2466:. Power cycles can be organized into two categories: real cycles and ideal cycles. Cycles encountered in real world devices (real cycles) are difficult to analyze because of the presence of complicating effects (friction), and the absence of sufficient time for the establishment of equilibrium conditions. For the purpose of analysis and design, idealized models (ideal cycles) are created; these ideal models allow engineers to study the effects of major parameters that dominate the cycle without having to spend significant time working out intricate details present in the real cycle model.
3214:. 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.
3750:
2445:
42:
1612:
3229:
3190:
2525:
2383:
3236:
4949:
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
3262:
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
3157:. 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 to warm or cool a house. Both work by moving heat from a cold space to a warm space. The most common refrigeration cycle is the
4413:
3201:
Thermodynamic cycles may be used to model real devices and systems, typically by making a series of assumptions. simplifying assumptions are often necessary to reduce the problem to a more manageable form. For example, as shown in the figure, devices such a
1899:
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
2075:
Equation (2) is consistent with the First Law; even though the internal energy changes during the course of the cyclic process, when the cyclic process finishes the system's internal energy is the same as the energy it had when the process began.
4954:. 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
2935:
2740:
3044:
2849:
2654:
3243:
1331:
1678:
to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a
3129:
5008:, 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.
2528:
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).
4929:
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.
4150:
4511:
2070:
4821:
5270:
4902:
5138:
1997:
4672:
3922:
5197:
1783:
4142:
3217:
The difference between an idealized cycle and actual performance may be significant. For example, the following images illustrate the differences in work output predicted by an ideal
4580:
Thus, the total heat flow per cycle is calculated without knowing the heat capacities and temperature changes for each step (although this information would be needed to assess the
3994:
2371:
4575:
4068:
1871:
would be the total work and heat output during the cycle. The repeating nature of the process path allows for continuous operation, making the cycle an important concept in
4029:
1166:
1111:
1056:
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2318:
2269:
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2199:
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2129:
863:
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684:
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1641:
767:
635:
4733:
4704:
2855:
2660:
1869:
1836:
1001:
5006:
4979:
3952:
3169:
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
2941:
2746:
5420:
4094:
2542:
1342:
500:
3862:
3842:
3818:
3798:
1806:
1230:
839:
792:
707:
660:
572:
525:
1924:
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.
3275:. Any thermodynamic processes may be used. However, when idealized cycles are modeled, often processes where one state variable is kept constant, such as:
464:
1320:
3193:
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
5582:
1353:
4618:
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:
923:
3055:
2432:
3→4: Isentropic / adiabatic compression: Constant entropy (s), Increase in pressure (P), Decrease in volume (v), Increase in temperature (T)
1634:
1221:
457:
335:
890:
4603:
2323:
1683:. 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
273:
4907:
The second law of thermodynamics limits the efficiency and COP for all cyclic devices to levels at or below the Carnot efficiency. The
1921:
5413:
1405:
1379:
900:
354:
5648:
5356:
5331:
3140:
306:
1458:
5732:
929:
328:
4408:{\displaystyle W_{cycle}=p_{A}(v_{2}-v_{1})+p_{C}(v_{4}-v_{3})=p_{A}(v_{2}-v_{1})+p_{C}(v_{1}-v_{2})=(p_{A}-p_{C})(v_{2}-v_{1})}
1905:
5686:
2469:
Power cycles can also be divided according to the type of heat engine they seek to model. The most common cycles used to model
1627:
5737:
5727:
3166:
1909:
1558:
90:
4418:
1453:
2435:
4→1: Isochoric heating: Constant volume (v), Increase in pressure (P), Increase in entropy (S), Increase in temperature (T)
2008:
5722:
5406:
4749:
1533:
1306:
283:
5209:
5633:
4836:
4415:, which is just the area of the rectangle. If the total heat flow per cycle is required, this is easily obtained. Since
3824:
vanishes. Therefore, the internal energy changes of a perfect gas undergoing various processes connecting initial state
918:
121:
111:
5077:
3714:. 1→2 accomplishes both the heat rejection and the compression. Originally developed for use in reciprocating engines.
3630:. Originally developed for use in reciprocating engines. The external combustion version of this cycle is known as the
5068:
1958:
1715:
126:
116:
4624:
5547:
5437:
5351:
Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 452.
4736:
3870:
3688:
3345:
2490:
2470:
1448:
1410:
1374:
86:
5701:
5294:
1688:
1203:
951:
397:
210:
200:
5153:
3049:
For the ideal
Stirling cycle, no volume change happens in process 4-1 and 2-3, thus equation (3) simplifies to:
1928:
Because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a
4581:
1724:
5656:
4099:
3170:
2458:
Thermodynamic power cycles are the basis for the operation of heat engines, which supply most of the world's
5742:
5681:
5666:
5612:
3957:
3684:
3158:
1929:
1901:
1615:
1443:
1240:
943:
882:
418:
407:
73:
2429:
cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T)
1702:
During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure.
2329:
1548:
1468:
1265:
349:
103:
78:
4516:
2236:). Energy transfer is considered as heat removed from the system, as the work done by the system is zero.
5527:
5487:
3272:
3174:
1711:
1659:
1483:
1060:
373:
219:
68:
3263:
idealized counterparts; e.g., isochoric expansion (process 1-2) occurs with some actual volume change.
5671:
5390:
Hill and
Peterson. "Mechanics and Thermodynamics of Propulsion", 2nd ed. Prentice Hall, 1991. 760 pp.
4034:
1675:
1563:
1488:
1478:
278:
152:
140:
2079:
If the cyclic process moves clockwise around the loop, then W will be positive, and it represents a
5676:
5577:
3560:
3531:
3309:
2274:
1876:
1508:
1503:
1270:
258:
253:
166:
5203:
In general, for any cyclic process the state points can be connected by reversible paths, so that
2536:
output from the ideal
Stirling cycle (net work out), consisting of 4 thermodynamic processes, is:
5533:
4615:
4002:
3392:
3353:
3303:
3285:
3146:
2280:
1703:
1597:
1260:
1208:
1121:
1066:
1011:
440:
424:
311:
263:
248:
238:
47:
41:
5034:
3749:
2930:{\displaystyle W_{3\to 4}=\int _{V_{3}}^{V_{4}}P\,dV,\,\,{\text{positive, work done by system}}}
2735:{\displaystyle W_{1\to 2}=\int _{V_{1}}^{V_{2}}P\,dV,\,\,{\text{negative, work done on system}}}
2286:
2245:
2210:
2175:
2140:
2105:
1255:
845:
798:
713:
666:
578:
531:
5323:
5316:
5696:
5518:
5352:
5327:
3821:
3445:
3297:
3279:
3039:{\displaystyle W_{4\to 1}=\int _{V_{4}}^{V_{1}}P\,dV,\,\,{\text{zero work since }}V_{4}=V_{1}}
2844:{\displaystyle W_{2\to 3}=\int _{V_{2}}^{V_{3}}P\,dV,\,\,{\text{zero work since }}V_{2}=V_{3}}
2426:
2204:
2095:
The following processes are often used to describe different stages of a thermodynamic cycle:
1592:
1553:
1543:
1115:
913:
749:
741:
614:
243:
233:
175:
4709:
4680:
1841:
5638:
3291:
2649:{\displaystyle {\text{(3)}}\qquad W_{\rm {net}}=W_{1\to 2}+W_{2\to 3}+W_{3\to 4}+W_{4\to 1}}
2169:
2137: : The process is at a constant temperature during that part of the cycle (T=constant,
1811:
1513:
1498:
1438:
1433:
1250:
1245:
971:
895:
363:
228:
4984:
4957:
4915:
are two other reversible cycles that use regeneration to obtain isothermal heat transfer.
3930:
5661:
3736:
3506:
2533:
2478:
1896:
1671:
1463:
1311:
965:
606:
429:
190:
157:
4073:
1714:
are process dependent. For a cycle for which the system returns to its initial state the
17:
482:
5628:
5587:
5572:
5557:
5492:
5482:
5477:
5452:
5021:
4924:
4912:
4908:
3847:
3827:
3803:
3783:
3663:
3631:
3568:
3538:
3489:
3399:
3218:
2518:
2514:
2510:
2459:
1872:
1791:
1696:
1667:
1518:
1288:
824:
777:
692:
645:
557:
510:
388:
268:
205:
195:
63:
33:
2277: : The process that proceeds without any change in enthalpy or specific enthalpy.
5716:
5691:
5607:
5562:
5523:
5497:
5467:
5462:
5144:
3656:
3598:
3513:
3466:
3421:
3211:
2506:
2502:
2494:
2486:
2463:
1663:
1587:
905:
474:
435:
147:
2444:
5597:
5592:
5567:
5513:
5472:
4827:
4599:
4593:
3695:
3639:
3438:
3375:
3154:
2482:
1691:, the cycle is reversible. Whether carried out reversible or irreversibly, the net
1538:
1523:
1473:
956:
3316:
Some example thermodynamic cycles and their constituent processes are as follows:
2201:). Energy transfer is considered as heat removed from or work done by the system.
2166:). Energy transfer is considered as heat removed from or work done by the system.
3777:
3271:
In practice, simple idealized thermodynamic cycles are usually made out of four
3235:
3203:
3162:
2498:
2453:
2419:
2080:
1680:
1493:
301:
5275:
meaning that the net entropy change of the working fluid over a cycle is zero.
3173:. Multiple compression and expansion cycles allow gas refrigeration systems to
5602:
5289:
4611:
4607:
3719:
3627:
3207:
2474:
2399:
2391:
2239:
2172: : Pressure in that part of the cycle will remain constant. (P=constant,
2134:
1582:
1528:
2083:. If it moves counterclockwise, then W will be negative, and it represents a
5067:
Entropy is a state function and is defined in an absolute sense through the
4740:
3711:
3680:
3623:
3228:
3150:
2524:
2403:
2382:
2099:
2084:
1920:
1684:
180:
3189:
2002:
This work is equal to the balance of heat (Q) transferred into the system:
1670:
into and out of the system, while varying pressure, temperature, and other
3619:
2411:
1296:
1213:
1005:
413:
185:
5398:
5284:
2407:
1692:
402:
3124:{\displaystyle {\text{(4)}}\qquad W_{\rm {net}}=W_{1\to 2}+W_{3\to 4}}
2102: : No energy transfer as heat (Q) during that part of the cycle (
3615:
2415:
3242:
3748:
2381:
1919:
5147:
to the final state, so that for an isothermal reversible process
3753:
An illustration of an ideal cycle heat engine (arrows clockwise).
2131:). Energy transfer is considered as work done by the system only.
1788:
The above states that there is no change of the internal energy (
1707:
378:
5402:
1895:. Power cycles are cycles which convert some heat input into a
1875:. Thermodynamic cycles are often represented mathematically as
4981:
and the bottom isotherm is all at the same cooler temperature
2326: : The process where the net entropy production is zero;
2271:). It is adiabatic (no heat nor mass exchange) and reversible.
1912:
directions indicate power and heat pump cycles, respectively.
1838:
represents the total work and heat input during the cycle and
3999:
Under this set of assumptions, for processes A and C we have
3256:
Actual and ideal overlaid, showing difference in work output
2242: : The process is one of constant entropy (S=constant,
5376:, 5th edition. John Wiley & Sons, 1997. Chapter 21,
3768:
RIGHT (B) and LEFT (D) of the loop: a pair of parallel
3761:
TOP (A) and BOTTOM (C) of the loop: a pair of parallel
4506:{\displaystyle \Delta U_{cycle}=Q_{cycle}-W_{cycle}=0}
2386:
Description of each point in the thermodynamic cycles.
5212:
5156:
5080:
5037:
4987:
4960:
4941:
LEFT and RIGHT sides of the loop: a pair of parallel
4934:
TOP and BOTTOM of the loop: a pair of quasi-parallel
4839:
4752:
4712:
4683:
4627:
4519:
4421:
4153:
4102:
4076:
4037:
4005:
3960:
3933:
3873:
3850:
3830:
3806:
3786:
3757:
An ideal cycle is simple to analyze and consists of:
3058:
2944:
2858:
2749:
2663:
2545:
2332:
2289:
2248:
2213:
2178:
2143:
2108:
2065:{\displaystyle {\text{(2)}}\qquad W=Q=Q_{in}-Q_{out}}
2011:
1961:
1879:
in the modeling of the workings of an actual device.
1844:
1814:
1794:
1727:
1124:
1069:
1014:
974:
848:
827:
801:
780:
752:
716:
695:
669:
648:
617:
581:
560:
534:
513:
485:
4816:{\displaystyle \ COP=1+{\frac {T_{L}}{T_{H}-T_{L}}}}
2207: : The process is constant volume (V=constant,
5647:
5621:
5546:
5506:
5447:
5436:
5265:{\displaystyle \oint dS=\oint {dQ_{rev} \over T}=0}
2394:is an example of a reversible thermodynamic cycle.
1674:within the system, and that eventually returns the
5315:
5264:
5191:
5132:
5055:
5000:
4973:
4897:{\displaystyle \ COP={\frac {T_{L}}{T_{H}-T_{L}}}}
4896:
4815:
4727:
4698:
4666:
4569:
4505:
4407:
4136:
4088:
4062:
4023:
3988:
3946:
3916:
3856:
3836:
3812:
3792:
3123:
3038:
2929:
2843:
2734:
2648:
2365:
2312:
2263:
2228:
2193:
2158:
2123:
2064:
1991:
1863:
1830:
1800:
1777:
1687:. If at every point in the cycle the system is in
1160:
1105:
1050:
995:
857:
833:
810:
786:
761:
725:
701:
678:
654:
629:
590:
566:
543:
519:
494:
5133:{\displaystyle S=\int _{0}^{T}{dQ_{rev} \over T}}
3221:and the actual performance of a Stirling engine:
1992:{\displaystyle {\text{(1)}}\qquad W=\oint P\ dV}
1887:Two primary classes of thermodynamic cycles are
27:Linked cyclic series of thermodynamic processes
4667:{\displaystyle \eta =1-{\frac {T_{L}}{T_{H}}}}
1948:). The area enclosed by the loop is the work (
1695:change of the system is zero, as entropy is a
5414:
5387:, 7th ed. New York: McGraw-Hill, 2011. Print.
4950:isothermal processes, which are described by
3917:{\displaystyle \Delta U=\int _{a}^{b}C_{v}dT}
1635:
8:
5378:Entropy and the Second Law of Thermodynamics
5314:Cengel, Yunus A.; Boles, Michael A. (2002).
3996:for any process undergone by a perfect gas.
2283: : The process that obeys the relation
5028:remains unchanged during a cyclic process:
5444:
5421:
5407:
5399:
5192:{\displaystyle \Delta S={Q_{rev} \over T}}
1642:
1628:
1191:
343:
162:
40:
29:
5238:
5228:
5211:
5172:
5166:
5155:
5112:
5102:
5096:
5091:
5079:
5036:
4992:
4986:
4965:
4959:
4885:
4872:
4861:
4855:
4838:
4804:
4791:
4780:
4774:
4751:
4735:the highest. For Carnot power cycles the
4718:
4713:
4711:
4689:
4684:
4682:
4656:
4646:
4640:
4626:
4549:
4524:
4518:
4479:
4454:
4429:
4420:
4396:
4383:
4367:
4354:
4335:
4322:
4309:
4293:
4280:
4267:
4251:
4238:
4225:
4209:
4196:
4183:
4158:
4152:
4122:
4101:
4075:
4048:
4036:
4004:
3974:
3959:
3938:
3932:
3902:
3892:
3887:
3872:
3849:
3829:
3805:
3785:
3109:
3090:
3070:
3069:
3059:
3057:
3030:
3017:
3008:
3007:
3006:
2996:
2985:
2980:
2973:
2968:
2949:
2943:
2922:
2921:
2920:
2910:
2899:
2894:
2887:
2882:
2863:
2857:
2835:
2822:
2813:
2812:
2811:
2801:
2790:
2785:
2778:
2773:
2754:
2748:
2727:
2726:
2725:
2715:
2704:
2699:
2692:
2687:
2668:
2662:
2634:
2615:
2596:
2577:
2557:
2556:
2546:
2544:
2342:
2331:
2298:
2297:
2288:
2247:
2212:
2177:
2142:
2107:
2050:
2034:
2012:
2010:
1962:
1960:
1849:
1843:
1819:
1813:
1793:
1778:{\displaystyle \Delta U=E_{in}-E_{out}=0}
1757:
1741:
1726:
1123:
1068:
1013:
973:
847:
826:
800:
779:
751:
715:
694:
668:
647:
616:
580:
559:
533:
512:
484:
5383:Çengel, Yunus A., and Michael A. Boles.
5347:
5345:
5343:
4137:{\displaystyle Q=\Delta U=C_{v}\Delta T}
4070:, whereas for processes B and D we have
3558:
3343:
3318:
3188:
2532:For example :--the pressure-volume
2523:
2443:
5583:Homogeneous charge compression ignition
5385:Thermodynamics: An Engineering Approach
5318:Thermodynamics: an engineering approach
5306:
5143:where a reversible path is chosen from
3145:Thermodynamic heat pump cycles are the
1388:
1365:
1319:
1279:
1229:
1194:
387:
362:
291:
218:
165:
32:
4602:is a cycle composed of the totally
3989:{\displaystyle \Delta U=C_{v}\Delta T}
2521:, which also models hot air engines.
7:
4830:the coefficient of performance is:
4706:is the lowest cycle temperature and
3416:The second Ericsson cycle from 1853
2366:{\displaystyle dS-{\frac {dQ}{T}}=0}
4570:{\displaystyle Q_{cycle}=W_{cycle}}
5157:
4614:heat addition and rejection. The
4422:
4128:
4109:
4054:
4015:
3980:
3961:
3874:
3077:
3074:
3071:
2564:
2561:
2558:
1728:
849:
802:
717:
670:
582:
535:
355:Intensive and extensive properties
25:
4147:The total work done per cycle is
3585:Differs from Otto cycle in that V
3141:Heat pump and refrigeration cycle
2091:A list of thermodynamic processes
5372:Halliday, Resnick & Walker.
5322:. Boston: McGraw-Hill. pp.
3864:are always given by the formula
3241:
3234:
3227:
1808:) of the system over the cycle.
1658:consists of linked sequences of
1611:
1610:
930:Table of thermodynamic equations
4063:{\displaystyle Q=C_{p}\Delta T}
3267:Well-known thermodynamic cycles
3223:
3184:
3064:
2551:
2017:
1967:
1406:Maxwell's thermodynamic surface
4610:compression and expansion and
4402:
4376:
4373:
4347:
4341:
4315:
4299:
4273:
4257:
4231:
4215:
4189:
3820:for a closed system since its
3776:If the working substance is a
3167:absorption refrigeration cycle
3113:
3094:
2953:
2867:
2758:
2672:
2638:
2619:
2600:
2581:
1910:clockwise and counterclockwise
1706:(or path quantities), such as
1140:
1128:
1085:
1073:
1030:
1018:
990:
978:
1:
3689:continuous detonation engines
3161:, which models systems using
2924:positive, work done by system
2729:negative, work done on system
2462:and run the vast majority of
1307:Mechanical equivalent of heat
1902:pressure–volume (PV) diagram
919:Onsager reciprocal relations
5488:Stirling (pseudo/adiabatic)
5069:Third Law of Thermodynamics
5012:State functions and entropy
4024:{\displaystyle W=p\Delta v}
3559:Power cycles normally with
3344:Power cycles normally with
2491:external combustion engines
2471:internal combustion engines
1906:temperature–entropy diagram
1716:first law of thermodynamics
1411:Entropy as energy dispersal
1222:"Perpetual motion" machines
1161:{\displaystyle G(T,p)=H-TS}
1106:{\displaystyle A(T,V)=U-TS}
1051:{\displaystyle H(S,p)=U+pV}
5759:
5056:{\displaystyle \oint dZ=0}
4922:
4737:coefficient of performance
4591:
3138:
2451:
2313:{\displaystyle pV^{\,n}=C}
2264:{\displaystyle \delta S=0}
2229:{\displaystyle \delta V=0}
2194:{\displaystyle \delta P=0}
2159:{\displaystyle \delta T=0}
2124:{\displaystyle \delta Q=0}
858:{\displaystyle \partial T}
811:{\displaystyle \partial V}
726:{\displaystyle \partial p}
679:{\displaystyle \partial V}
591:{\displaystyle \partial T}
544:{\displaystyle \partial S}
5295:Thermogravitational cycle
3737:Gasoline / petrol engines
3527:isochoric then adiabatic
3370:A reversed Brayton cycle
1689:thermodynamic equilibrium
1332:An Inquiry Concerning the
18:Thermodynamic power cycle
4582:thermodynamic efficiency
1345:Heterogeneous Substances
762:{\displaystyle \alpha =}
630:{\displaystyle \beta =-}
5733:Thermodynamic processes
5374:Fundamentals of Physics
4728:{\displaystyle {T_{H}}}
4699:{\displaystyle {T_{L}}}
3348:- or heat pump cycles:
3273:thermodynamic processes
3165:that change phase. The
3159:vapor compression cycle
2378:Example: The Otto cycle
1952:) done by the process:
1864:{\displaystyle E_{out}}
1660:thermodynamic processes
5266:
5193:
5134:
5057:
5002:
4975:
4898:
4817:
4729:
4700:
4668:
4571:
4507:
4409:
4138:
4090:
4064:
4025:
3990:
3948:
3918:
3858:
3838:
3814:
3800:is only a function of
3794:
3754:
3288:(constant temperature)
3194:
3125:
3040:
2931:
2845:
2736:
2650:
2529:
2449:
2387:
2367:
2314:
2265:
2230:
2195:
2160:
2125:
2066:
1993:
1925:
1865:
1832:
1831:{\displaystyle E_{in}}
1802:
1779:
1162:
1107:
1052:
997:
996:{\displaystyle U(S,V)}
859:
835:
812:
788:
763:
727:
703:
680:
656:
631:
592:
568:
545:
521:
496:
475:Specific heat capacity
79:Quantum thermodynamics
5738:Thermodynamic systems
5728:Equilibrium chemistry
5267:
5194:
5135:
5058:
5003:
5001:{\displaystyle T_{C}}
4976:
4974:{\displaystyle T_{H}}
4899:
4818:
4730:
4701:
4669:
4572:
4508:
4410:
4139:
4091:
4065:
4026:
3991:
3949:
3947:{\displaystyle C_{v}}
3919:
3859:
3839:
3815:
3795:
3752:
3250:Ideal Stirling cycle
3192:
3181:Modeling real systems
3126:
3041:
3010:zero work since
2932:
2846:
2815:zero work since
2737:
2651:
2527:
2447:
2385:
2368:
2315:
2266:
2231:
2196:
2161:
2126:
2067:
1994:
1936:axis shows pressure (
1923:
1877:quasistatic processes
1866:
1833:
1803:
1780:
1343:On the Equilibrium of
1163:
1108:
1061:Helmholtz free energy
1053:
998:
860:
836:
813:
789:
764:
728:
704:
681:
657:
632:
593:
569:
546:
522:
497:
5723:Thermodynamic cycles
5672:Regenerative cooling
5550:combustion / thermal
5449:Without phase change
5440:combustion / thermal
5430:Thermodynamic cycles
5210:
5154:
5078:
5035:
5024:then the balance of
4985:
4958:
4837:
4750:
4710:
4681:
4625:
4604:reversible processes
4517:
4419:
4151:
4100:
4074:
4035:
4003:
3958:
3931:
3871:
3848:
3828:
3804:
3784:
3632:first Ericsson cycle
3532:Manson-Guise engines
3336:Heat rejection, 4→1
3210:can be modeled as a
3056:
2942:
2856:
2747:
2661:
2543:
2489:. Cycles that model
2448:Heat engine diagram.
2406:expansion: Constant
2330:
2287:
2246:
2211:
2176:
2141:
2106:
2009:
1959:
1916:Relationship to work
1842:
1812:
1792:
1725:
1356:Motive Power of Fire
1122:
1067:
1012:
972:
924:Bridgman's equations
901:Fundamental relation
846:
825:
799:
778:
750:
714:
693:
667:
646:
615:
579:
558:
532:
511:
483:
5101:
4089:{\displaystyle W=0}
3897:
3561:internal combustion
3346:external combustion
3330:Heat addition, 2→3
3320:
3312:(constant enthalpy)
3294:(constant pressure)
3253:Actual performance
3171:Hampson–Linde cycle
2992:
2906:
2797:
2711:
1944:axis shows volume (
1656:thermodynamic cycle
1334:Source ... Friction
1266:Loschmidt's paradox
458:Material properties
336:Conjugate variables
5262:
5189:
5130:
5087:
5053:
4998:
4971:
4894:
4813:
4725:
4696:
4664:
4616:thermal efficiency
4567:
4503:
4405:
4134:
4086:
4060:
4021:
3986:
3944:
3914:
3883:
3854:
3834:
3810:
3790:
3755:
3393:Carnot heat engine
3319:
3306:(constant entropy)
3195:
3121:
3036:
2964:
2927:
2878:
2841:
2769:
2732:
2683:
2646:
2530:
2450:
2388:
2363:
2310:
2261:
2226:
2191:
2156:
2121:
2062:
1989:
1926:
1861:
1828:
1798:
1775:
1704:Process quantities
1598:Order and disorder
1354:Reflections on the
1261:Heat death paradox
1158:
1103:
1048:
993:
855:
831:
808:
784:
759:
723:
699:
676:
652:
627:
588:
564:
541:
517:
495:{\displaystyle c=}
492:
465:Property databases
441:Reduced properties
425:Chemical potential
389:Functions of state
312:Thermal efficiency
48:Carnot heat engine
5710:
5709:
5687:Vapor-compression
5613:Staged combustion
5542:
5541:
5507:With phase change
5254:
5187:
5128:
4892:
4842:
4811:
4755:
4662:
3857:{\displaystyle b}
3837:{\displaystyle a}
3822:internal pressure
3813:{\displaystyle T}
3793:{\displaystyle U}
3742:
3741:
3474:variable pressure
3327:Compression, 1→2
3300:(constant volume)
3260:
3259:
3199:
3198:
3062:
3011:
2925:
2816:
2730:
2549:
2418:(v), Decrease in
2414:(P), Increase in
2410:(s), Decrease in
2355:
2015:
1982:
1965:
1932:. A PV diagram's
1801:{\displaystyle U}
1652:
1651:
1593:Self-organization
1418:
1417:
1116:Gibbs free energy
914:Maxwell relations
872:
871:
868:
867:
834:{\displaystyle V}
787:{\displaystyle 1}
742:Thermal expansion
736:
735:
702:{\displaystyle V}
655:{\displaystyle 1}
601:
600:
567:{\displaystyle N}
520:{\displaystyle T}
448:
447:
364:Process functions
350:Property diagrams
329:System properties
319:
318:
284:Endoreversibility
176:Equation of state
16:(Redirected from
5750:
5682:Vapor absorption
5445:
5423:
5416:
5409:
5400:
5360:
5349:
5338:
5337:
5321:
5311:
5271:
5269:
5268:
5263:
5255:
5250:
5249:
5248:
5229:
5198:
5196:
5195:
5190:
5188:
5183:
5182:
5167:
5139:
5137:
5136:
5131:
5129:
5124:
5123:
5122:
5103:
5100:
5095:
5062:
5060:
5059:
5054:
5007:
5005:
5004:
4999:
4997:
4996:
4980:
4978:
4977:
4972:
4970:
4969:
4903:
4901:
4900:
4895:
4893:
4891:
4890:
4889:
4877:
4876:
4866:
4865:
4856:
4840:
4822:
4820:
4819:
4814:
4812:
4810:
4809:
4808:
4796:
4795:
4785:
4784:
4775:
4753:
4734:
4732:
4731:
4726:
4724:
4723:
4722:
4705:
4703:
4702:
4697:
4695:
4694:
4693:
4673:
4671:
4670:
4665:
4663:
4661:
4660:
4651:
4650:
4641:
4576:
4574:
4573:
4568:
4566:
4565:
4541:
4540:
4512:
4510:
4509:
4504:
4496:
4495:
4471:
4470:
4446:
4445:
4414:
4412:
4411:
4406:
4401:
4400:
4388:
4387:
4372:
4371:
4359:
4358:
4340:
4339:
4327:
4326:
4314:
4313:
4298:
4297:
4285:
4284:
4272:
4271:
4256:
4255:
4243:
4242:
4230:
4229:
4214:
4213:
4201:
4200:
4188:
4187:
4175:
4174:
4143:
4141:
4140:
4135:
4127:
4126:
4095:
4093:
4092:
4087:
4069:
4067:
4066:
4061:
4053:
4052:
4030:
4028:
4027:
4022:
3995:
3993:
3992:
3987:
3979:
3978:
3953:
3951:
3950:
3945:
3943:
3942:
3923:
3921:
3920:
3915:
3907:
3906:
3896:
3891:
3863:
3861:
3860:
3855:
3843:
3841:
3840:
3835:
3819:
3817:
3816:
3811:
3799:
3797:
3796:
3791:
3507:Stirling engines
3321:
3245:
3238:
3231:
3224:
3185:
3135:Heat pump cycles
3130:
3128:
3127:
3122:
3120:
3119:
3101:
3100:
3082:
3081:
3080:
3063:
3060:
3045:
3043:
3042:
3037:
3035:
3034:
3022:
3021:
3012:
3009:
2991:
2990:
2989:
2979:
2978:
2977:
2960:
2959:
2936:
2934:
2933:
2928:
2926:
2923:
2905:
2904:
2903:
2893:
2892:
2891:
2874:
2873:
2850:
2848:
2847:
2842:
2840:
2839:
2827:
2826:
2817:
2814:
2796:
2795:
2794:
2784:
2783:
2782:
2765:
2764:
2741:
2739:
2738:
2733:
2731:
2728:
2710:
2709:
2708:
2698:
2697:
2696:
2679:
2678:
2655:
2653:
2652:
2647:
2645:
2644:
2626:
2625:
2607:
2606:
2588:
2587:
2569:
2568:
2567:
2550:
2547:
2479:gasoline engines
2372:
2370:
2369:
2364:
2356:
2351:
2343:
2319:
2317:
2316:
2311:
2303:
2302:
2270:
2268:
2267:
2262:
2235:
2233:
2232:
2227:
2200:
2198:
2197:
2192:
2165:
2163:
2162:
2157:
2130:
2128:
2127:
2122:
2071:
2069:
2068:
2063:
2061:
2060:
2042:
2041:
2016:
2013:
1998:
1996:
1995:
1990:
1980:
1966:
1963:
1893:heat pump cycles
1870:
1868:
1867:
1862:
1860:
1859:
1837:
1835:
1834:
1829:
1827:
1826:
1807:
1805:
1804:
1799:
1784:
1782:
1781:
1776:
1768:
1767:
1749:
1748:
1664:transfer of heat
1644:
1637:
1630:
1614:
1613:
1321:Key publications
1302:
1301:("living force")
1251:Brownian ratchet
1246:Entropy and life
1241:Entropy and time
1192:
1167:
1165:
1164:
1159:
1112:
1110:
1109:
1104:
1057:
1055:
1054:
1049:
1002:
1000:
999:
994:
896:Clausius theorem
891:Carnot's theorem
864:
862:
861:
856:
840:
838:
837:
832:
817:
815:
814:
809:
793:
791:
790:
785:
772:
771:
768:
766:
765:
760:
732:
730:
729:
724:
708:
706:
705:
700:
685:
683:
682:
677:
661:
659:
658:
653:
640:
639:
636:
634:
633:
628:
597:
595:
594:
589:
573:
571:
570:
565:
550:
548:
547:
542:
526:
524:
523:
518:
505:
504:
501:
499:
498:
493:
471:
470:
344:
163:
44:
30:
21:
5758:
5757:
5753:
5752:
5751:
5749:
5748:
5747:
5713:
5712:
5711:
5706:
5643:
5617:
5549:
5538:
5528:Organic Rankine
5502:
5456:
5453:hot air engines
5450:
5439:
5432:
5427:
5397:
5369:
5367:Further reading
5364:
5363:
5350:
5341:
5334:
5313:
5312:
5308:
5303:
5281:
5234:
5230:
5208:
5207:
5168:
5152:
5151:
5108:
5104:
5076:
5075:
5033:
5032:
5014:
4988:
4983:
4982:
4961:
4956:
4955:
4927:
4921:
4881:
4868:
4867:
4857:
4835:
4834:
4800:
4787:
4786:
4776:
4748:
4747:
4714:
4708:
4707:
4685:
4679:
4678:
4652:
4642:
4623:
4622:
4596:
4590:
4584:of the cycle).
4545:
4520:
4515:
4514:
4475:
4450:
4425:
4417:
4416:
4392:
4379:
4363:
4350:
4331:
4318:
4305:
4289:
4276:
4263:
4247:
4234:
4221:
4205:
4192:
4179:
4154:
4149:
4148:
4118:
4098:
4097:
4072:
4071:
4044:
4033:
4032:
4001:
4000:
3970:
3956:
3955:
3934:
3929:
3928:
3898:
3869:
3868:
3846:
3845:
3844:to final state
3826:
3825:
3802:
3801:
3782:
3781:
3747:
3592:
3588:
3475:
3333:Expansion, 3→4
3282:(constant heat)
3269:
3183:
3143:
3137:
3105:
3086:
3065:
3054:
3053:
3026:
3013:
2981:
2969:
2945:
2940:
2939:
2895:
2883:
2859:
2854:
2853:
2831:
2818:
2786:
2774:
2750:
2745:
2744:
2700:
2688:
2664:
2659:
2658:
2630:
2611:
2592:
2573:
2552:
2541:
2540:
2534:mechanical work
2515:hot air engines
2513:, which models
2505:, which models
2497:, which models
2485:, which models
2477:, which models
2456:
2442:
2380:
2344:
2328:
2327:
2293:
2285:
2284:
2244:
2243:
2209:
2208:
2174:
2173:
2139:
2138:
2104:
2103:
2093:
2046:
2030:
2007:
2006:
1957:
1956:
1918:
1897:mechanical work
1885:
1845:
1840:
1839:
1815:
1810:
1809:
1790:
1789:
1753:
1737:
1723:
1722:
1672:state variables
1648:
1603:
1602:
1578:
1570:
1569:
1568:
1428:
1420:
1419:
1398:
1384:
1359:
1355:
1348:
1344:
1337:
1333:
1300:
1293:
1275:
1256:Maxwell's demon
1218:
1189:
1188:
1172:
1171:
1170:
1120:
1119:
1118:
1065:
1064:
1063:
1010:
1009:
1008:
970:
969:
968:
966:Internal energy
961:
946:
936:
935:
910:
885:
875:
874:
873:
844:
843:
823:
822:
797:
796:
776:
775:
748:
747:
712:
711:
691:
690:
665:
664:
644:
643:
613:
612:
607:Compressibility
577:
576:
556:
555:
530:
529:
509:
508:
481:
480:
460:
450:
449:
430:Particle number
383:
342:
331:
321:
320:
279:Irreversibility
191:State of matter
158:Isolated system
143:
133:
132:
131:
106:
96:
95:
91:Non-equilibrium
83:
58:
50:
28:
23:
22:
15:
12:
11:
5:
5756:
5754:
5746:
5745:
5743:Thermodynamics
5740:
5735:
5730:
5725:
5715:
5714:
5708:
5707:
5705:
5704:
5699:
5694:
5689:
5684:
5679:
5674:
5669:
5664:
5659:
5653:
5651:
5645:
5644:
5642:
5641:
5636:
5631:
5625:
5623:
5619:
5618:
5616:
5615:
5610:
5605:
5600:
5595:
5590:
5585:
5580:
5575:
5570:
5565:
5560:
5554:
5552:
5544:
5543:
5540:
5539:
5537:
5536:
5531:
5521:
5516:
5510:
5508:
5504:
5503:
5501:
5500:
5495:
5490:
5485:
5480:
5475:
5470:
5465:
5459:
5457:
5448:
5442:
5434:
5433:
5428:
5426:
5425:
5418:
5411:
5403:
5396:
5395:External links
5393:
5392:
5391:
5388:
5381:
5368:
5365:
5362:
5361:
5339:
5332:
5305:
5304:
5302:
5299:
5298:
5297:
5292:
5287:
5280:
5277:
5273:
5272:
5261:
5258:
5253:
5247:
5244:
5241:
5237:
5233:
5227:
5224:
5221:
5218:
5215:
5201:
5200:
5186:
5181:
5178:
5175:
5171:
5165:
5162:
5159:
5141:
5140:
5127:
5121:
5118:
5115:
5111:
5107:
5099:
5094:
5090:
5086:
5083:
5065:
5064:
5052:
5049:
5046:
5043:
5040:
5022:state function
5013:
5010:
4995:
4991:
4968:
4964:
4947:
4946:
4939:
4925:Stirling cycle
4923:Main article:
4920:
4919:Stirling cycle
4917:
4913:Ericsson cycle
4909:Stirling cycle
4905:
4904:
4888:
4884:
4880:
4875:
4871:
4864:
4860:
4854:
4851:
4848:
4845:
4824:
4823:
4807:
4803:
4799:
4794:
4790:
4783:
4779:
4773:
4770:
4767:
4764:
4761:
4758:
4721:
4717:
4692:
4688:
4675:
4674:
4659:
4655:
4649:
4645:
4639:
4636:
4633:
4630:
4592:Main article:
4589:
4586:
4564:
4561:
4558:
4555:
4552:
4548:
4544:
4539:
4536:
4533:
4530:
4527:
4523:
4502:
4499:
4494:
4491:
4488:
4485:
4482:
4478:
4474:
4469:
4466:
4463:
4460:
4457:
4453:
4449:
4444:
4441:
4438:
4435:
4432:
4428:
4424:
4404:
4399:
4395:
4391:
4386:
4382:
4378:
4375:
4370:
4366:
4362:
4357:
4353:
4349:
4346:
4343:
4338:
4334:
4330:
4325:
4321:
4317:
4312:
4308:
4304:
4301:
4296:
4292:
4288:
4283:
4279:
4275:
4270:
4266:
4262:
4259:
4254:
4250:
4246:
4241:
4237:
4233:
4228:
4224:
4220:
4217:
4212:
4208:
4204:
4199:
4195:
4191:
4186:
4182:
4178:
4173:
4170:
4167:
4164:
4161:
4157:
4133:
4130:
4125:
4121:
4117:
4114:
4111:
4108:
4105:
4085:
4082:
4079:
4059:
4056:
4051:
4047:
4043:
4040:
4020:
4017:
4014:
4011:
4008:
3985:
3982:
3977:
3973:
3969:
3966:
3963:
3941:
3937:
3927:Assuming that
3925:
3924:
3913:
3910:
3905:
3901:
3895:
3890:
3886:
3882:
3879:
3876:
3853:
3833:
3809:
3789:
3774:
3773:
3766:
3746:
3743:
3740:
3739:
3734:
3731:
3728:
3725:
3722:
3716:
3715:
3709:
3706:
3703:
3700:
3698:
3692:
3691:
3678:
3675:
3672:
3669:
3666:
3660:
3659:
3654:
3651:
3648:
3645:
3642:
3636:
3635:
3613:
3610:
3607:
3604:
3601:
3595:
3594:
3590:
3586:
3583:
3580:
3577:
3574:
3571:
3565:
3564:
3556:
3555:
3553:
3550:
3547:
3544:
3541:
3535:
3534:
3528:
3525:
3522:
3519:
3516:
3510:
3509:
3504:
3501:
3498:
3495:
3492:
3486:
3485:
3483:
3480:
3477:
3472:
3469:
3463:
3462:
3460:
3457:
3454:
3451:
3448:
3442:
3441:
3436:
3433:
3430:
3427:
3424:
3418:
3417:
3414:
3411:
3408:
3405:
3402:
3396:
3395:
3390:
3387:
3384:
3381:
3378:
3372:
3371:
3368:
3365:
3362:
3359:
3356:
3350:
3349:
3341:
3340:
3337:
3334:
3331:
3328:
3325:
3314:
3313:
3307:
3301:
3295:
3289:
3283:
3268:
3265:
3258:
3257:
3254:
3251:
3247:
3246:
3239:
3232:
3219:Stirling cycle
3197:
3196:
3182:
3179:
3149:for household
3139:Main article:
3136:
3133:
3132:
3131:
3118:
3115:
3112:
3108:
3104:
3099:
3096:
3093:
3089:
3085:
3079:
3076:
3073:
3068:
3047:
3046:
3033:
3029:
3025:
3020:
3016:
3005:
3002:
2999:
2995:
2988:
2984:
2976:
2972:
2967:
2963:
2958:
2955:
2952:
2948:
2937:
2919:
2916:
2913:
2909:
2902:
2898:
2890:
2886:
2881:
2877:
2872:
2869:
2866:
2862:
2851:
2838:
2834:
2830:
2825:
2821:
2810:
2807:
2804:
2800:
2793:
2789:
2781:
2777:
2772:
2768:
2763:
2760:
2757:
2753:
2742:
2724:
2721:
2718:
2714:
2707:
2703:
2695:
2691:
2686:
2682:
2677:
2674:
2671:
2667:
2656:
2643:
2640:
2637:
2633:
2629:
2624:
2621:
2618:
2614:
2610:
2605:
2602:
2599:
2595:
2591:
2586:
2583:
2580:
2576:
2572:
2566:
2563:
2560:
2555:
2519:Ericsson cycle
2511:Stirling cycle
2507:steam turbines
2487:diesel engines
2464:motor vehicles
2460:electric power
2452:Main article:
2441:
2438:
2437:
2436:
2433:
2430:
2423:
2379:
2376:
2375:
2374:
2362:
2359:
2354:
2350:
2347:
2341:
2338:
2335:
2321:
2309:
2306:
2301:
2296:
2292:
2278:
2272:
2260:
2257:
2254:
2251:
2237:
2225:
2222:
2219:
2216:
2202:
2190:
2187:
2184:
2181:
2167:
2155:
2152:
2149:
2146:
2132:
2120:
2117:
2114:
2111:
2092:
2089:
2073:
2072:
2059:
2056:
2053:
2049:
2045:
2040:
2037:
2033:
2029:
2026:
2023:
2020:
2000:
1999:
1988:
1985:
1979:
1976:
1973:
1970:
1917:
1914:
1884:
1881:
1873:thermodynamics
1858:
1855:
1852:
1848:
1825:
1822:
1818:
1797:
1786:
1785:
1774:
1771:
1766:
1763:
1760:
1756:
1752:
1747:
1744:
1740:
1736:
1733:
1730:
1697:state function
1650:
1649:
1647:
1646:
1639:
1632:
1624:
1621:
1620:
1619:
1618:
1605:
1604:
1601:
1600:
1595:
1590:
1585:
1579:
1576:
1575:
1572:
1571:
1567:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1436:
1430:
1429:
1426:
1425:
1422:
1421:
1416:
1415:
1414:
1413:
1408:
1400:
1399:
1397:
1396:
1393:
1389:
1386:
1385:
1383:
1382:
1377:
1375:Thermodynamics
1371:
1368:
1367:
1363:
1362:
1361:
1360:
1351:
1349:
1340:
1338:
1329:
1324:
1323:
1317:
1316:
1315:
1314:
1309:
1304:
1292:
1291:
1289:Caloric theory
1285:
1282:
1281:
1277:
1276:
1274:
1273:
1268:
1263:
1258:
1253:
1248:
1243:
1237:
1234:
1233:
1227:
1226:
1225:
1224:
1217:
1216:
1211:
1206:
1200:
1197:
1196:
1190:
1187:
1186:
1183:
1179:
1178:
1177:
1174:
1173:
1169:
1168:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1127:
1113:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1075:
1072:
1058:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1003:
992:
989:
986:
983:
980:
977:
962:
960:
959:
954:
948:
947:
942:
941:
938:
937:
934:
933:
926:
921:
916:
909:
908:
903:
898:
893:
887:
886:
881:
880:
877:
876:
870:
869:
866:
865:
854:
851:
841:
830:
819:
818:
807:
804:
794:
783:
769:
758:
755:
745:
738:
737:
734:
733:
722:
719:
709:
698:
687:
686:
675:
672:
662:
651:
637:
626:
623:
620:
610:
603:
602:
599:
598:
587:
584:
574:
563:
552:
551:
540:
537:
527:
516:
502:
491:
488:
478:
469:
468:
467:
461:
456:
455:
452:
451:
446:
445:
444:
443:
438:
433:
422:
411:
392:
391:
385:
384:
382:
381:
376:
370:
367:
366:
360:
359:
358:
357:
352:
333:
332:
327:
326:
323:
322:
317:
316:
315:
314:
309:
304:
296:
295:
289:
288:
287:
286:
281:
276:
271:
269:Free expansion
266:
261:
256:
251:
246:
241:
236:
231:
223:
222:
216:
215:
214:
213:
208:
206:Control volume
203:
198:
196:Phase (matter)
193:
188:
183:
178:
170:
169:
161:
160:
155:
150:
144:
139:
138:
135:
134:
130:
129:
124:
119:
114:
108:
107:
102:
101:
98:
97:
94:
93:
82:
81:
76:
71:
66:
60:
59:
56:
55:
52:
51:
46:The classical
45:
37:
36:
34:Thermodynamics
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5755:
5744:
5741:
5739:
5736:
5734:
5731:
5729:
5726:
5724:
5721:
5720:
5718:
5703:
5700:
5698:
5695:
5693:
5690:
5688:
5685:
5683:
5680:
5678:
5677:Transcritical
5675:
5673:
5670:
5668:
5665:
5663:
5660:
5658:
5657:Hampson–Linde
5655:
5654:
5652:
5650:
5649:Refrigeration
5646:
5640:
5637:
5635:
5632:
5630:
5627:
5626:
5624:
5620:
5614:
5611:
5609:
5606:
5604:
5601:
5599:
5596:
5594:
5591:
5589:
5586:
5584:
5581:
5579:
5578:Gas-generator
5576:
5574:
5571:
5569:
5566:
5564:
5563:Brayton/Joule
5561:
5559:
5556:
5555:
5553:
5551:
5545:
5535:
5532:
5529:
5525:
5522:
5520:
5517:
5515:
5512:
5511:
5509:
5505:
5499:
5496:
5494:
5491:
5489:
5486:
5484:
5481:
5479:
5476:
5474:
5471:
5469:
5468:Brayton/Joule
5466:
5464:
5461:
5460:
5458:
5454:
5446:
5443:
5441:
5435:
5431:
5424:
5419:
5417:
5412:
5410:
5405:
5404:
5401:
5394:
5389:
5386:
5382:
5379:
5375:
5371:
5370:
5366:
5358:
5357:0-07-238332-1
5354:
5348:
5346:
5344:
5340:
5335:
5333:0-07-238332-1
5329:
5325:
5320:
5319:
5310:
5307:
5300:
5296:
5293:
5291:
5288:
5286:
5283:
5282:
5278:
5276:
5259:
5256:
5251:
5245:
5242:
5239:
5235:
5231:
5225:
5222:
5219:
5216:
5213:
5206:
5205:
5204:
5184:
5179:
5176:
5173:
5169:
5163:
5160:
5150:
5149:
5148:
5146:
5145:absolute zero
5125:
5119:
5116:
5113:
5109:
5105:
5097:
5092:
5088:
5084:
5081:
5074:
5073:
5072:
5070:
5050:
5047:
5044:
5041:
5038:
5031:
5030:
5029:
5027:
5023:
5019:
5011:
5009:
4993:
4989:
4966:
4962:
4953:
4944:
4940:
4937:
4933:
4932:
4931:
4926:
4918:
4916:
4914:
4910:
4886:
4882:
4878:
4873:
4869:
4862:
4858:
4852:
4849:
4846:
4843:
4833:
4832:
4831:
4829:
4805:
4801:
4797:
4792:
4788:
4781:
4777:
4771:
4768:
4765:
4762:
4759:
4756:
4746:
4745:
4744:
4742:
4738:
4719:
4715:
4690:
4686:
4657:
4653:
4647:
4643:
4637:
4634:
4631:
4628:
4621:
4620:
4619:
4617:
4613:
4609:
4605:
4601:
4595:
4587:
4585:
4583:
4578:
4562:
4559:
4556:
4553:
4550:
4546:
4542:
4537:
4534:
4531:
4528:
4525:
4521:
4500:
4497:
4492:
4489:
4486:
4483:
4480:
4476:
4472:
4467:
4464:
4461:
4458:
4455:
4451:
4447:
4442:
4439:
4436:
4433:
4430:
4426:
4397:
4393:
4389:
4384:
4380:
4368:
4364:
4360:
4355:
4351:
4344:
4336:
4332:
4328:
4323:
4319:
4310:
4306:
4302:
4294:
4290:
4286:
4281:
4277:
4268:
4264:
4260:
4252:
4248:
4244:
4239:
4235:
4226:
4222:
4218:
4210:
4206:
4202:
4197:
4193:
4184:
4180:
4176:
4171:
4168:
4165:
4162:
4159:
4155:
4145:
4131:
4123:
4119:
4115:
4112:
4106:
4103:
4083:
4080:
4077:
4057:
4049:
4045:
4041:
4038:
4018:
4012:
4009:
4006:
3997:
3983:
3975:
3971:
3967:
3964:
3954:is constant,
3939:
3935:
3911:
3908:
3903:
3899:
3893:
3888:
3884:
3880:
3877:
3867:
3866:
3865:
3851:
3831:
3823:
3807:
3787:
3779:
3771:
3767:
3764:
3760:
3759:
3758:
3751:
3744:
3738:
3735:
3732:
3729:
3726:
3723:
3721:
3718:
3717:
3713:
3710:
3707:
3704:
3701:
3699:
3697:
3694:
3693:
3690:
3686:
3682:
3679:
3676:
3673:
3670:
3667:
3665:
3662:
3661:
3658:
3657:Diesel engine
3655:
3652:
3649:
3646:
3643:
3641:
3638:
3637:
3633:
3629:
3625:
3621:
3617:
3614:
3611:
3608:
3605:
3602:
3600:
3597:
3596:
3584:
3581:
3578:
3575:
3572:
3570:
3567:
3566:
3562:
3557:
3554:
3551:
3548:
3545:
3542:
3540:
3537:
3536:
3533:
3529:
3526:
3523:
3520:
3517:
3515:
3512:
3511:
3508:
3505:
3502:
3499:
3496:
3493:
3491:
3488:
3487:
3484:
3481:
3478:
3473:
3470:
3468:
3465:
3464:
3461:
3458:
3455:
3452:
3449:
3447:
3444:
3443:
3440:
3439:Steam engines
3437:
3434:
3431:
3428:
3425:
3423:
3420:
3419:
3415:
3412:
3409:
3406:
3403:
3401:
3398:
3397:
3394:
3391:
3388:
3385:
3382:
3379:
3377:
3374:
3373:
3369:
3366:
3363:
3360:
3357:
3355:
3352:
3351:
3347:
3342:
3338:
3335:
3332:
3329:
3326:
3323:
3322:
3317:
3311:
3308:
3305:
3302:
3299:
3296:
3293:
3290:
3287:
3284:
3281:
3278:
3277:
3276:
3274:
3266:
3264:
3255:
3252:
3249:
3248:
3244:
3240:
3237:
3233:
3230:
3226:
3225:
3222:
3220:
3215:
3213:
3212:Brayton cycle
3209:
3205:
3191:
3187:
3186:
3180:
3178:
3176:
3175:liquify gases
3172:
3168:
3164:
3160:
3156:
3155:refrigerators
3152:
3148:
3142:
3134:
3116:
3110:
3106:
3102:
3097:
3091:
3087:
3083:
3066:
3052:
3051:
3050:
3031:
3027:
3023:
3018:
3014:
3003:
3000:
2997:
2993:
2986:
2982:
2974:
2970:
2965:
2961:
2956:
2950:
2946:
2938:
2917:
2914:
2911:
2907:
2900:
2896:
2888:
2884:
2879:
2875:
2870:
2864:
2860:
2852:
2836:
2832:
2828:
2823:
2819:
2808:
2805:
2802:
2798:
2791:
2787:
2779:
2775:
2770:
2766:
2761:
2755:
2751:
2743:
2722:
2719:
2716:
2712:
2705:
2701:
2693:
2689:
2684:
2680:
2675:
2669:
2665:
2657:
2641:
2635:
2631:
2627:
2622:
2616:
2612:
2608:
2603:
2597:
2593:
2589:
2584:
2578:
2574:
2570:
2553:
2539:
2538:
2537:
2535:
2526:
2522:
2520:
2516:
2512:
2508:
2504:
2503:Rankine cycle
2500:
2496:
2495:Brayton cycle
2492:
2488:
2484:
2480:
2476:
2472:
2467:
2465:
2461:
2455:
2446:
2439:
2434:
2431:
2428:
2424:
2421:
2417:
2413:
2409:
2405:
2401:
2397:
2396:
2395:
2393:
2384:
2377:
2360:
2357:
2352:
2348:
2345:
2339:
2336:
2333:
2325:
2322:
2307:
2304:
2299:
2294:
2290:
2282:
2279:
2276:
2273:
2258:
2255:
2252:
2249:
2241:
2238:
2223:
2220:
2217:
2214:
2206:
2203:
2188:
2185:
2182:
2179:
2171:
2168:
2153:
2150:
2147:
2144:
2136:
2133:
2118:
2115:
2112:
2109:
2101:
2098:
2097:
2096:
2090:
2088:
2086:
2082:
2077:
2057:
2054:
2051:
2047:
2043:
2038:
2035:
2031:
2027:
2024:
2021:
2018:
2005:
2004:
2003:
1986:
1983:
1977:
1974:
1971:
1968:
1955:
1954:
1953:
1951:
1947:
1943:
1939:
1935:
1931:
1922:
1915:
1913:
1911:
1907:
1903:
1898:
1894:
1890:
1883:Heat and work
1882:
1880:
1878:
1874:
1856:
1853:
1850:
1846:
1823:
1820:
1816:
1795:
1772:
1769:
1764:
1761:
1758:
1754:
1750:
1745:
1742:
1738:
1734:
1731:
1721:
1720:
1719:
1717:
1713:
1709:
1705:
1700:
1698:
1694:
1690:
1686:
1682:
1677:
1673:
1669:
1665:
1662:that involve
1661:
1657:
1645:
1640:
1638:
1633:
1631:
1626:
1625:
1623:
1622:
1617:
1609:
1608:
1607:
1606:
1599:
1596:
1594:
1591:
1589:
1588:Self-assembly
1586:
1584:
1581:
1580:
1574:
1573:
1565:
1562:
1560:
1559:van der Waals
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1484:von Helmholtz
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1435:
1432:
1431:
1424:
1423:
1412:
1409:
1407:
1404:
1403:
1402:
1401:
1394:
1391:
1390:
1387:
1381:
1378:
1376:
1373:
1372:
1370:
1369:
1364:
1358:
1357:
1350:
1347:
1346:
1339:
1336:
1335:
1328:
1327:
1326:
1325:
1322:
1318:
1313:
1310:
1308:
1305:
1303:
1299:
1295:
1294:
1290:
1287:
1286:
1284:
1283:
1278:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1242:
1239:
1238:
1236:
1235:
1232:
1228:
1223:
1220:
1219:
1215:
1212:
1210:
1207:
1205:
1202:
1201:
1199:
1198:
1193:
1184:
1181:
1180:
1176:
1175:
1155:
1152:
1149:
1146:
1143:
1137:
1134:
1131:
1125:
1117:
1114:
1100:
1097:
1094:
1091:
1088:
1082:
1079:
1076:
1070:
1062:
1059:
1045:
1042:
1039:
1036:
1033:
1027:
1024:
1021:
1015:
1007:
1004:
987:
984:
981:
975:
967:
964:
963:
958:
955:
953:
950:
949:
945:
940:
939:
932:
931:
927:
925:
922:
920:
917:
915:
912:
911:
907:
906:Ideal gas law
904:
902:
899:
897:
894:
892:
889:
888:
884:
879:
878:
852:
842:
828:
821:
820:
805:
795:
781:
774:
773:
770:
756:
753:
746:
743:
740:
739:
720:
710:
696:
689:
688:
673:
663:
649:
642:
641:
638:
624:
621:
618:
611:
608:
605:
604:
585:
575:
561:
554:
553:
538:
528:
514:
507:
506:
503:
489:
486:
479:
476:
473:
472:
466:
463:
462:
459:
454:
453:
442:
439:
437:
436:Vapor quality
434:
432:
431:
426:
423:
421:
420:
415:
412:
409:
405:
404:
399:
396:
395:
394:
393:
390:
386:
380:
377:
375:
372:
371:
369:
368:
365:
361:
356:
353:
351:
348:
347:
346:
345:
341:
337:
330:
325:
324:
313:
310:
308:
305:
303:
300:
299:
298:
297:
294:
290:
285:
282:
280:
277:
275:
274:Reversibility
272:
270:
267:
265:
262:
260:
257:
255:
252:
250:
247:
245:
242:
240:
237:
235:
232:
230:
227:
226:
225:
224:
221:
217:
212:
209:
207:
204:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
177:
174:
173:
172:
171:
168:
164:
159:
156:
154:
151:
149:
148:Closed system
146:
145:
142:
137:
136:
128:
125:
123:
120:
118:
115:
113:
110:
109:
105:
100:
99:
92:
88:
85:
84:
80:
77:
75:
72:
70:
67:
65:
62:
61:
54:
53:
49:
43:
39:
38:
35:
31:
19:
5534:Regenerative
5463:Bell Coleman
5429:
5384:
5377:
5373:
5317:
5309:
5274:
5202:
5142:
5066:
5025:
5017:
5015:
4951:
4948:
4942:
4935:
4928:
4906:
4828:refrigerator
4825:
4676:
4600:Carnot cycle
4597:
4594:Carnot cycle
4588:Carnot cycle
4579:
4146:
3998:
3926:
3775:
3769:
3762:
3756:
3354:Bell Coleman
3315:
3270:
3261:
3216:
3200:
3163:refrigerants
3144:
3048:
2531:
2499:gas turbines
2493:include the
2483:Diesel cycle
2468:
2457:
2440:Power cycles
2389:
2094:
2078:
2074:
2001:
1949:
1945:
1941:
1937:
1933:
1927:
1892:
1889:power cycles
1888:
1886:
1787:
1701:
1655:
1653:
1449:Carathéodory
1380:Heat engines
1352:
1341:
1330:
1312:Motive power
1297:
957:Free entropy
928:
428:
427: /
417:
416: /
408:introduction
401:
400: /
339:
302:Heat engines
292:
89: /
5702:Ionocaloric
5697:Vuilleumier
5519:Hygroscopic
3778:perfect gas
3745:Ideal cycle
3634:from 1833.
3530:Manson and
3446:Hygroscopic
3389:isothermal
3310:isenthalpic
3204:gas turbine
2454:Heat engine
2420:temperature
2275:Isenthalpic
2081:heat engine
1681:heat engine
1271:Synergetics
952:Free energy
398:Temperature
259:Quasistatic
254:Isenthalpic
211:Instruments
201:Equilibrium
153:Open system
87:Equilibrium
69:Statistical
5717:Categories
5667:Pulse tube
5639:Mixed/dual
5301:References
5290:Economizer
4936:isothermal
4826:and for a
4612:isothermal
4608:isentropic
4513:, we have
3733:isochoric
3730:isentropic
3724:isentropic
3712:Pulse jets
3681:Shcramjets
3674:isentropic
3668:isentropic
3653:isochoric
3582:isochoric
3579:isentropic
3573:isentropic
3524:isothermal
3518:isothermal
3503:isochoric
3500:isothermal
3494:isothermal
3482:isochoric
3476:and volume
3410:isothermal
3404:isothermal
3386:isentropic
3383:isothermal
3380:isentropic
3304:isentropic
3286:isothermal
3208:jet engine
3151:heat pumps
2517:, and the
2481:, and the
2475:Otto cycle
2400:Isentropic
2392:Otto Cycle
2324:Reversible
2281:Polytropic
2240:Isentropic
2135:Isothermal
1930:PV diagram
1583:Nucleation
1427:Scientists
1231:Philosophy
944:Potentials
307:Heat pumps
264:Polytropic
249:Isentropic
239:Isothermal
5662:Kleemenko
5548:Internal
5226:∮
5214:∮
5158:Δ
5089:∫
5039:∮
4945:processes
4943:isochoric
4938:processes
4879:−
4798:−
4741:heat pump
4638:−
4629:η
4473:−
4423:Δ
4390:−
4361:−
4329:−
4287:−
4245:−
4203:−
4129:Δ
4110:Δ
4055:Δ
4016:Δ
3981:Δ
3962:Δ
3885:∫
3875:Δ
3772:processes
3770:isochoric
3765:processes
3727:isochoric
3708:isobaric
3705:adiabatic
3702:isochoric
3677:isobaric
3671:isochoric
3650:adiabatic
3644:adiabatic
3620:turbojets
3612:isobaric
3609:adiabatic
3603:adiabatic
3576:isochoric
3552:isobaric
3549:adiabatic
3543:adiabatic
3521:isochoric
3497:isochoric
3479:adiabatic
3471:adiabatic
3459:isobaric
3456:adiabatic
3450:adiabatic
3435:isobaric
3432:adiabatic
3426:adiabatic
3413:isobaric
3367:isobaric
3364:adiabatic
3358:adiabatic
3298:isochoric
3280:adiabatic
3114:→
3095:→
2966:∫
2954:→
2880:∫
2868:→
2771:∫
2759:→
2685:∫
2673:→
2639:→
2620:→
2601:→
2582:→
2427:Isochoric
2404:adiabatic
2340:−
2250:δ
2215:δ
2205:Isochoric
2180:δ
2145:δ
2110:δ
2100:Adiabatic
2085:heat pump
2044:−
1975:∮
1751:−
1729:Δ
1718:applies:
1685:heat pump
1564:Waterston
1514:von Mayer
1469:de Donder
1459:Clapeyron
1439:Boltzmann
1434:Bernoulli
1395:Education
1366:Timelines
1150:−
1095:−
883:Equations
850:∂
803:∂
754:α
718:∂
671:∂
625:−
619:β
583:∂
536:∂
244:Adiabatic
234:Isochoric
220:Processes
181:Ideal gas
64:Classical
5629:Combined
5588:Humphrey
5573:Expander
5558:Atkinson
5493:Stoddard
5483:Stirling
5478:Ericsson
5438:External
5279:See also
3763:isobaric
3664:Humphrey
3647:isobaric
3606:isobaric
3569:Atkinson
3546:isobaric
3539:Stoddard
3490:Stirling
3453:isobaric
3429:isobaric
3407:isobaric
3400:Ericsson
3361:isobaric
3292:isobaric
2473:are the
2412:pressure
2170:Isobaric
1616:Category
1554:Thompson
1464:Clausius
1444:Bridgman
1298:Vis viva
1280:Theories
1214:Gas laws
1006:Enthalpy
414:Pressure
229:Isobaric
186:Real gas
74:Chemical
57:Branches
5692:Siemens
5608:Scuderi
5524:Rankine
5285:Entropy
3628:-shafts
3616:Ramjets
3599:Brayton
3467:Scuderi
3422:Rankine
2408:entropy
1693:entropy
1539:Smeaton
1534:Rankine
1524:Onsager
1509:Maxwell
1504:Massieu
1209:Entropy
1204:General
1195:History
1185:Culture
1182:History
406: (
403:Entropy
340:italics
141:Systems
5598:Miller
5593:Lenoir
5568:Diesel
5514:Kalina
5498:Manson
5473:Carnot
5355:
5330:
4841:
4754:
4739:for a
4677:where
3696:Lenoir
3685:pulse-
3640:Diesel
3626:, and
3624:-props
3589:< V
3514:Manson
3376:Carnot
3339:Notes
3324:Cycle
3147:models
2509:, the
2501:, the
2416:volume
1981:
1940:) and
1908:, the
1676:system
1529:Planck
1519:Nernst
1494:Kelvin
1454:Carnot
744:
609:
477:
419:Volume
334:Note:
293:Cycles
122:Second
112:Zeroth
5622:Mixed
5020:is a
4743:is:
4096:and
2425:2→3:
2398:1→2:
1577:Other
1544:Stahl
1499:Lewis
1489:Joule
1479:Gibbs
1474:Duhem
167:State
127:Third
117:First
5634:HEHC
5603:Otto
5353:ISBN
5328:ISBN
4911:and
4598:The
4031:and
3720:Otto
3687:and
3153:and
2390:The
1891:and
1712:work
1710:and
1708:heat
1668:work
1666:and
1549:Tait
379:Heat
374:Work
104:Laws
5071:as
5016:If
4952:Q=W
4606:of
3206:or
3061:(4)
2548:(3)
2422:(T)
2014:(2)
1964:(1)
1904:or
1392:Art
338:in
5719::
5342:^
5326:.
5324:14
4577:.
4144:.
3780:,
3683:,
3622:,
3618:,
3593:.
3563::
3177:.
2402:/
2087:.
1699:.
1654:A
5530:)
5526:(
5455:)
5451:(
5422:e
5415:t
5408:v
5380:.
5359:.
5336:.
5260:0
5257:=
5252:T
5246:v
5243:e
5240:r
5236:Q
5232:d
5223:=
5220:S
5217:d
5199:.
5185:T
5180:v
5177:e
5174:r
5170:Q
5164:=
5161:S
5126:T
5120:v
5117:e
5114:r
5110:Q
5106:d
5098:T
5093:0
5085:=
5082:S
5063:.
5051:0
5048:=
5045:Z
5042:d
5026:Z
5018:Z
4994:C
4990:T
4967:H
4963:T
4887:L
4883:T
4874:H
4870:T
4863:L
4859:T
4853:=
4850:P
4847:O
4844:C
4806:L
4802:T
4793:H
4789:T
4782:L
4778:T
4772:+
4769:1
4766:=
4763:P
4760:O
4757:C
4720:H
4716:T
4691:L
4687:T
4658:H
4654:T
4648:L
4644:T
4635:1
4632:=
4563:e
4560:l
4557:c
4554:y
4551:c
4547:W
4543:=
4538:e
4535:l
4532:c
4529:y
4526:c
4522:Q
4501:0
4498:=
4493:e
4490:l
4487:c
4484:y
4481:c
4477:W
4468:e
4465:l
4462:c
4459:y
4456:c
4452:Q
4448:=
4443:e
4440:l
4437:c
4434:y
4431:c
4427:U
4403:)
4398:1
4394:v
4385:2
4381:v
4377:(
4374:)
4369:C
4365:p
4356:A
4352:p
4348:(
4345:=
4342:)
4337:2
4333:v
4324:1
4320:v
4316:(
4311:C
4307:p
4303:+
4300:)
4295:1
4291:v
4282:2
4278:v
4274:(
4269:A
4265:p
4261:=
4258:)
4253:3
4249:v
4240:4
4236:v
4232:(
4227:C
4223:p
4219:+
4216:)
4211:1
4207:v
4198:2
4194:v
4190:(
4185:A
4181:p
4177:=
4172:e
4169:l
4166:c
4163:y
4160:c
4156:W
4132:T
4124:v
4120:C
4116:=
4113:U
4107:=
4104:Q
4084:0
4081:=
4078:W
4058:T
4050:p
4046:C
4042:=
4039:Q
4019:v
4013:p
4010:=
4007:W
3984:T
3976:v
3972:C
3968:=
3965:U
3940:v
3936:C
3912:T
3909:d
3904:v
3900:C
3894:b
3889:a
3881:=
3878:U
3852:b
3832:a
3808:T
3788:U
3591:4
3587:1
3117:4
3111:3
3107:W
3103:+
3098:2
3092:1
3088:W
3084:=
3078:t
3075:e
3072:n
3067:W
3032:1
3028:V
3024:=
3019:4
3015:V
3004:,
3001:V
2998:d
2994:P
2987:1
2983:V
2975:4
2971:V
2962:=
2957:1
2951:4
2947:W
2918:,
2915:V
2912:d
2908:P
2901:4
2897:V
2889:3
2885:V
2876:=
2871:4
2865:3
2861:W
2837:3
2833:V
2829:=
2824:2
2820:V
2809:,
2806:V
2803:d
2799:P
2792:3
2788:V
2780:2
2776:V
2767:=
2762:3
2756:2
2752:W
2723:,
2720:V
2717:d
2713:P
2706:2
2702:V
2694:1
2690:V
2681:=
2676:2
2670:1
2666:W
2642:1
2636:4
2632:W
2628:+
2623:4
2617:3
2613:W
2609:+
2604:3
2598:2
2594:W
2590:+
2585:2
2579:1
2575:W
2571:=
2565:t
2562:e
2559:n
2554:W
2373:.
2361:0
2358:=
2353:T
2349:Q
2346:d
2337:S
2334:d
2320:.
2308:C
2305:=
2300:n
2295:V
2291:p
2259:0
2256:=
2253:S
2224:0
2221:=
2218:V
2189:0
2186:=
2183:P
2154:0
2151:=
2148:T
2119:0
2116:=
2113:Q
2058:t
2055:u
2052:o
2048:Q
2039:n
2036:i
2032:Q
2028:=
2025:Q
2022:=
2019:W
1987:V
1984:d
1978:P
1972:=
1969:W
1950:W
1946:V
1942:X
1938:P
1934:Y
1857:t
1854:u
1851:o
1847:E
1824:n
1821:i
1817:E
1796:U
1773:0
1770:=
1765:t
1762:u
1759:o
1755:E
1746:n
1743:i
1739:E
1735:=
1732:U
1643:e
1636:t
1629:v
1156:S
1153:T
1147:H
1144:=
1141:)
1138:p
1135:,
1132:T
1129:(
1126:G
1101:S
1098:T
1092:U
1089:=
1086:)
1083:V
1080:,
1077:T
1074:(
1071:A
1046:V
1043:p
1040:+
1037:U
1034:=
1031:)
1028:p
1025:,
1022:S
1019:(
1016:H
991:)
988:V
985:,
982:S
979:(
976:U
853:T
829:V
806:V
782:1
757:=
721:p
697:V
674:V
650:1
622:=
586:T
562:N
539:S
515:T
490:=
487:c
410:)
20:)
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