A heat engine is a physical or theoretical device that converts thermal energy to mechanical output. The mechanical output is called work, and the thermal energy input is called heat. Heat engines typically run on a specific thermodynamic cycle. Heat engines are often named after the thermodynamic cycle they are modeled by. They often pick up alternate names, such as gasoline/petrol, turbine, or steam engines. Heat engines can generate heat inside the engine itself or it can absorb heat from an external source. Heat engines can be open to the atmospheric air or sealed and closed off to the outside (Open or closed cycle).
In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot "source" and a cold "sink". Heat is transferred from the source, through the "working body" of the engine, to the sink, and in this process some of the heat is converted into work by exploiting the properties of a working substance (usually a gas or liquid).
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 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 of the cycle. On Earth, the cold side of any heat engine is limited to 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 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 kelvins.
The efficiency of various heat engines proposed or used today ranges from 3 percent (97 percent waste heat) for the OTEC 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 gas turbine. All of these processes gain their efficiency (or lack thereof) due to the temperature drop across them.
OTEC uses the temperature difference of ocean water on the surface and ocean water from the depths, a small difference of perhaps 25 degrees Celsius, and so the efficiency must be low. The combined cycle gas turbines use natural-gas fired burners to heat air to near 1530 degrees Celsius, a difference of a large 1500 degrees Celsius, and so the efficiency can be large when the steam-cooling cycle is added in.
What this boils down to is there are thermodynamic cycles and a large number of ways of implementing them with mechanical devices called 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.
From the laws of thermodynamics:
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, although other engines using different cycles can also attain maximum efficiency. Mathematically, this is because in reversible processes, the change in entropy of the cold reservoir is the negative of that of the hot reservoir (i.e., ), keeping the overall change of entropy zero. Thus:
where is the absolute temperature of the hot source and that of the cold sink, usually measured in kelvin. Note that is positive while is negative; in any reversible work-extracting process, entropy is overall not increased, but rather is moved from a hot (high-entropy) system to a cold (low-entropy one), decreasing the entropy of the heat source and increasing that of the heat sink.
The reasoning behind this being the maximal efficiency goes as follows. It is first assumed that if a more efficient heat engine than a Carnot engine is possible, then it could be driven in reverse as a heat pump. Mathematical analysis can be used to show that this assumed combination would result in a net decrease in entropy. Since, by the second law of thermodynamics, this is statistically improbable, 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.
Here are two plots, Figure 2 and Figure 3, for the Carnot cycle efficiency. One plot indicates how the cycle efficiency changes with an increase in the heat addition temperature for a constant compressor inlet temperature, while the other indicates how the cycle efficiency changes with an increase in the heat rejection temperature for a constant turbine inlet temperature.
A different measure of heat engine efficiency is given by the endoreversible process, which is identical to the Carnot cycle except in that the two processes of heat transfer are not reversible. As derived in Callen (1985), the efficiency for such a process is given by:
(Note: This equation is quite frequently traced to a paper by F.L. Curzon and B. Ahlborn, American Journal of Physics, vol. 43, pp. 22-24 (1975). The book by Herbert Callen probably copied from this paper. In a 1996 review paper by Adrian Bejan (J. Appl. Phys., vol. 79, pp. 1191-1218, 1 Feb. 1996), Adrian Bejan pointed out that this equation was also derived by P. Chambadal and I.I. Novikov earlier than Curzon and Ahlborn in the 1950s. Probably, this equation was just re-discovered by Curzon and Ahlborn in 1975. Therefore, some scientists call this efficiency the Chambadal-Novikov-Curzon-Ahlborn efficiency.)
This model does a better job of predicting how well real-world heat engines can do, as can be seen in the following table (Callen):
(Note: This table appeared in the paper by F.L. Curzon and B. Ahlborn, American Journal of Physics, vol. 43, pp. 22-24 (1975). The book by Herbert Callen probably copied from this paper.)
|West Thurrock (UK) coal-fired power plant||25||565||0.64||0.40||0.36|
|CANDU (Canada) nuclear power plant||25||300||0.48||0.28||0.30|
|Larderello (Italy) geothermal power plant||80||250||0.33||0.178||0.16|
As shown, the endoreversible efficiency much more closely models the observed data.
|Cycle/Process||Compression||Heat Addition||Expansion||Heat Rejection|
|Power cycles normally with external combustion|
|Power cycles normally with internal combustion|
Each process is one of the following: