In thermodynamics and engineering, a heat engine is a system that converts heat to usable energy, particularly mechanical energy, which can then be used to do mechanical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, particularly electrical, since at least the late 19th century. The heat engine does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the higher temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a lower 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 is any machine that 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 reactions (such as combustion), nuclear fission, 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.
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 developed an external heated engine running on a cycle very much like the earlier Diesel cycle. In addition, externally heated engines can often be implemented in open or closed cycles. In a closed cycle the working fluid is retained within the engine at the completion of the cycle whereas is an open cycle the working fluid is either exchanged with the environment together with the products of combustion in the case of the internal combustion engine or simply vented to the environment in the case of external combustion engines like steam engines and turbines.
Everyday examples of heat engines include the thermal power station, internal combustion engine, firearms, refrigerators and heat pumps. 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 or the properties associated with phase changes between gas and liquid states.
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 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.
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.
In these cycles and engines the working fluid is always a gas (i.e., there is no phase change):
In these cycles and engines the working fluid are always like liquid:
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:
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 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
The efficiency of a heat engine relates how much useful work is output for a given amount of heat energy input.
In other words, a heat engine absorbs heat energy from the high temperature heat source, converting part of it to useful work and giving off the rest as waste heat to the cold temperature heat sink.
In general, the efficiency of a given heat transfer process is defined by the ratio of "what is taken out" to "what is put in". (For a refrigerator or heat pump, which can be considered as a heat engine run in reverse, this is the coefficient of performance and it is ≥ 1.) In the case of an engine, one desires to extract work and has to put in heat , for instance from combustion 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, 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 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,
The reasoning behind this being the maximal efficiency goes as follows. It is first assumed that if a more efficient heat engine than a Carnot engine is possible, then it could be driven in reverse as a heat pump. Mathematical analysis can be used to show that this assumed combination would result in a net decrease in entropy. Since, by the second law of thermodynamics, this is statistically improbable to the point of exclusion, the Carnot efficiency is a theoretical upper bound on the reliable efficiency of any thermodynamic cycle.
Empirically, no heat engine has ever been shown to run at a greater efficiency than a Carnot cycle heat engine.
Figure 2 and Figure 3 show variations on Carnot cycle efficiency with temperature. Figure 2 indicates how efficiency changes with an increase in the heat addition temperature for a constant compressor inlet temperature. Figure 3 indicates how the efficiency changes with an increase in the heat rejection temperature for a constant turbine inlet temperature.
By its nature, any maximally efficient Carnot cycle must operate at an infinitesimal temperature gradient; this is because any transfer of heat between two bodies of differing temperatures is irreversible, therefore the Carnot efficiency expression applies only to the infinitesimal limit. The major problem is that the objective of most heat-engines is to output power, and infinitesimal power is seldom desired.
A different measure of ideal heat-engine efficiency is given by considerations of endoreversible thermodynamics, where the system is broken into reversible subsystems, but with non reversible interactions between them. A classical example is the Curzon–Ahlborn engine, 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 chooses to operate the engine at its maximum output power, the efficiency becomes
This model does a better job of predicting how well real-world heat-engines can do (Callen 1985, see also endoreversible thermodynamics):
|West Thurrock (UK) coal-fired power station||25||565||0.64||0.40||0.36|
|CANDU (Canada) nuclear power station||25||300||0.48||0.28||0.30|
|Larderello (Italy) geothermal power station||80||250||0.33||0.178||0.16|
As shown, the Curzon–Ahlborn efficiency much more closely models that observed.
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:
|Cycle||Compression, 1→2||Heat addition, 2→3||Expansion, 3→4||Heat rejection, 4→1||Notes|
|Power cycles normally with external combustion - or heat pump cycles:|
|Bell Coleman||adiabatic||isobaric||adiabatic||isobaric||A reversed Brayton cycle|
|Carnot||isentropic||isothermal||isentropic||isothermal||Carnot heat engine|
|Ericsson||isothermal||isobaric||isothermal||isobaric||The second Ericsson cycle from 1853|
|Manson||isothermal||isochoric||isothermal||isochoric then adiabatic||Manson and Manson-Guise engines|
|Power cycles normally with internal combustion:|
|Atkinson||isentropic||isochoric||isentropic||isochoric||Differs from Otto cycle in that V1 < V4.|
|Brayton||adiabatic||isobaric||adiabatic||isobaric||Ramjets, turbojets, -props, and -shafts. Originally developed for use in reciprocating engines. The external combustion version of this cycle is known as the first Ericsson cycle from 1833.|
|Humphrey||isentropic||isochoric||isentropic||isobaric||Shcramjets, pulse- and continuous detonation engines|
|Lenoir||isochoric||adiabatic||isobaric||Pulse jets. Note that 1→2 accomplishes both the heat rejection and the compression. Originally developed for use in reciprocating engines.|
|Otto||isentropic||isochoric||isentropic||isochoric||Gasoline / petrol engines|
Each process is one of the following:
eqs.(39), (40), & (65).