Heat engine
In thermodynamics and engineering, a heat engine is a system that converts heat to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low temperature state. During this process some of the thermal energy is converted into work by  exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag. In general, an engine 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. Overview. 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. 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 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. 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 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 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 fluids are gases and liquids. The engine converts the working fluid from a gas to a liquid, from liquid to gas, or both, generating work from the fluid expansion or compression. Gas-only cycles. In these cycles and engines the working  fluid is always a gas (i.e., there is no phase change): Liquid-only cycles. In these cycles and engines the working fluid are always like liquid: Cycles used for refrigeration. A domestic refrigerator is an example of a heat pump: a heat engine in reverse. Work is used to create a heat differential. Many cycles can run in reverse to move heat from the cold side to the hot side, making the cold side cooler and the hot side hotter. Internal combustion engine versions of these cycles are, by their nature, not reversible. Refrigeration cycles include: Evaporative heat engines. The  Barton evaporation engine is a heat engine based on a cycle producing power and cooled moist air from the evaporation of water into hot dry air. Mesoscopic heat engines. Mesoscopic heat engines are nanoscale devices that may serve the goal of processing heat fluxes and perform useful work at small scales. Potential applications include e.g. electric cooling devices. In such mesoscopic heat engines, work per cycle of operation fluctuates due to thermal noise. There is exact equality that relates average of exponents of work performed by any heat engine and the heat transfer from the hotter heat bath. 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, after a completed cycle: 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 formula_6, 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 formula_8 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: formula_9 Note that formula_10 is positive because isothermal expansion in the power stroke increases the multiplicity of the working fluid while formula_11 is negative since recompression decreases the multiplicity. If the engine is  ideal and runs reversibly, formula_12 and formula_13, and thus formula_14, which gives formula_15 and thus the Carnot limit for heat-engine efficiency, where formula_17 is the absolute temperature of the hot source and formula_18 that of the cold sink, usually measured in kelvins. 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. Endo-reversible heat-engines. By its nature, any maximally efficient Carnot cycle must operate at an infinitesimal temperature gradient; this is because any transfer of heat between two bodies of differing temperatures is irreversible, therefore the Carnot efficiency expression applies only to the infinitesimal limit. The major problem is that the objective of most heat-engines is to output power, and infinitesimal power is seldom desired. A different measure of ideal heat-engine efficiency is given by considerations of endoreversible thermodynamics, where the 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 formula_17 and formula_18 are allowed to be different from the temperatures of the substance going through the reversible Carnot cycle: formula_21 and formula_22. The heat transfers between the reservoirs and the substance are considered as conductive (and irreversible) in the form formula_23. 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, formula_24 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 This model does a better job of predicting how well real-world heat-engines can do (Callen 1985, see also endoreversible thermodynamics): 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: Heat engine processes. Each process is one of the following: