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| {{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}
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| A '''thermodynamic cycle''' consists of a linked sequence of [[thermodynamic process]]es that involve the transference of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the [[thermodynamic system|system]] to its initial state.<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 0-07-238332-1 | pages = 14}}
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| </ref> In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source heat into useful work and dispose of the remaining heat to a cold sink, thereby acting as a [[heat engine]]. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a [[heat pump]].
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| During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. [[Process quantities]] (or path quantities), such as [[heat]] and [[work (thermodynamics)|work]] are process dependent. For a cycle for which the system returns to its initial state the first law of thermodynamics applies:
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| :<math>\Delta E = E_{out} - E_{in} = 0</math>
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| The above states that there is no change of the energy of the system over the cycle. E<sub>in</sub> might be the work and heat input during the cycle and E<sub>out</sub> would be the work and heat ouput during the cycle. The [[first law of thermodynamics]] also dictates that the net heat input is equal to the net work output over a cycle (we account for heat, Q<sub>in</sub>, as positive and Q<sub>out</sub> as negative). The repeating nature of the process path allows for continuous operation, making the cycle an important concept in [[thermodynamics]]. Thermodynamic cycles are often represented mathematically as [[quasistatic process]]es in the modeling of the workings of an actual device.
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| ==Heat and work==
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| Two primary classes of thermodynamic cycles are '''power cycles''' and '''heat pump cycles'''. Power cycles are cycles which convert some heat input into a [[mechanical work]] output, while heat pump cycles transfer heat from low to high temperatures by using mechanical work as the input. Cycles composed entirely of quasistatic processes can operate as power or heat pump cycles by controlling the process direction. On a [[pressure-volume diagram]] or [[temperature-entropy diagram]], the [[clockwise and counterclockwise]] directions indicate power and heat pump cycles, respectively.
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| ===Relationship to work===
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| [[File:PdV work cycle.gif|thumb|The net work equals the area inside because it is (a) the Riemann sum of work done on the substance due to expansion, minus (b) the work done to re-compress.]]
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| Because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a PV diagram. A PV diagram's ''Y'' axis shows pressure (''P'') and ''X'' axis shows volume (''V''). The area enclosed by the loop is the work (''W'') done by the process:
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| :<math> \text{(1)} \qquad W = \oint P \ dV </math>
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| This work is equal to the balance of heat (Q) transferred into the system:
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| :<math> \text{(2)} \qquad W = Q = Q_{in} - Q_{out} </math>
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| Equation (2) makes a cyclic process similar to an [[isothermal process]]: even though the internal energy changes during the course of the cyclic process, when the cyclic process finishes the system's energy is the same as the energy it had when the process began.
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| If the cyclic process moves clockwise around the loop, then W will be positive, and it represents a [[heat engine]]. If it moves counterclockwise, then W will be negative, and it represents a [[heat pump]].
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| {{Clear}}
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| ===Each Point in the Cycle===
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| [[Image:Stirling Cycle.png|thumb|left|200px|Description of each point in the thermodynamic cycles.]]
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| Otto Cycle:
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| 1→2: [[Isentropic]] Expansion: Constant [[entropy]] (s), Decrease in [[pressure]] (P), Increase in [[volume]] (v), Decrease in [[temperature]] (T)
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| 2→3: [[Isochoric]] Cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T)
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| 3→4: Isentropic Compression: Constant entropy (s), Increase in pressure (P), Decrease in volume (v), Increase in temperature (T)
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| 4→1: Isochoric Heating: Constant volume (v), Increase in pressure (P), Increase in entropy (S), Increase in temperature (T)
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| {{Clear}}
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| A List of Thermodynamic Processes:
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| [[Adiabatic]] : No energy transfer as heat (Q) during that part of the cycle would amount to δQ=0. This does not exclude energy transfer as work.
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| [[Isothermal]] : The process is at a constant temperature during that part of the cycle (T=constant, δT=0). This does not exclude energy transfer as heat or work.
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| [[Isobaric]] : Pressure in that part of the cycle will remain constant. (P=constant, δP=0). This does not exclude energy transfer as heat or work.
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| [[Isochoric]] : The process is constant volume (V=constant, δV=0). This does not exclude energy transfer as heat or work.
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| [[Isentropic]] : The process is one of constant entropy (S=constant, δS=0). This excludes the transfer of heat but not work.
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| ===Power cycles===
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| [[Image:Carnot heat engine 2.svg|200px|thumb|Heat engine diagram.]]
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| {{Main|Heat engine}}
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| Thermodynamic power cycles are the basis for the operation of heat engines, which supply most of the world's [[electric power]] and run the vast majority of [[motor vehicles]]. Power cycles can be divided according to the type of heat engine they seek to model. The most common cycles used to model [[internal combustion engines]] are the [[Otto cycle]], which models [[gasoline engine]]s, and the [[Diesel cycle]], which models [[diesel engines]]. Cycles that model [[external combustion engines]] include the [[Brayton cycle]], which models [[gas turbines]], and the [[Rankine cycle]], which models [[steam turbines]].
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| [[Image:Stirling Cycle.png|thumb|200px|The clockwise thermodynamic cycle indicated by the arrows shows that the cycle represents a heat engine. The cycle consists of four states (the point shown by crosses) and four thermodynamic processes (lines).]]
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| For example the pressure-volume [[mechanical work]] output from the heat engine cycle (net work out), consisting of 4 thermodynamic processes, is:
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| :<math> \text{(3)} \qquad W_{net} = W_{1\to 2} + W_{2\to 3} + W_{3\to 4} + W_{4\to 1} </math>
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| :<math> W_{1\to 2} = \int_{V_1}^{V_2} P \, dV, \, \, \text{negative, work done on system} </math>
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| :<math> W_{2\to 3} = \int_{V_2}^{V_3} P \, dV, \, \, \text{zero work if V2 equal V3} </math>
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| :<math> W_{3\to 4} = \int_{V_3}^{V_4} P \, dV, \, \, \text{positive, work done on system} </math>
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| :<math> W_{4\to 1} = \int_{V_4}^{V_1} P \, dV, \, \, \text{zero work if V4 equal V1} </math>
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| If no volume change happens in process 4-1 and 2-3, equation (3) simplifies to:
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| :<math> \text{(4)} \qquad W_{net} = W_{1\to 2} + W_{3\to 4} </math>
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| ===Heat pump cycles===
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| {{Main|Heat pump and refrigeration cycle}}
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| Thermodynamic heat pump cycles are the [[Mathematical model|model]]s for household [[heat pumps]] and [[refrigerators]]. There is no difference between the two except the purpose of the refrigerator is to cool a very small space while the household heat pump is intended warm a house. Both work by moving heat from a cold space to a warm space. The most common refrigeration cycle is the [[Vapor compression refrigeration|vapor compression cycle]], which models systems using [[refrigerants]] that change phase. The [[Gas absorption refrigeration|absorption refrigeration cycle]] is an alternative that absorbs the refrigerant in a liquid solution rather than evaporating it. Gas refrigeration cycles include the reversed Brayton cycle and the [[Hampson-Linde cycle]]. Multiple compression and expansion cycles allow gas refrigeration systems to [[liquefaction of gases|liquify gases]].
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| ==Modelling real systems==
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| {| align="center"
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| |-
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| |[[Image:Brayton cycle.svg|thumb|745px|Example of a real system modelled by an idealized process: PV and TS diagrams of a Brayton cycle mapped to actual processes of a gas turbine engine]]
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| |}
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| Thermodynamic cycles may be used to model real devices and systems, typically by making a series of assumptions.<ref name=boles1>Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 452. ISBN 0-07-238332-1.</ref> simplifying assumptions are often necessary to reduce the problem to a more manageable form.<ref name=boles1/> For example, as shown in the figure, devices such a [[gas turbine]] or [[jet engine]] can be modeled as a [[Brayton cycle]]. The actual device is made up of a series of stages, each of which is itself modeled as an idealized thermodynamic process. Although each stage which acts on the working fluid is a complex real device, they may be modelled as idealized processes which approximate their real behavior. If energy is added by means other than combustion, then a further assumption is that the exhaust gases would be passed from the exhaust to a heat exchanger that would sink the waste heat to the environment and the working gas would be reused at the inlet stage.
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| The difference between an idealized cycle and actual performance may be significant.<ref name=boles1/> For example, the following images illustrate the differences in work output predicted by an ideal [[Stirling cycle]] and the actual performance of a Stirling engine:
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| {| align="center"
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| |[[File:Stirling Cycle.svg|250px|]]
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| |[[File:PV plot adiab sim.png|350px|]]
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| |[[File:PV real1.PNG|350px|]]
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| |-
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| |style="text-align:center"|Ideal Stirling cycle
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| |style="text-align:center"|Actual performance
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| |style="text-align:center"|Actual and ideal overlaid, showing difference in work output
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| |}
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| As the net work output for a cycle is represented by the interior of the cycle, there is a significant difference between the predicted work output of the ideal cycle and the actual work output shown by a real engine. It may also be observed that the real individual processes diverge from their idealized counterparts; e.g., isochoric expansion (process 1-2) occurs with some actual volume change.
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| ==Well-known thermodynamic cycles==
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| In practice, simple idealized thermodynamic cycles are usually made out of four [[thermodynamic process]]es. Any thermodynamic processes may be used. However, when idealized cycles are modeled, often processes where one state variable is kept constant are used, such as an [[isothermal process]] (constant temperature), [[isobaric process]] (constant pressure), [[isochoric process]] (constant volume), [[isentropic process]] (constant entropy), or an [[isenthalpic process]] (constant enthalpy). Often [[adiabatic process]]es are also used, where no heat is exchanged.
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| Some example thermodynamic cycles and their constituent processes are as follows:
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| {{Table of thermodynamic cycles}}
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| ===Ideal cycle===
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| [[Image:Cyclic process.PNG|thumb|350px|left|An illustration of an ideal cycle heat engine (arrows clockwise).]]
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| An ideal cycle is constructed out of:
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| # TOP and BOTTOM of the loop: a pair of parallel '''isobaric''' processes
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| # LEFT and RIGHT of the loop: a pair of parallel '''isochoric''' processes
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| {{clear}}
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| ===Carnot cycle===
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| {{main|Carnot cycle}}
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| The [[Carnot cycle]] is a cycle composed of the totally [[reversible processes]] of [[isentropic]] compression and expansion and [[isothermal]] heat addition and rejection. The [[thermal efficiency]] of a Carnot cycle depends only on the absolute temperatures of the two reservoirs in which heat transfer takes place, and for a power cycle is:
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| :<math>\eta=1-\frac{T_L}{T_H}</math>
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| where <math>{T_L}</math> is the lowest cycle temperature and <math>{T_H}</math> the highest. For Carnot power cycles the [[coefficient of performance]] for a [[heat pump]] is:
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| :<math>\ COP = 1+\frac{T_L}{T_H - T_L}</math>
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| and for a [[refrigerator]] the coefficient of performance is:
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| :<math>\ COP = \frac{T_L}{T_H - T_L}</math>
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| The second law of thermodynamics limits the efficiency and COP for all cyclic devices to levels at or below the Carnot efficiency. The [[Stirling cycle]] and [[Ericsson cycle]] are two other reversible cycles that use regeneration to obtain isothermal heat transfer.
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| ===Stirling cycle===
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| {{Main|Stirling cycle}}
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| A Stirling cycle is like an Otto cycle, except that the adiabats are replaced by isotherms. It is also the same as an Ericsson cycle with the isobaric processes substituted for constant volume processes.
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| # TOP and BOTTOM of the loop: a pair of quasi-parallel '''isothermal''' processes
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| # LEFT and RIGHT sides of the loop: a pair of parallel '''isochoric''' processes
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| Heat flows into the loop through the top isotherm and the left isochore, and some of this heat flows back out through the bottom isotherm and the right isochore, but most of the heat flow is through the pair of isotherms. This makes sense since all the work done by the cycle is done by the pair of isothermal processes, which are described by ''Q=W''. This suggests that all the net heat comes in through the top isotherm. In fact, all of the heat which comes in through the left isochore comes out through the right isochore: since the top isotherm is all at the same warmer temperature <math> T_H </math> and the bottom isotherm is all at the same cooler temperature <math> T_C </math>, and since change in energy for an isochore is proportional to change in temperature, then all of the heat coming in through the left isochore is cancelled out exactly by the heat going out the right isochore.
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| ==State functions and entropy==
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| If ''Z'' is a [[state function]] then the balance of ''Z'' remains unchanged during a cyclic process:
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| :<math> \oint dZ = 0 </math>.
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| Entropy is a state function and is defined as
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| :<math> S = {Q \over T} </math>
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| so that
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| :<math> \Delta S = {\Delta Q \over T} </math>,
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| then it is clear that for any cyclic process,
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| :<math> \oint dS = \oint {dQ \over T} = 0</math>
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| meaning that the net entropy change over a cycle is 0.
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| ==See also==
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| * [[Entropy]]
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| * [[Economizer]]
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| {{Thermodynamic cycles|state=uncollapsed}}
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| * Halliday, Resnick & Walker. ''Fundamentals of Physics'', 5th edition. John Wiley & Sons, 1997. Chapter 21, ''Entropy and the Second Law of Thermodynamics''.
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| * Çengel, Yunus A., and Michael A. Boles. ''Thermodynamics: An Engineering Approach'', 7th ed. New York: McGraw-Hill, 2011. Print.
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| * Hill and Peterson. "Mechanics and Thermodynamics of Propulsion", 2nd ed. Prentice Hall, 1991. 760 pp.
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| == External links ==
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| {{Commons category|Thermodynamics cycles}}
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| {{DEFAULTSORT:Thermodynamic Cycle}}
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| [[Category:Thermodynamic cycles| ]]
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| [[Category:Thermodynamics]]
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