intensity of electromagnetic radiation can be expressed in W/m2...

, which is typically given in kilowatts per litre
Litre
pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

of engine displacement
Engine displacement
Engine displacement is the volume swept by all the pistons inside the cylinders of an internal combustion engine in a single movement from top dead centre to bottom dead centre . It is commonly specified in cubic centimeters , litres , or cubic inches...

(in the U.S. also horsepower
Horsepower
Horsepower is the name of several units of measurement of power. The most common definitions equal between 735.5 and 750 watts.Horsepower was originally defined to compare the output of steam engines with the power of draft horses in continuous operation. The unit was widely adopted to measure the...

per cubic inch
Cubic inch
The cubic inch is a unit of measurement for volume in the Imperial units and United States customary units systems. It is the volume of a cube with each of its 3 sides being one inch long....

). The result offers an approximation of the peak-power output of an engine. This is not to be confused with fuel efficiency
Fuel efficiency
Fuel efficiency is a form of thermal efficiency, meaning the efficiency of a process that converts chemical potential energy contained in a carrier fuel into kinetic energy or work. Overall fuel efficiency may vary per device, which in turn may vary per application, and this spectrum of variance is...

, since high-efficiency often requires a lean fuel-air ratio, and thus lower power density. A modern high-performance car engine makes in excess of 75 kW/L (1.65 hp/in³).

## Everyday examples

Examples of everyday heat engines include the steam engine
Steam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...

, the diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...

, and the gasoline (petrol) engine
Internal combustion engine
The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber. In an internal combustion engine, the expansion of the high-temperature and high -pressure gases produced by combustion apply direct force to some component of the engine...

in an automobile
Automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...

.
A common toy that is also a heat engine is a drinking bird
Drinking bird
Drinking birds, also known as dippy birds and dipping birds, are toy heat engines that mimic the motions of a bird drinking from a fountain or other water source. They are sometimes incorrectly considered examples of a perpetual motion device....

. Also the stirling engine
Stirling engine
A Stirling engine is a heat engine operating by cyclic compression and expansion of air or other gas, the working fluid, at different temperature levels such that there is a net conversion of heat energy to mechanical work....

is a heat engine.
All of these familiar heat engines are powered by the expansion of heated gases.
The general surroundings are the heat sink, providing relatively cool gases which, when heated, expand rapidly to drive the mechanical motion of the engine.

## Examples of heat engines

It is important to note that although some cycles have a typical combustion location (internal or external), they often can be implemented with the other. For example, John Ericsson
John Ericsson
John Ericsson was a Swedish-American inventor and mechanical engineer, as was his brother Nils Ericson. He was born at Långbanshyttan in Värmland, Sweden, but primarily came to be active in England and the United States...

developed an external heated engine running on a cycle very much like the earlier Diesel cycle
Diesel cycle
The Diesel cycle is the thermodynamic cycle which approximates the pressure and volume of the combustion chamber of the Diesel engine, invented by Rudolph Diesel in 1897. It is assumed to have constant pressure during the first part of the "combustion" phase...

. In addition, the externally heated engines can often be implemented in open or closed cycles.

What this boils down to is that there are thermodynamic cycles and a large number of ways to implement them.

### 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.
• Rankine cycle
Rankine cycle
The Rankine cycle is a cycle that converts heat into work. The heat is supplied externally to a closed loop, which usually uses water. This cycle generates about 90% of all electric power used throughout the world, including virtually all solar thermal, biomass, coal and nuclear power plants. It is...

(classical steam engine
Steam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...

)
• Regenerative cycle (steam engine
Steam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...

more efficient than Rankine cycle
Rankine cycle
The Rankine cycle is a cycle that converts heat into work. The heat is supplied externally to a closed loop, which usually uses water. This cycle generates about 90% of all electric power used throughout the world, including virtually all solar thermal, biomass, coal and nuclear power plants. It is...

)
• Organic Rankine Cycle
Organic Rankine Cycle
The Organic Rankine cycle is named for its use of an organic, high molecular mass fluid with a liquid-vapor phase change, or boiling point, occurring at a lower temperature than the water-steam phase change. The fluid allows Rankine cycle heat recovery from lower temperature sources such as...

(Coolant changing phase in temperature ranges of ice and hot liquid water)
• Vapor to liquid cycle (Drinking bird
Drinking bird
Drinking birds, also known as dippy birds and dipping birds, are toy heat engines that mimic the motions of a bird drinking from a fountain or other water source. They are sometimes incorrectly considered examples of a perpetual motion device....

, Injector
Injector
ʎ̩An injector, ejector, steam ejector, steam injector, eductor-jet pump or thermocompressor is a pump-like device that uses the Venturi effect of a converging-diverging nozzle to convert the pressure energy of a motive fluid to velocity energy which creates a low pressure zone that dɯaws in and...

, Minto wheel
Minto wheel
The Minto wheel is a heat engine developed by Wally Minto.The engine consists of a set of sealed chambers arranged in a circle, with each chamber connected to the chamber opposite it. One chamber in each connected pair is filled with a liquid with a low boiling point...

)
• Liquid to solid cycle (Frost heaving
Frost heaving
Frost heaving results from ice forming beneath the surface of soil during freezing conditions in the atmosphere. The ice grows in the direction of heat loss , starting at the freezing front or boundary in the soil...

— water changing from ice to liquid and back again can lift rock up to 60 cm.)
• Solid to gas cycle (Dry ice cannon — Dry ice sublimes to gas.)

### Gas only cycles

In these cycles and engines the working fluid is always a gas (i.e., there is no phase change):
• Carnot cycle
Carnot cycle
The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It can be shown that it is the most efficient cycle for converting a given amount of thermal energy into work, or conversely,...

(Carnot heat engine
Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

)
• Ericsson Cycle
Ericsson cycle
The Ericsson cycle is named after inventor John Ericsson, who designed and built many unique heat engines based on various thermodynamic cycles. He is credited with inventing two unique heat engine cycles and developing practical engines based on these cycles...

(Caloric Ship John Ericsson)
• Stirling cycle
Stirling cycle
The Stirling cycle is a thermodynamic cycle that describes the general class of Stirling devices. This includes the original Stirling engine that was invented, developed and patented in 1816 by Reverend Dr...

(Stirling engine
Stirling engine
A Stirling engine is a heat engine operating by cyclic compression and expansion of air or other gas, the working fluid, at different temperature levels such that there is a net conversion of heat energy to mechanical work....

, thermoacoustic
Thermoacoustic refrigeration
Thermoacoustic engines are thermoacoustic devices which use high-amplitude sound waves to pump heat from one place to another, or conversely use a heat difference to induce high-amplitude sound waves. In general, thermoacoustic engines can be divided into standing wave and travelling wave devices...

devices)
• Internal combustion engine
Internal combustion engine
The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber. In an internal combustion engine, the expansion of the high-temperature and high -pressure gases produced by combustion apply direct force to some component of the engine...

(ICE):
• Otto cycle
Otto cycle
An Otto cycle is an idealized thermodynamic cycle which describes the functioning of a typical reciprocating piston engine, the thermodynamic cycle most commonly found in automobile engines....

(e.g. Gasoline/Petrol engine, high-speed diesel engine)
• Diesel cycle
Diesel cycle
The Diesel cycle is the thermodynamic cycle which approximates the pressure and volume of the combustion chamber of the Diesel engine, invented by Rudolph Diesel in 1897. It is assumed to have constant pressure during the first part of the "combustion" phase...

(e.g. low-speed diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...

)
• Atkinson Cycle
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, and is used in some modern hybrid electric applications.-Design:...

(Atkinson Engine)
• Brayton cycle
Brayton cycle
The Brayton cycle is a thermodynamic cycle that describes the workings of the gas turbine engine, basis of the airbreathing jet engine and others. It is named after George Brayton , the American engineer who developed it, although it was originally proposed and patented by Englishman John Barber...

or Joule cycle originally Ericsson Cycle
Ericsson cycle
The Ericsson cycle is named after inventor John Ericsson, who designed and built many unique heat engines based on various thermodynamic cycles. He is credited with inventing two unique heat engine cycles and developing practical engines based on these cycles...

(gas turbine
Gas turbine
A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....

)
• Lenoir cycle
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 produced internal combustion engine...

(e.g., pulse jet engine
Pulse jet engine
A pulse jet engine is a type of jet engine in which combustion occurs in pulses. Pulsejet engines can be made with few or no moving parts, and are capable of running statically....

)
• Miller cycle
Miller cycle
In engineering, the Miller cycle is a combustion process used in a type of four-stroke internal combustion engine. The Miller cycle was patented by Ralph Miller, an American engineer, in the 1940s.- Overview :...

### Liquid only cycles

In these cycles and engines the working fluid are always like liquid:
• Stirling Cycle
Stirling cycle
The Stirling cycle is a thermodynamic cycle that describes the general class of Stirling devices. This includes the original Stirling engine that was invented, developed and patented in 1816 by Reverend Dr...

(Malone engine
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. Malone's first 50 hp prototype was completed in 1925, and used coal to heat high...

)
• Heat Regenerative Cyclone

### Electron cycles

• Johnson thermoelectric energy converter
Johnson thermoelectric energy converter
A Johnson thermoelectric energy converter or JTEC is a type of solid-state heat engine that relies on the photodecomposition and recombination of hydrogen in a fuel cell using an approximate Ericsson cycle. It was invented by Lonnie Johnson and is under investigation as a viable alternative to...

• Thermoelectric (Peltier-Seebeck effect)
• Thermionic emission
Thermionic emission
Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the binding potential, also known as work function of the metal. The charge carriers can be electrons or ions, and...

• Thermotunnel cooling
Thermotunnel cooling
Thermotunnel cooling is similar to thermionic emission cooling in that fast moving electrons carry heat across a gap but cannot return due to a voltage difference...

### Cycles used for refrigeration

A domestic refrigerator
Refrigerator
A refrigerator is a common household appliance that consists of a thermally insulated compartment and a heat pump that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the ambient temperature of the room...

is an example of a heat pump
Heat pump
A heat pump is a machine or device that effectively "moves" thermal energy from one location called the "source," which is at a lower temperature, to another location called the "sink" or "heat sink", which is at a higher temperature. An air conditioner is a particular type of heat pump, but the...

: 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:
• Vapor-compression refrigeration
Vapor-compression refrigeration
Vapor-compression refrigeration is one of the many refrigeration cycles available for use. It has been and is the most widely used method for air-conditioning of large public buildings, offices, private residences, hotels, hospitals, theaters, restaurants and automobiles...

• Stirling cryocoolers
• Gas-absorption refrigerator
• Air cycle machine
Air cycle machine
An air cycle machine is the refrigeration unit of the environmental control system 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 an Air Conditioning Pack.The air cycle cooling process uses...

• Vuilleumier refrigeration
• Magnetic refrigeration
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, depending on the design of the system.The effect was first observed by the German physicist Emil...

### Evaporative Heat Engines

The Barton evaporation engine
Barton Evaporation Engine
The Barton evaporation engine is a heat engine developed by Sunoba Pty Ltd.-Principle:The principle of the BEE is based on: adiabatic expansion of unsaturated air; evaporative cooling at reduced pressure; and re-compression back to atmospheric pressure with further evaporation...

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.

## 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
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

:
where
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 you get out" to "what you put in."

In the case of an engine, one desires to extract work and puts in a heat transfer.

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
Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

, although other engines using different cycles can also attain maximum efficiency. Mathematically, this is because in reversible processes, the change in entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

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 kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

. 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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. Since, by the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

, this is statistically improbable to the point of exclusion, the Carnot efficiency is a theoretical upper bound on the reliable efficiency of any process.

Empirically, no 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.

### Endoreversible heat engines

The most Carnot efficiency as a criterion of heat engine performance is the fact that by its nature, any maximally efficient Carnot cycle must operate at an infinitesimal temperature gradient. This is because any transfer of heat between two bodies at differing temperatures is irreversible, and therefore the Carnot efficiency expression only applies in the infinitesimal limit. The major problem with that is that the object of most heat engines is to output some sort of power, and infinitesimal power is usually not what is being sought.

A different measure of ideal heat engine efficiency is given by considerations of endoreversible thermodynamics
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...

, where the cycle is identical to the Carnot cycle except in that the two processes of heat transfer are not reversible (Callen 1985):
(Note: Units K
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

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
Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer than are typically made in reversible thermodynamics...

):
Efficiencies of Power Plants
Power Plant (°C) (°C) (Carnot) (Endoreversible) (Observed)
West Thurrock
West Thurrock
West Thurrock is a traditional Church of England parish and town in Thurrock, Essex, England, located 17.5 miles east south-east of Charing Cross, London.-Location:...

(UK
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

) coal-fired power plant
Fossil fuel power plant
A fossil-fuel power station is a power station that burns fossil fuels such as coal, natural gas or petroleum to produce electricity. Central station fossil-fuel power plants are designed on a large scale for continuous operation...

25 565 0.64 0.40 0.36
CANDU
CANDU reactor
The CANDU reactor is a Canadian-invented, pressurized heavy water reactor. The acronym refers to its deuterium-oxide moderator and its use of uranium fuel...

Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

) nuclear power plant
Nuclear power plant
A nuclear power plant is a thermal power station in which the heat source is one or more nuclear reactors. As in a conventional thermal power station the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity.Nuclear power plants are usually...

25 300 0.48 0.28 0.30
Larderello
Larderello
Larderello is a frazione of the comune of Pomarance, in Tuscany in central Italy. It is a geologically active area, renowned for its geothermal productivity.- Geography :...

(Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

) geothermal power plant
Geothermal power
Geothermal energy is thermal energy generated and stored in the Earth. Thermal energy is the energy that determines the temperature of matter. Earth's geothermal energy originates from the original formation of the planet and from radioactive decay of minerals...

80 250 0.33 0.178 0.16

As shown, the endoreversible efficiency much more closely models the observed data.

## History

Heat engines have been known since antiquity but were only made into useful devices at the time of the industrial revolution in the eighteenth century. They continue to be developed today.

## Heat engine enhancements

Engineers have studied the various heat engine cycles extensively in an effort to improve the amount of usable work they could extract from a given power source. The Carnot Cycle limit cannot be reached with any gas-based cycle, but engineers have worked out at least two ways to possibly go around that limit, and one way to get better efficiency without bending any rules.
1. Increase the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

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
Gas turbine
A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....

s. Unfortunately, physical limits (such as the melting point of the materials from which the engine is constructed) and environmental concerns regarding NOx
NOx
NOx is a generic term for the mono-nitrogen oxides NO and NO2 . They are produced from the reaction of nitrogen and oxygen gases in the air during combustion, especially at high temperatures...

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 . Another way of increasing efficiency is to lower the output temperature. One new method of doing so is to use mixed chemical working fluids, and then exploit the changing behavior of the mixtures. One of the most famous is the so-called Kalina cycle
Kalina cycle
The Kalina cycle 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 boils over a range of temperatures as in distillation, more of the heat can be extracted...

, which uses a 70/30 mix of ammonia
Ammonia
Ammonia is a compound of nitrogen and hydrogen with the formula . It is a colourless gas with a characteristic pungent odour. Ammonia contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to food and fertilizers. Ammonia, either directly or...

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 so-called critical point, or so-called supercritical steam. The behavior of fluids above their critical point changes radically, and with materials such as water and carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

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
Xenon
Xenon is a chemical element with the symbol Xe and atomic number 54. The element name is pronounced or . A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...

have also been considered for such applications, although SO2 is a little toxic for most.
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
Nitrogen dioxide
Nitrogen dioxide is the 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. This reddish-brown toxic gas has a characteristic sharp, biting odor and is a prominent...

(NO2), a toxic component of smog
Smog
Smog is a type of air pollution; the word "smog" is a portmanteau of smoke and fog. Modern smog is a type of air pollution derived from vehicular emission from internal combustion engines and industrial fumes that react in the atmosphere with sunlight to form secondary pollutants that also combine...

, 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
Heat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...

, which causes it to recombine into N2O4. This is then fed back to the compressor for another cycle. Such species as aluminium bromide
Aluminium bromide
Aluminium bromide is any chemical compound with the empirical formula AlBrx. The species called "aluminium tribromide," is the most common aluminium bromide. The species aluminium monobromide forms from the reaction of HBr with Al metal at high temperature...

(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.

## Heat engine processes

Each process is one of the following:
• isothermal
Isothermal process
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir , and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir...

(at constant temperature, maintained with heat added or removed from a heat source or sink)
• isobaric
Isobaric process
An isobaric process is a thermodynamic process in which the pressure stays constant. The term derives from the Greek isos, , and barus,...

(at constant pressure)
• isometric/isochoric
Isochoric process
An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant...

(at constant volume), also referred to as iso-volumetric
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

(no heat is added or removed from the system during adiabatic process which is equivalent to saying that the entropy remains constant, if the process is also reversible.)

• Drinking bird
Drinking bird
Drinking birds, also known as dippy birds and dipping birds, are toy heat engines that mimic the motions of a bird drinking from a fountain or other water source. They are sometimes incorrectly considered examples of a perpetual motion device....

An example of a basic heat engine.
• Reciprocating engine
Reciprocating engine
A reciprocating engine, also often known as a piston engine, is a heat engine that uses one or more reciprocating pistons to convert pressure into a rotating motion. This article describes the common features of all types...

for a general description of the mechanics of piston engines
• Heat pump
Heat pump
A heat pump is a machine or device that effectively "moves" thermal energy from one location called the "source," which is at a lower temperature, to another location called the "sink" or "heat sink", which is at a higher temperature. An air conditioner is a particular type of heat pump, but the...

• Carnot heat engine
Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

• Timeline of heat engine technology
Timeline of heat engine technology
This Timeline of heat engine technology describes how heat engines have been known since antiquity but have been made into increasingly useful devices since the seventeenth century as a better understanding of the processes involved was gained...

• Thermosynthesis
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 structure of convection in this gradient, to drive a...