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# PowerPedia:Heat engine

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".

## Introduction

History of Heat Engines

Pre Eighteenth century
c200BC
Temple fire anvil of Cestisibus used to magically open the temple doors. [1]
c200BC
Hero's Engine. Demonstrates rotary motion produced by the reaction from jets of steam.
1120
Gerbert, a professor in the schools at Rheims designed and built an organ blown by air escaping from a vessel in which it was compressed " by heated water.
c1500
Leonardo da Vinci builds the Architonnerre a steam powered cannon
1665
Edward Somerset, the Second Marquis of Worcester builds a working steam fountain.
1680
Huyghens publishes a design for a piston engine powered by gunpowder but it is never built.
1690
Denis Papin - produces design for the first piston steam engine.
1698
Thomas Savery builds a pistonless steam-powered water pump for pumping water out of mines.

Eighteenth century
1707
Denis Papin - produces design for his second piston steam engine in conjunction with Gottfried Leibniz.
1712
Thomas Newcomen builds a piston-and-cylinder steam-powered water pump for pumping water out of mines
1769
James Watt patents his first improved steam engine

Nineteenth century
1816
Robert Stirling invented his hot air Stirling engine
1859
Etienne Lenoir developed the first internal combustion engine, a single-cylinder, two-stroke engine with electric ignition of illumination gas (not gasoline).
1877
Nikolaus Otto patents a four-stroke internal combustion engine (U.S. Patent 194047 (G.patent; PDF))
1892
Rudolf Diesel patents the Diesel engine (U.S. Patent 608845 (G.patent; PDF))

Twentieth century
1929
Felix Wankel patents the Wankel rotary engine (U.S. Patent 2988008 (G.patent; PDF))
1937
Hans von Ohain builds a gas turbine

Heat engines relates to devices where the prime mover or engine is one in which a combustible material is "burned" within an inclosed space or chamber and the heat energy thus developed converted into work by permitting the resulting products of combustion to act upon and through mechanical powers. 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. 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 to the sink from the source, and in this process some of the heat is converted into work.

The engine in question includes suitable mechanism whose functions are continually and automatically carried out. Such engine are designed to communicate power to some machine or device exterior to itself. The space or combustion chamber is ordinarily the interior of the working cylinder of the engine. The products of combustion acting immediately upon a reciprocating, rotating, or oscillating piston moving within a chamber in which combustion takes place or in an extension thereof. Some types of heat engines, however, besides operating as mentioned, have a transfer valve operated by and in unison with the valve which is located between the combustion chamber and the elements upon and through which the products of combustion act to thereby control the product flow. In such cases, the transfer valve is operated to establish communication between the combustion chamber and the working cylinder at the instant of ignition or prior thereto, so that the piston is driven by burning products of combustion.

Heat is transferred in a heat engine to the sink from the source, 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). The working fluid is ordinarily such as results from combustion alone; but in some of the engines in this class a small quantity of water is supplied to the engine, generally by injecting it directly into the interior of the combustion-chamber during or after the combustion of the combustible material; but in all engines using water the amount used is comparatively small, so that the resulting steam is necessarily in a superheated condition. Heat enegines also includes separate parts of engines coming within the above definition and also subordinate elements designed for use with such engines, and incapable of use in the manner contemplated with other devices or in other relations. Any given structure adapted for use as an internal-combustion engine could generally with slight modification be used with steam or other media, and often as an air, gas, or water pump, a hydraulic motor, a meter.

In general terms, the larger the difference in temperature between the hot source and the cold sink, the larger is the potential 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. Examples of everyday heat engines include: the steam engine, the diesel engine, and the gasoline (petrol) engine in an automobile. A common toy that is also a heat engine is a drinking bird. 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

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 35 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, and so the efficiency can be large when the steam-cooling cycle is added in.

## Heat engine types and operation

### 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. The Rankine cycle is a thermodynamic cycle, especially applicable to the classical steam engines. Like other thermodynamic cycles, the maximum efficiency of the Rankine cycle is given by calculating the maximum efficiency of the Carnot cycle. It is named after William John Macquorn Rankine, a Scottish polymath. The Regenerative cycle is more efficient than Rankine cycle.

The Drinking bird cycle is ued bby "Drinking birds" toys. They are a thermodynamically powered toy heat engine. They are also known as happy birds, dippy birds, tippy birds, sippy birds, sipping birds, dunking birds, and tipping birds. The drinking bird is basically a heat engine that exploits a temperature differential to convert heat energy to kinetic energy and perform mechanical work. Like all heat engines, the drinking bird works through a thermodynamic cycle. The initial state of the system is a bird with a wet head oriented vertically with an initial oscillation on its pivot.

The cycle operates as follows:

1. The water evaporates from the head (Maxwell-Boltzmann distribution)
2. Evaporation lowers the temperature of the glass head (heat of vaporization)
3. The temperature drop causes some of the dichloromethane vapour in the head to condense
4. The lower temperature and condensation together cause the pressure to drop in the head (ideal gas law)
5. The pressure differential between the head and base causes the liquid to be pushed up from the base.
6. As liquid flows into the head, the bird becomes top heavy and tips over during its oscillations.
7. When the bird tips over, the bottom end of the neck tube rises above the surface of the liquid.
8. A bubble of vapour rises up the tube through this gap, displacing liquid as it goes
9. Liquid flows back to the bottom bulb, and vapour pressure equalizes between the top and bottom bulbs
10. The weight of the liquid in the bottom bulb restores the bird to its vertical position

If a glass of water is placed so that the beak dips into it on its descent, the bird will continue to absorb water and the cycle will continue as long as there is enough water in the glass to keep the head wet. However, the bird will continue to dip even without a source of water, as long as the head is wet, or as long as a temperature differential is maintained between the head and body. This differential can be generated without evaporative cooling in the head -- for instance, a heat source directed at the bottom bulb will create a pressure differential between top and bottom that will drive the engine. The ultimate source of energy is heat in the surrounding environment -- the toy is not a perpetual motion machine.

Frost heaving (or frost heave) occurs when soil expands and contracts due to freezing and thawing. This process can damage plant roots through breaking or desiccation, cause cracks in pavement, and damage the foundations of buildings, even below the frost line. Moist, fine-grained soil at certain temperatures is most susceptible to frost heaving. The water changing from ice to liquid and back again can lift rock up to 60m. Originally, frost heaving was thought to occur due simply to the freezing of water in soil. However, the vertical displacement of soil in frost heaving can be significantly greater than the expansion that occurs when ice freezes. In the 1960s, frost heaving was demonstrated in soil saturated in benzene and nitrobenzene, which contract when they freeze. The current understanding is that certain soil particles have a high affinity for liquid water. As the liquid water around them freezes, these soils draw in liquid water from the unfrozen soils around them. If the air temperature is below freezing but relatively stable, the heat of fusion from the water that freezes can cause the temperature gradient in the soil to remain constant. The soil at the point where freezing is occurring continues to draw in liquid water from the soils below it, which then freezes and builds u

### Gas only cycles

The Carnot cycle is a particular thermodynamic cycle, modeled on the Carnot heat engine, studied by Nicolas Léonard Sadi Carnot in the 1820s and expanded upon by Benoit Paul Émile Clapeyron in the 1830s and 40s. Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine. A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator rather than a heat engine. The Carnot cycle is a special type of thermodynamic cycle. It is special because it is the most efficient cycle possible for converting a given amount of thermal energy into work or, conversely, for using a given amount of work for refrigeration purposes.

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 the 1824. The Carnot engine model was graphically expanded upon by Benoit Paul Émile Clapeyron in 1834 and mathematically elaborated upon by Rudolf Clausius in the 1850s and 60s from which the concept of entropy emerged. Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine. A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator rather than a heat engine. In the adjacent diagram, from the original 1824 paper by Sadi Carnot entitled On the Motive Power of Fire, we are told to “imagine two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies, to which we can give or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of caloric. We shall call the first the furnace and the second the refrigerator". Carnot then explains how we can obtain motive power, i.e. “work", by carrying a certain quantity of heat from the body A to the body B.

The "Brayton cycle" is a constant pressure cycle named after George Brayton (1830-1892), the American engineer who developed it in gas turbines. In 1872 Brayton filed a patent for his "Ready Motor"; unlike the Otto or Diesel cycles Brayton's engine used a separate compressor and expansion cylinder. Today the Brayton cycle is a cyclic process generally associated with the gas turbine. Like other internal combustion power cycles it is an open system, though for thermodynamic analysis it is a convenient fiction to assume that the exhaust gases are reused in the intake, enabling analysis as a closed system. It is also sometimes known as the Joule cycle.

The Ericsson Cycle is named after inventor John Ericsson. The Ericsson cycle is very similar to what we now call the "Brayton Cycle". The main difference is that the all Ericsson engines are externally heated and usually have a recuperator or regenerator between the compressor and the expander. The Ericsson cycle is often compared to the Stirling Cycle because of its external combustion capabilities, use of a regenerator and the high potential efficiency. Barber was the first to propose a similar engine in 1791 but the Barber engine lacked a regenerator/ recuperator. Ericsson invented and patented his first engine in 1833 (number 6409/1833 British). This was 18 years before Joule and 43 years before Brayton. Brayton engines were for the most part an internal combustion version of the Ericsson Cycle which was a considerable improvement to external heating. The "Brayton Cycle" is now known as the gas turbine cycle, which differs from the original "Brayton Cycle" in the use of a turbine compressor and expander. The gas turbine cycle is used for all modern gas turbine and turbojet engines. Ericsson eventually abandoned the open cycle in favor of the traditional closed Stirling cycle. At one point an Ericsson cycle engine was used to power a 2000 ton ship, The Caloric Ship Ericsson and the engine ran flawlessly for 73 hours. The combination engine produced about 300 horsepower. It had a combination of 4 2-piston engines; the larger, the expansion piston/cylinder, being 4.267 meters or 14 feet in diameter--perhaps the largest piston diameter of any engine ever built. Rumor has it that tables were placed on top of those pistons and dinner was served and eaten, while the engine was running at full power. At 6.5 Rpm the pressure was limited to 8 psi. Ericsson also introduced the twin-screw propeller for ship design, in the USS Princeton.

The Stirling engine is a heat engine of the external combustion piston engine type whose heat-exchange process allows for near-ideal efficiency in conversion of heat into mechanical movement by following the Carnot cycle as closely as is practically possible with given materials. Its invention is credited to the Scottish clergyman Rev. Robert Stirling in 1816 who made significant improvements to earlier designs and took out the first patent. He was later assisted in its development by his engineer brother James Stirling.

The internal combustion engine is a heat engine in which the burning of a fuel occurs in a confined space called a combustion chamber. This exothermic reaction of a fuel with an oxidizer creates gases of high temperature and pressure, which are permitted to expand. The defining feature of an internal combustion engine is that useful work is performed by the expanding hot gases acting directly to cause movement, for example by acting on pistons, rotors, or even by pressing on and moving the entire engine itself. This contrasts with external combustion engines such as steam engines which use the combustion process to heat a separate working fluid, typically water or steam, which then in turn does work, for example by pressing on a steam actuated piston. The term Internal Combustion Engine (ICE) is almost always used to refer specifically to reciprocating engines, Wankel engines and similar designs in which combustion is intermittent. However, continuous combustion engines, such as Jet engines, most rockets and many gas turbines are also very definitely internal combustion engines.

The four-stroke cycle (or Otto cycle) of an internal combustion engine is the cycle most commonly used for automotive and industrial purposes today (cars and trucks, generators, etc). The Thermodynamics cycles used in internal combustion reciprocating engines are the Otto Cycle (the ideal cycle for spark-ignition engines) and the Diesel Cycle (the ideal cycle for compression-ignition engines). The Otto Cycle consists of Adiabatic compression,heat addition at constant volume,Adiabatic expansion and rejection of heat at constant volume. It was conceptualized by the French engineer, Alphonse Beau de Rochas in 1862, and independently, by the German engineer Nicolaus Otto in 1876. The four-stroke cycle is more fuel efficient and clean burning than the two-stroke cycle, but requires considerably more moving parts and manufacturing expertise. Moreover, it is more easily manufactured in multi-cylinder configurations than the two-stroke, making it especially useful in high-output applications such as cars. The later-invented Wankel engine has four similar phases but is a rotary combustion engine rather than the much more usual, reciprocating engine of the four-stroke cycle.

The Otto cycle is characterized by four strokes, or straight movements alternately, back and forth, of a piston inside a cylinder:

1. intake (induction) stroke
2. compression stroke
3. power (combustion) stroke
4. exhaust stroke

The cycle begins at top dead center, when the piston is at its uppermost point. On the first downward stroke (intake) of the piston, a mixture of fuel and air is drawn into the cylinder through the intake (inlet) port. The intake (inlet) valve (or valves) then close(s), and the following upward stroke (compression) compresses the fuel-air mixture. The air-fuel mixture is then ignited, usually by a spark plug for a gasoline or Otto cycle engine, or by the heat and pressure of compression for a Diesel cycle of compression ignition engine, at approximately the top of the compression stroke. The resulting expansion of burning gases then forces the piston downward for the third stroke (power), and the fourth and final upward stroke (exhaust) evacuates the spent exhaust gases from the cylinder past the then-open exhaust valve or valves, through the exhaust port.

The Diesel cycle is the combustion process of a type of internal combustion engine, in which the burning of the fuel is triggered by the heat generated in first compressing air in the piston cavity, into which is then injected the fuel - as opposed to it being ignited by a spark plug, as combustion is in the Otto cycle (four-stroke/petrol) engine. Diesel engines (Heat engines utilizing the Diesel cycle) are used in automobiles, power generation, diesel-electric locomotives, and submarines.

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. The Atkinson cycle allows the intake, compression, power, and exhaust strokes of the four-stroke cycle to occur in a single turn of the crankshaft. Owing to the linkage, the expansion ratio is greater than the compression ratio, leading to greater efficiency than with engines using the alternative Otto cycle. The Atkinson cycle may also refer to a four stroke engine in which the intake valve is held open longer than normal to allow a reverse flow of intake air into the intake manifold. This reduces the effective compression ratio and, when combined with an increased stroke and/or reduced combustion chamber volume, allows the expansion ratio to exceed the compression ratio while retaining a normal compression pressure. This is desirable for improved fuel economy because the compression ratio in a spark ignition engine is limited by the octane rating of the fuel used. A high expansion ratio delivers a longer power stroke, allowing more expansion of the combustion gases and reducing the amount of heat wasted in the exhaust. This makes for a more efficient engine.

The Lenoir cycle is an idealised thermodynamic cycle for the pulse jet engine. An ideal gas undergoes:

1. constant volume heating
3. isobaric compression to the volume at the start of the cycle.

The expansion process is isentropic and hence involves no heat interaction. Energy is absorbed as heat during the constant volume process and rejected as heat during the constant pressure process. A pulse jet engine (or pulsejet) is a very simple form of internal combustion engine wherein the combustion occurs in pulses and the propulsive effort is a jet, this is, a reaction to the rearward flow of hot gases. A typical pulsejet comprises an air intake fitted with a one-way valve, a combustion chamber, and an acoustically resonant exhaust pipe. The valving is accomplished though the use of reed valves or, in a valveless pulse jet engine, through aerodynamics. Fuel in the form of a gas or liquid aerosol is either mixed with the air in the intake or injected into the combustion chamber. Once the engine is running it requires only an input of fuel, but it usually requires forced air and an ignition method for the fuel-air mix. Once running, the engine is self-sustaining.

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 (engineer), an American engineer, in the 1940s. This type of engine was first used in ships and stationary power-generating plants, but was adapted by Mazda for their KJ-ZEM V6, used in the Millenia sedan. More recently, Subaru has combined a Miller cycle flat-4 with a hybrid driveline for their "Turbo Parallel Hybrid" car, known as the Subaru B5-TPH. A traditional Otto cycle engine uses four "strokes", of which two can be considered "high power" – the compression stroke (high power consumption) and power stroke (high power production). Much of the internal power loss of an engine is due to the energy needed to compress the charge during the compression stroke, so systems that reduce this power consumption can lead to greater efficiency.

In the Miller cycle, the intake valve is left open longer than it would be in an Otto cycle engine. In effect, the compression stroke is two discrete cycles: the initial portion when the intake valve is open and final portion when the intake valve is closed. This two-stage intake stroke creates the so called "fifth" cycle that the Miller cycle introduces. As the piston initially moves upwards in what is traditionally the compression stroke, the charge is being pushed back out the still-open valve. Typically this loss of charge air would result in a loss of power. However, in the Miller cycle, the piston is over-fed with charge air from a supercharger, so pushing some of the charge air back out into the intake manifold is entirely planned. The supercharger typically will need to be of the positive displacement type due its ability to produce boost at relatively low engine speeds. Otherwise, low-rpm torque will suffer. A key aspect of the Miller cycle is that the compression stroke actually starts only after the piston has pushed out this "extra" charge and the intake valve closes. This happens at around 20% to 30% into the compression stroke. In other words, the actual compression occurs in the latter 70% to 80% of the compression stroke. The piston gets the same resulting compression as it would in a standard Otto cycle engine for 70% of the work.

The Miller cycle results in an advantage as long as the supercharger can compress the charge using less energy than the piston would use to do the same work. Over the entire compression range required by an engine, the supercharger is used to generate low levels of compression, where it is most efficient. Then, the piston is used to generate the remaining higher levels compression, operating in the range where it is more efficient than a supercharger. Thus the Miller cycle uses the supercharger for the portion of the compression where it is best, and the piston for the portion where it is best. In total, this reduces in the power needed to run the engine by 10% to 15%. To this end, successful production engines using this cycle have typically used variable valve timing to effectively switch off the Miller cycle in regions of operation where it does not offer an advantage. In a typical spark ignition engine, the Miller cycle yields an additional benefit. The intake air is first compressed by the supercharger and then cooled by an intercooler. This lower intake charge temperature, combined with the lower compression of the intake stroke, yields a lower final charge temperature than would be obtained by simply increasing the compression of the piston. This allows ignition timing to be altered to beyond what is normally allowed before the onset of detonation, thus increasing the overall efficiency still further.

Efficiency is increased by raising the compression ratio. In a typical gasoline engine, the compression ratio is limited due to self-ignition (detonation) of the compressed, and therefore hot, air/fuel mixture. Due to the reduced compression stroke of a Miller cycle engine, a higher overall compression ratio (supercharger compression plus piston compression) is possible, and therefore a Miller cycle engine has a better efficiency. It should be noted that the benefits of utilizing positive displacement superchargers do not come without a cost. 15% to 20% of the power generated by a supercharged engine is usually required to do the work of driving the supercharger, which compresses the intake charge (also known as boost). A similar delayed-valve closing method is used in some modern versions of Atkinson cycle engines, but without the supercharging. These engines are generally found on hybrid electric vehicles, where efficiency is the goal, and the power lost compared to the Miller cycle is made up through the use of electric motors.

### Electron cycles

Thermoelectricity is the conversion from temperature differentials to electricity or vice versa. It is accomplished in one of several ways:

1. The Peltier-Seebeck effect
2. Thermionic emission
3. Indirectly through magnetohydrodynamics

The Peltier–Seebeck effect, or thermoelectric effect, is the direct conversion of heat differentials to electric voltage and vice versa. Related effects are the Thomson effect and Joule heating. The Peltier–Seebeck and Thomson effects are reversible (in fact, the Peltier and Seebeck effects are reversals of one another); Joule heating cannot be reversible under the laws of thermodynamics. The Seebeck effect is the conversion of heat differences directly into electricity. This effect was first discovered, accidentally, by the Estonian physicist Thomas Johann Seebeck in 1821, who found that a voltage existed between two ends of a metal bar when a temperature gradient \nabla T existed in the bar. He also discovered that a compass needle would be deflected when a closed loop was formed of two metals with a temperature difference between the junctions. This is because the metals respond differently to the heat difference, which creates a current loop, which produces a magnetic field. A voltage, the thermoelectric EMF, is created in the presence of a temperature difference between two different metals or semiconductors. This usually causes a continuous current to flow in the conductors. The voltage created is on the order of several microvolts per degree of difference. The Peltier effect is the reverse of the Seebeck effect; a creation of a heat difference from an electric voltage. It occurs when a current is passed through two dissimilar metals or semiconductors (n-type and p-type) that are connected to each other at two junctions (Peltier junctions). The current drives a transfer of heat from one junction to the other: one junction cools off while the other heats up; as a result, the effect is often used for thermoelectric cooling. This effect was observed in 1834 by Jean Peltier, 13 years after Seebeck's initial discovery.

The conducting material is not limited to solids with electrons as charge carriers. Such effects can be observed in conductors where the carriers are ions, or in semiconductors where the carriers are holes or electrons. It is the principle behind heat engines, heat pumps, thermocouples, thermal diodes, and solid-state refrigerators, etc. It can be used to electrically measure temperature, or to generate power from a heat source. The heat from radioactive decay has been used to electrically power several space probes, in the form of radioisotope thermoelectric generators. Thermoelectric power sometimes refers to this direct conversion, but usually just refers to a power plant which converts heat into electricity, through the use of steam turbines or similar device. Thermoelectricity was widely used in the remote parts of the Soviet Union from the 1920s to power radios. The equipment comprised some bi-metal rods, one end of which could be inserted into the fireplace to get hot with the other end left out in the cold. Another way of achieving the same function is a Clockwork radio.

Thermionic emission (archaically known as the Edison effect) is the flow of electrons from a metal or metal oxide surface, caused by thermal vibrational energy overcoming the electrostatic forces holding electrons to the surface. The effect increases dramatically with increasing temperature (1000–3000 K), but is always present at temperatures above absolute zero. The science dealing with this phenomenon is thermionics. The charged particles are called thermions. 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. The problem with using thermal electrons to carry heat is the fact that, due to the high work function of metals (the only practical emitters), the lowest cooling temperate is around 600C - clearly not useful except in the most unusual applications. Thermotunnel cooling avoids this problem by making the gap narrow enough that electrons can tunnel across the gap, carrying the heat with them. The problem with this approach has been getting two surfaces near enough that they can tunnel over a large area, yet not touch at any point (which would short the device out preventing it from doing any useful cooling). Cool Chips[1] is a startup trying to optimise a new process for production of these very close surfaces in preparation for selling practical devices. Their approach is to make a thin (5nm) spacer layer in a special sandwich of materials. Once the chip is assembled, the spacer layer is chemically removed and tiny piezoelectric actuators maintain the precise spacing required. At this point no devices are available commercially as the technology is still undergoing refinement.

### Photon cycles

Solar sails (also called light sails, especially when they use light sources other than the Sun) are a proposed form of spacecraft propulsion using large membrane mirrors. Radiation pressure is small and decreases by the square of the distance from the sun, but unlike rockets, solar sails require no fuel. Although the thrust is small, it continues as long as the sun shines and the sail exists. The spacecraft deploys a large membrane mirror which reflects light from the Sun or some other source. The radiation pressure on the mirror provides a minuscule amount of thrust by reflecting photons. Tilting the reflective sail at an angle from the Sun produces thrust at an angle that bisects the angle between the Sun and the spacecraft. In most designs, steering would be done with auxiliary vanes, acting as small solar sails to change the attitude of the large solar sail (see the vanes on the illustration). The vanes would be adjusted by electric motors. Sails orbit, and therefore do not need to hover or move directly toward or away from the sun. Almost all missions would use the sail to change orbit, rather than thrusting directly away from a planet or the sun. The sail is rotated slowly as the sail orbits around a planet so the thrust is in the direction of the orbital movement to move to a higher orbit or against it to move to a lower orbit. When an orbit is far enough away from a planet, the sail then begins similar maneuvers in orbit around the sun.

The best sort of missions for a solar sail involves a dive near the sun, where the light is intense, and sail efficiencies are high. For this reason, most sails are designed to tolerate much higher temperatures than one might expect. Going close to the Sun may be done for different mission aims: for exploring the solar poles from a short distance, for observing the Sun and its near environment from a non-Keplerian circular orbit the plane of which may be shifted some solar radii, for flying-by the Sun such that the sail gets a very high speed. An unsuspected feature, until the first half of the Nineties, of the solar sail propulsion is to allow a sailcraft to escape the solar system with a cruise speed higher (or even much higher) than a spacecraft powered by a nuclear electric rocket system. The spacecraft mass to sail area ratio does not need to achieve ultra-low values, even though the sail should be an advanced all-metal sail. This flight mode is also known as the fast solar sailing. Proven mathematically (like many other astronautical items well in advance of their actual launches), such sailing mode has been considered by NASA/Marshall as one of the options for a future precursor interstellar probe (NASA/CR 2002-211730, the chapter IV) exploring the near interstellar space beyond the heliosphere. Most theoretical studies of interstellar missions with a solar sail plan to push the sail with a very large laser. The thrust vector would therefore be away from the Sun and toward the target

### Cycles used for refrigeration

A refrigerator is a heat pump: a heat engine in reverse. Work is used to create a heat differential. The [Carnot refrigeration]] uses the Carnot cycle in reverse. The absorption refrigerator is a refrigerator that utilizes a heat source to provide the energy needed to drive the cooling system rather than being dependent on electricity to run a compressor. These refrigerators are popular where electricity is unreliable, costly, or unavailable, or where surplus heat is available, e.g., from turbine exhausts or industrial processes. An absorption refrigerator is similar to a regular compressor refrigerator in that the refrigeration takes place by evaporating a liquid with a very low (sub-zero) boiling point. In both cases, when a liquid evaporates or boils, it takes some heat away with it, and can continue to do so either until the liquid is all boiled, or until everything has become so cold that the sub-zero boiling point has been reached. The difference between the two is how the gas is changed back into a liquid so that it may be used again. A regular refrigerator uses a compressor to increase the pressure on the gas, forcing it to become a liquid again. An absorption refrigerator uses a different method that requires no moving parts and is powered only by heat.

### Heat engine processes

Cycle/Process Compression Heat Addition Expansion Heat Rejection
Stirling isothermal isometric isothermal isometric
Ericsson isothermal isobaric isothermal isobaric

Each process is either isothermal (at constant temperature, maintained with heat added or removed from a heat source or sink), isobaric (at constant pressure), isometric/isochoric (at constant volume), or adiabatic (no heat is added or removed from the working fluid).

## Efficiency

The efficiency of a heat engine relates how much useful power is output for a given amount of heat energy input. From the laws of thermodynamics:

$dW \ = \ dQ_c \ - \ (-dQ_h)$

where

dW = − PdV is the work extracted from the engine. (It is negative since work is done by the engine.)
dQh = ThdSh is the heat energy taken from the high temperature system .(It is negative since heat is extracted from the source, hence ( − dQh) is positive.)
dQc = TcdSc 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" to "what you put in." In the case of an engine, one desires to extract work and puts in a heat transfer.

$\eta = \frac{-dW}{-dQ_h} = \frac{-dQ_h - dQ_c}{-dQ_h} = 1 - \frac{dQ_c}{-dQ_h}$

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 due to the fact that in reversible processes, the change in entropy of the cold reservoir is the negative of that of the hot reservoir (i.e., dSc = − dSh), keeping the overall change of entropy zero. Thus:

$\eta_{max} = 1 - \frac{T_cdS_c}{-T_hdS_h} \equiv 1 - \frac{T_c}{T_h}$

where Th is the absolute temperature of the hot source and Tc that of the cold sink, usually measured in kelvins. Note that dSc is positive while dSh 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 forbidden, the Carnot efficiency is a theoretical upper bound on the efficiency of any process. Empirically, no engine has ever been shown to run at a greater efficiency than a Carnot cycle heat engine.

## Other performance criteria

One problem with the ideal 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 due to the fact that 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 much more accurate 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 treated as reversible. As derived in Callen (1985), the efficiency for such a process is given by:

$\eta = 1 - \sqrt{\frac{T_c}{T_h}}$

The accuracy of this model can be seen in the following table:

Efficiencies of Power Plants
Power Plant Tc (°C) Th (°C) η (Carnot) η (Endoreversible) η (Observed)
West Thurrock (United Kingdom) Fossil fuel power plant 25 565 0.64 0.40 0.36
CANDU reactor (Canada) nuclear power plant 25 300 0.48 0.28 0.30
Larderello (Italy) geothermal power plant 80 250 0.32 0.175 0.16

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

## 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.

Increase the temperature difference in the heat engine
The simplest way to do this is to increase the hot side temperature, and is the approach used in modern combined-cycle gas turbines. Unfortunately, NOx production and material limits (melting the turbine blades) place a hard limit to how hot you can make a workable heat engine. Modern gas turbines are about as hot as they can become and still maintain acceptable NOx pollution levels. Another way of increasing efficiency is to lower the output temperature. Once 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, which uses a 70/30 mix of ammonia 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 exploit 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 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 have also been considered for such applications, although SO2 is a little toxic for most.
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(NO2), a toxic component of smog, 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, which causes it to re-combine into N2O4. This is then fed back to the compressor for another cycle. Such species as aluminum bromide (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.

## Patents

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