2455:. 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.
3203:. 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.
3739:
2434:
31:
1601:
3218:
3179:
2514:
2372:
3225:
4938:
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
3251:
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
3146:. 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
3232:
4402:
3190:
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
1888:
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
2064:
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.
4943:. 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
2924:
2729:
3033:
2838:
2643:
1667:
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
3118:
4997:, 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.
2517:
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).
4918:
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.
4139:
4500:
1320:
2059:
4810:
5259:
4891:
5127:
1986:
4661:
3911:
5186:
1772:
4131:
3206:
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
4569:
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
3983:
1910:
2360:
4564:
4057:
1860:
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
4018:
1155:
1100:
1045:
5050:
2307:
2258:
2223:
2188:
2153:
2118:
852:
805:
720:
673:
585:
538:
756:
624:
4722:
4693:
2844:
2649:
1858:
1825:
990:
4995:
4968:
3941:
3158:
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
2930:
2735:
4083:
2531:
489:
3851:
3831:
3807:
3787:
1795:
828:
781:
696:
649:
561:
514:
1913:
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.
3264:. Any thermodynamic processes may be used. However, when idealized cycles are modeled, often processes where one state variable is kept constant, such as:
3182:
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
1630:
4607:
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:
5409:
1331:
1219:
3044:
2421:
3→4: Isentropic / adiabatic compression: Constant entropy (s), Increase in pressure (P), Decrease in volume (v), Increase in temperature (T)
453:
1672:. 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
4896:
The second law of thermodynamics limits the efficiency and COP for all cyclic devices to levels at or below the Carnot efficiency. The
1309:
5571:
1342:
4397:{\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})}
2458:
Power cycles can also be divided according to the type of heat engine they seek to model. The most common cycles used to model
912:
4407:
2424:
4→1: Isochoric heating: Constant volume (v), Increase in pressure (P), Increase in entropy (S), Increase in temperature (T)
1997:
1623:
1210:
879:
446:
324:
4738:
5198:
4592:
2312:
262:
4825:
4404:, which is just the area of the rectangle. If the total heat flow per cycle is required, this is easily obtained. Since
3813:
vanishes. Therefore, the internal energy changes of a perfect gas undergoing various processes connecting initial state
5402:
5066:
3703:. 1→2 accomplishes both the heat rejection and the compression. Originally developed for use in reciprocating engines.
3619:. Originally developed for use in reciprocating engines. The external combustion version of this cycle is known as the
1394:
1368:
889:
343:
1947:
5637:
5345:
5320:
3129:
295:
4613:
5721:
5340:
Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 452.
3859:
1447:
918:
317:
5675:
3620:
1894:
1616:
5142:
3038:
For the ideal
Stirling cycle, no volume change happens in process 4-1 and 2-3, thus equation (3) simplifies to:
1917:
Because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a
5726:
5716:
3155:
1898:
1713:
1547:
79:
4088:
1442:
5711:
5395:
2447:
Thermodynamic power cycles are the basis for the operation of heat engines, which supply most of the world's
1522:
1295:
272:
3946:
5622:
2418:
cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T)
1691:
During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure.
907:
110:
100:
2318:
5057:
4505:
2225:). Energy transfer is considered as heat removed from the system, as the work done by the system is zero.
1704:
115:
105:
5536:
5426:
4725:
3677:
3334:
3252:
idealized counterparts; e.g., isochoric expansion (process 1-2) occurs with some actual volume change.
2479:
2459:
1399:
1363:
141:
75:
1437:
5690:
5379:
Hill and
Peterson. "Mechanics and Thermodynamics of Propulsion", 2nd ed. Prentice Hall, 1991. 760 pp.
5283:
4023:
1677:
1192:
940:
386:
199:
189:
2068:
If the cyclic process moves clockwise around the loop, then W will be positive, and it represents a
5451:
4570:
5192:
In general, for any cyclic process the state points can be connected by reversible paths, so that
2525:
output from the ideal
Stirling cycle (net work out), consisting of 4 thermodynamic processes, is:
5731:
5670:
5655:
5645:
5601:
3991:
3673:
3159:
3147:
1918:
1890:
1604:
1432:
1229:
1110:
1055:
1000:
932:
871:
407:
396:
62:
5023:
2919:{\displaystyle W_{3\to 4}=\int _{V_{3}}^{V_{4}}P\,dV,\,\,{\text{positive, work done by system}}}
2724:{\displaystyle W_{1\to 2}=\int _{V_{1}}^{V_{2}}P\,dV,\,\,{\text{negative, work done on system}}}
2275:
2234:
2199:
2164:
2129:
2094:
834:
787:
702:
655:
567:
520:
5312:
5305:
1537:
1254:
338:
92:
67:
3028:{\displaystyle W_{4\to 1}=\int _{V_{4}}^{V_{1}}P\,dV,\,\,{\text{zero work since }}V_{4}=V_{1}}
2833:{\displaystyle W_{2\to 3}=\int _{V_{2}}^{V_{3}}P\,dV,\,\,{\text{zero work since }}V_{2}=V_{3}}
2084:
The following processes are often used to describe different stages of a thermodynamic cycle:
1457:
738:
603:
5516:
5476:
4698:
4669:
3261:
3163:
1830:
1700:
1648:
1472:
1049:
362:
208:
57:
2638:{\displaystyle {\text{(3)}}\qquad W_{\rm {net}}=W_{1\to 2}+W_{2\to 3}+W_{3\to 4}+W_{4\to 1}}
2126: : The process is at a constant temperature during that part of the cycle (T=constant,
1800:
960:
5660:
4973:
4946:
4904:
are two other reversible cycles that use regeneration to obtain isothermal heat transfer.
3919:
1664:
1552:
1477:
1467:
267:
129:
8:
5665:
5566:
4062:
3549:
3520:
3298:
2263:
1865:
1703:
are process dependent. For a cycle for which the system returns to its initial state the
1497:
1259:
247:
242:
155:
1492:
471:
5522:
4604:
3836:
3816:
3792:
3772:
3381:
3342:
3292:
3274:
3135:
2269:
1780:
1692:
1586:
1249:
1244:
1197:
813:
766:
681:
634:
546:
499:
429:
413:
300:
252:
237:
227:
36:
30:
2266: : The process that proceeds without any change in enthalpy or specific enthalpy.
5685:
5507:
5341:
5316:
3810:
3434:
3286:
3268:
2415:
2193:
1581:
1542:
1532:
1104:
902:
730:
232:
222:
164:
5627:
3280:
2158:
1680:, the cycle is reversible. Whether carried out reversible or irreversibly, the net
1502:
1487:
1427:
1422:
1239:
1234:
884:
352:
217:
3305:
Some example thermodynamic cycles and their constituent processes are as follows:
5650:
3725:
3495:
2522:
2467:
2190:). Energy transfer is considered as heat removed from or work done by the system.
2155:). Energy transfer is considered as heat removed from or work done by the system.
1885:
1660:
1452:
1300:
954:
595:
418:
179:
146:
3738:
3260:
In practice, simple idealized thermodynamic cycles are usually made out of four
5617:
5576:
5561:
5546:
5481:
5471:
5466:
5441:
5264:
meaning that the net entropy change of the working fluid over a cycle is zero.
5010:
4913:
4901:
4897:
3652:
3557:
3527:
3478:
3388:
3207:
3162:. Multiple compression and expansion cycles allow gas refrigeration systems to
2507:
2503:
2499:
2448:
1861:
1685:
1656:
1507:
1277:
377:
257:
194:
184:
52:
22:
2161: : Pressure in that part of the cycle will remain constant. (P=constant,
5705:
5680:
5596:
5551:
5512:
5486:
5456:
5133:
3645:
3587:
3502:
3455:
3410:
3200:
2495:
2491:
2483:
2475:
2452:
2072:. If it moves counterclockwise, then W will be negative, and it represents a
1652:
1576:
894:
463:
424:
136:
5056:
Entropy is a state function and is defined in an absolute sense through the
5586:
5581:
5556:
5502:
5461:
4816:
4588:
4582:
3684:
3628:
3427:
3364:
3143:
2471:
1991:
This work is equal to the balance of heat (Q) transferred into the system:
1659:
into and out of the system, while varying pressure, temperature, and other
1527:
1512:
1462:
945:
3766:
3192:
3151:
2487:
2442:
2408:
2069:
1669:
1482:
290:
5591:
5387:
5278:
4600:
4596:
3708:
3616:
3196:
2463:
2433:
2388:
2380:
2228:
2123:
1571:
1517:
3113:{\displaystyle {\text{(4)}}\qquad W_{\rm {net}}=W_{1\to 2}+W_{3\to 4}}
2091: : No energy transfer as heat (Q) during that part of the cycle (
4729:
3700:
3669:
3612:
3139:
2392:
2088:
2073:
1673:
169:
3224:
3608:
2400:
1285:
1202:
994:
402:
174:
5273:
5136:
to the final state, so that for an isothermal reversible process
3742:
An illustration of an ideal cycle heat engine (arrows clockwise).
3217:
2513:
2396:
2371:
2120:). Energy transfer is considered as work done by the system only.
1909:
1777:
The above states that there is no change of the internal energy (
1681:
391:
3178:
3604:
2404:
1884:. Power cycles are cycles which convert some heat input into a
1864:. Thermodynamic cycles are often represented mathematically as
4970:
and the bottom isotherm is all at the same cooler temperature
2315: : The process where the net entropy production is zero;
2260:). It is adiabatic (no heat nor mass exchange) and reversible.
1901:
directions indicate power and heat pump cycles, respectively.
1827:
represents the total work and heat input during the cycle and
3988:
Under this set of assumptions, for processes A and C we have
3245:
Actual and ideal overlaid, showing difference in work output
2231: : The process is one of constant entropy (S=constant,
3231:
1696:
367:
5365:, 5th edition. John Wiley & Sons, 1997. Chapter 21,
3757:
RIGHT (B) and LEFT (D) of the loop: a pair of parallel
3750:
TOP (A) and BOTTOM (C) of the loop: a pair of parallel
4495:{\displaystyle \Delta U_{cycle}=Q_{cycle}-W_{cycle}=0}
2375:
Description of each point in the thermodynamic cycles.
5201:
5145:
5069:
5026:
4976:
4949:
4930:
LEFT and RIGHT sides of the loop: a pair of parallel
4923:
TOP and BOTTOM of the loop: a pair of quasi-parallel
4828:
4741:
4701:
4672:
4616:
4508:
4410:
4142:
4091:
4065:
4026:
3994:
3949:
3922:
3862:
3839:
3819:
3795:
3775:
3746:
An ideal cycle is simple to analyze and consists of:
3047:
2933:
2847:
2738:
2652:
2534:
2321:
2278:
2237:
2202:
2167:
2132:
2097:
2054:{\displaystyle {\text{(2)}}\qquad W=Q=Q_{in}-Q_{out}}
2000:
1950:
1868:
in the modeling of the workings of an actual device.
1833:
1803:
1783:
1716:
1113:
1058:
1003:
963:
837:
816:
790:
769:
741:
705:
684:
658:
637:
606:
570:
549:
523:
502:
474:
4805:{\displaystyle \ COP=1+{\frac {T_{L}}{T_{H}-T_{L}}}}
2196: : The process is constant volume (V=constant,
2079:
5254:{\displaystyle \oint dS=\oint {dQ_{rev} \over T}=0}
2383:is an example of a reversible thermodynamic cycle.
1663:within the system, and that eventually returns the
5304:
5253:
5180:
5121:
5044:
4989:
4962:
4886:{\displaystyle \ COP={\frac {T_{L}}{T_{H}-T_{L}}}}
4885:
4804:
4716:
4687:
4655:
4558:
4494:
4396:
4125:
4077:
4051:
4012:
3977:
3935:
3905:
3845:
3825:
3801:
3781:
3255:
3112:
3027:
2918:
2832:
2723:
2637:
2354:
2301:
2252:
2217:
2182:
2147:
2112:
2053:
1980:
1852:
1819:
1789:
1766:
1676:. If at every point in the cycle the system is in
1149:
1094:
1039:
984:
846:
822:
799:
775:
750:
714:
690:
667:
643:
618:
579:
555:
532:
508:
483:
5122:{\displaystyle S=\int _{0}^{T}{dQ_{rev} \over T}}
3210:and the actual performance of a Stirling engine:
5703:
1981:{\displaystyle {\text{(1)}}\qquad W=\oint P\ dV}
1876:Two primary classes of thermodynamic cycles are
16:Linked cyclic series of thermodynamic processes
5000:
4656:{\displaystyle \eta =1-{\frac {T_{L}}{T_{H}}}}
1937:). The area enclosed by the loop is the work (
1684:change of the system is zero, as entropy is a
5403:
5376:, 7th ed. New York: McGraw-Hill, 2011. Print.
4939:isothermal processes, which are described by
3906:{\displaystyle \Delta U=\int _{a}^{b}C_{v}dT}
1624:
5367:Entropy and the Second Law of Thermodynamics
5303:Cengel, Yunus A.; Boles, Michael A. (2002).
3985:for any process undergone by a perfect gas.
2272: : The process that obeys the relation
5302:
5017:remains unchanged during a cyclic process:
5410:
5396:
5181:{\displaystyle \Delta S={Q_{rev} \over T}}
2366:
1631:
1617:
29:
4724:the highest. For Carnot power cycles the
2996:
2995:
2985:
2910:
2909:
2899:
2801:
2800:
2790:
2715:
2714:
2704:
2287:
1767:{\displaystyle \Delta U=E_{in}-E_{out}=0}
5417:
5372:Çengel, Yunus A., and Michael A. Boles.
5336:
5334:
5332:
4126:{\displaystyle Q=\Delta U=C_{v}\Delta T}
4059:, whereas for processes B and D we have
3737:
3547:
3332:
3177:
3169:
2521:For example :--the pressure-volume
2512:
2432:
2370:
1908:
5572:Homogeneous charge compression ignition
5374:Thermodynamics: An Engineering Approach
5307:Thermodynamics: an engineering approach
5132:where a reversible path is chosen from
3134:Thermodynamic heat pump cycles are the
1904:
5704:
4591:is a cycle composed of the totally
3978:{\displaystyle \Delta U=C_{v}\Delta T}
5391:
5329:
2510:, which also models hot air engines.
4819:the coefficient of performance is:
4695:is the lowest cycle temperature and
3405:The second Ericsson cycle from 1853
2355:{\displaystyle dS-{\frac {dQ}{T}}=0}
4559:{\displaystyle Q_{cycle}=W_{cycle}}
3123:
13:
5355:
5146:
4603:heat addition and rejection. The
4411:
4117:
4098:
4043:
4004:
3969:
3950:
3863:
3066:
3063:
3060:
2553:
2550:
2547:
1717:
838:
791:
706:
659:
571:
524:
344:Intensive and extensive properties
14:
5743:
5383:
4907:
4136:The total work done per cycle is
3574:Differs from Otto cycle in that V
3130:Heat pump and refrigeration cycle
2080:A list of thermodynamic processes
5361:Halliday, Resnick & Walker.
5311:. Boston: McGraw-Hill. pp.
3853:are always given by the formula
3230:
3223:
3216:
1871:
1797:) of the system over the cycle.
1647:consists of linked sequences of
1600:
1599:
919:Table of thermodynamic equations
4576:
4052:{\displaystyle Q=C_{p}\Delta T}
3256:Well-known thermodynamic cycles
3212:
3173:
3053:
2540:
2428:
2006:
1956:
1395:Maxwell's thermodynamic surface
5296:
4599:compression and expansion and
4391:
4365:
4362:
4336:
4330:
4304:
4288:
4262:
4246:
4220:
4204:
4178:
3809:for a closed system since its
3765:If the working substance is a
3733:
3156:absorption refrigeration cycle
3102:
3083:
2942:
2856:
2747:
2661:
2627:
2608:
2589:
2570:
1899:clockwise and counterclockwise
1695:(or path quantities), such as
1129:
1117:
1074:
1062:
1019:
1007:
979:
967:
1:
5289:
3678:continuous detonation engines
3150:, which models systems using
2913:positive, work done by system
2718:negative, work done on system
2451:and run the vast majority of
1296:Mechanical equivalent of heat
1891:pressure–volume (PV) diagram
908:Onsager reciprocal relations
7:
5477:Stirling (pseudo/adiabatic)
5267:
5058:Third Law of Thermodynamics
5001:State functions and entropy
4013:{\displaystyle W=p\Delta v}
3548:Power cycles normally with
3333:Power cycles normally with
2480:external combustion engines
2460:internal combustion engines
1895:temperature–entropy diagram
1705:first law of thermodynamics
1400:Entropy as energy dispersal
1211:"Perpetual motion" machines
1150:{\displaystyle G(T,p)=H-TS}
1095:{\displaystyle A(T,V)=U-TS}
1040:{\displaystyle H(S,p)=U+pV}
10:
5748:
5045:{\displaystyle \oint dZ=0}
4911:
4726:coefficient of performance
4580:
3127:
2440:
2302:{\displaystyle pV^{\,n}=C}
2253:{\displaystyle \delta S=0}
2218:{\displaystyle \delta V=0}
2183:{\displaystyle \delta P=0}
2148:{\displaystyle \delta T=0}
2113:{\displaystyle \delta Q=0}
847:{\displaystyle \partial T}
800:{\displaystyle \partial V}
715:{\displaystyle \partial p}
668:{\displaystyle \partial V}
580:{\displaystyle \partial T}
533:{\displaystyle \partial S}
5636:
5610:
5535:
5495:
5436:
5425:
5284:Thermogravitational cycle
3726:Gasoline / petrol engines
3516:isochoric then adiabatic
3359:A reversed Brayton cycle
1678:thermodynamic equilibrium
1321:An Inquiry Concerning the
4571:thermodynamic efficiency
1334:Heterogeneous Substances
751:{\displaystyle \alpha =}
619:{\displaystyle \beta =-}
5722:Thermodynamic processes
5363:Fundamentals of Physics
4717:{\displaystyle {T_{H}}}
4688:{\displaystyle {T_{L}}}
3337:- or heat pump cycles:
3262:thermodynamic processes
3154:that change phase. The
3148:vapor compression cycle
2367:Example: The Otto cycle
1941:) done by the process:
1853:{\displaystyle E_{out}}
1649:thermodynamic processes
5255:
5182:
5123:
5046:
4991:
4964:
4887:
4806:
4718:
4689:
4657:
4560:
4496:
4398:
4127:
4079:
4053:
4014:
3979:
3937:
3907:
3847:
3827:
3803:
3789:is only a function of
3783:
3743:
3277:(constant temperature)
3183:
3114:
3029:
2920:
2834:
2725:
2639:
2518:
2438:
2376:
2356:
2303:
2254:
2219:
2184:
2149:
2114:
2055:
1982:
1914:
1854:
1821:
1820:{\displaystyle E_{in}}
1791:
1768:
1151:
1096:
1041:
986:
985:{\displaystyle U(S,V)}
848:
824:
801:
777:
752:
716:
692:
669:
645:
620:
581:
557:
534:
510:
485:
464:Specific heat capacity
68:Quantum thermodynamics
5727:Thermodynamic systems
5717:Equilibrium chemistry
5256:
5183:
5124:
5047:
4992:
4990:{\displaystyle T_{C}}
4965:
4963:{\displaystyle T_{H}}
4888:
4807:
4719:
4690:
4658:
4561:
4497:
4399:
4128:
4080:
4054:
4015:
3980:
3938:
3936:{\displaystyle C_{v}}
3908:
3848:
3828:
3804:
3784:
3741:
3239:Ideal Stirling cycle
3181:
3170:Modeling real systems
3115:
3030:
2999:zero work since
2921:
2835:
2804:zero work since
2726:
2640:
2516:
2436:
2374:
2357:
2304:
2255:
2220:
2185:
2150:
2115:
2056:
1983:
1925:axis shows pressure (
1912:
1866:quasistatic processes
1855:
1822:
1792:
1769:
1332:On the Equilibrium of
1152:
1097:
1050:Helmholtz free energy
1042:
987:
849:
825:
802:
778:
753:
717:
693:
670:
646:
621:
582:
558:
535:
511:
486:
5712:Thermodynamic cycles
5661:Regenerative cooling
5539:combustion / thermal
5438:Without phase change
5429:combustion / thermal
5419:Thermodynamic cycles
5199:
5143:
5067:
5024:
5013:then the balance of
4974:
4947:
4826:
4739:
4699:
4670:
4614:
4593:reversible processes
4506:
4408:
4140:
4089:
4063:
4024:
3992:
3947:
3920:
3860:
3837:
3817:
3793:
3773:
3621:first Ericsson cycle
3521:Manson-Guise engines
3325:Heat rejection, 4→1
3199:can be modeled as a
3045:
2931:
2845:
2736:
2650:
2532:
2478:. Cycles that model
2437:Heat engine diagram.
2395:expansion: Constant
2319:
2276:
2235:
2200:
2165:
2130:
2095:
1998:
1948:
1905:Relationship to work
1831:
1801:
1781:
1714:
1345:Motive Power of Fire
1111:
1056:
1001:
961:
913:Bridgman's equations
890:Fundamental relation
835:
814:
788:
767:
739:
703:
682:
656:
635:
604:
568:
547:
521:
500:
472:
5090:
4078:{\displaystyle W=0}
3886:
3550:internal combustion
3335:external combustion
3319:Heat addition, 2→3
3309:
3301:(constant enthalpy)
3283:(constant pressure)
3242:Actual performance
3160:Hampson–Linde cycle
2981:
2895:
2786:
2700:
1933:axis shows volume (
1645:thermodynamic cycle
1323:Source ... Friction
1255:Loschmidt's paradox
447:Material properties
325:Conjugate variables
5251:
5178:
5119:
5076:
5042:
4987:
4960:
4883:
4802:
4714:
4685:
4653:
4605:thermal efficiency
4556:
4492:
4394:
4123:
4075:
4049:
4010:
3975:
3933:
3903:
3872:
3843:
3823:
3799:
3779:
3744:
3382:Carnot heat engine
3308:
3295:(constant entropy)
3184:
3110:
3025:
2953:
2916:
2867:
2830:
2758:
2721:
2672:
2635:
2519:
2439:
2377:
2352:
2299:
2250:
2215:
2180:
2145:
2110:
2051:
1978:
1915:
1850:
1817:
1787:
1764:
1693:Process quantities
1587:Order and disorder
1343:Reflections on the
1250:Heat death paradox
1147:
1092:
1037:
982:
844:
820:
797:
773:
748:
712:
688:
665:
641:
616:
577:
553:
530:
506:
484:{\displaystyle c=}
481:
454:Property databases
430:Reduced properties
414:Chemical potential
378:Functions of state
301:Thermal efficiency
37:Carnot heat engine
5699:
5698:
5676:Vapor-compression
5602:Staged combustion
5531:
5530:
5496:With phase change
5243:
5176:
5117:
4881:
4831:
4800:
4744:
4651:
3846:{\displaystyle b}
3826:{\displaystyle a}
3811:internal pressure
3802:{\displaystyle T}
3782:{\displaystyle U}
3731:
3730:
3463:variable pressure
3316:Compression, 1→2
3289:(constant volume)
3249:
3248:
3188:
3187:
3051:
3000:
2914:
2805:
2719:
2538:
2407:(v), Decrease in
2403:(P), Increase in
2399:(s), Decrease in
2344:
2004:
1971:
1954:
1921:. A PV diagram's
1790:{\displaystyle U}
1641:
1640:
1582:Self-organization
1407:
1406:
1105:Gibbs free energy
903:Maxwell relations
861:
860:
857:
856:
823:{\displaystyle V}
776:{\displaystyle 1}
731:Thermal expansion
725:
724:
691:{\displaystyle V}
644:{\displaystyle 1}
590:
589:
556:{\displaystyle N}
509:{\displaystyle T}
437:
436:
353:Process functions
339:Property diagrams
318:System properties
308:
307:
273:Endoreversibility
165:Equation of state
5739:
5671:Vapor absorption
5434:
5433:
5412:
5405:
5398:
5389:
5388:
5349:
5338:
5327:
5326:
5310:
5300:
5260:
5258:
5257:
5252:
5244:
5239:
5238:
5237:
5218:
5187:
5185:
5184:
5179:
5177:
5172:
5171:
5156:
5128:
5126:
5125:
5120:
5118:
5113:
5112:
5111:
5092:
5089:
5084:
5051:
5049:
5048:
5043:
4996:
4994:
4993:
4988:
4986:
4985:
4969:
4967:
4966:
4961:
4959:
4958:
4892:
4890:
4889:
4884:
4882:
4880:
4879:
4878:
4866:
4865:
4855:
4854:
4845:
4829:
4811:
4809:
4808:
4803:
4801:
4799:
4798:
4797:
4785:
4784:
4774:
4773:
4764:
4742:
4723:
4721:
4720:
4715:
4713:
4712:
4711:
4694:
4692:
4691:
4686:
4684:
4683:
4682:
4662:
4660:
4659:
4654:
4652:
4650:
4649:
4640:
4639:
4630:
4565:
4563:
4562:
4557:
4555:
4554:
4530:
4529:
4501:
4499:
4498:
4493:
4485:
4484:
4460:
4459:
4435:
4434:
4403:
4401:
4400:
4395:
4390:
4389:
4377:
4376:
4361:
4360:
4348:
4347:
4329:
4328:
4316:
4315:
4303:
4302:
4287:
4286:
4274:
4273:
4261:
4260:
4245:
4244:
4232:
4231:
4219:
4218:
4203:
4202:
4190:
4189:
4177:
4176:
4164:
4163:
4132:
4130:
4129:
4124:
4116:
4115:
4084:
4082:
4081:
4076:
4058:
4056:
4055:
4050:
4042:
4041:
4019:
4017:
4016:
4011:
3984:
3982:
3981:
3976:
3968:
3967:
3942:
3940:
3939:
3934:
3932:
3931:
3912:
3910:
3909:
3904:
3896:
3895:
3885:
3880:
3852:
3850:
3849:
3844:
3832:
3830:
3829:
3824:
3808:
3806:
3805:
3800:
3788:
3786:
3785:
3780:
3496:Stirling engines
3310:
3307:
3234:
3227:
3220:
3213:
3174:
3124:Heat pump cycles
3119:
3117:
3116:
3111:
3109:
3108:
3090:
3089:
3071:
3070:
3069:
3052:
3049:
3034:
3032:
3031:
3026:
3024:
3023:
3011:
3010:
3001:
2998:
2980:
2979:
2978:
2968:
2967:
2966:
2949:
2948:
2925:
2923:
2922:
2917:
2915:
2912:
2894:
2893:
2892:
2882:
2881:
2880:
2863:
2862:
2839:
2837:
2836:
2831:
2829:
2828:
2816:
2815:
2806:
2803:
2785:
2784:
2783:
2773:
2772:
2771:
2754:
2753:
2730:
2728:
2727:
2722:
2720:
2717:
2699:
2698:
2697:
2687:
2686:
2685:
2668:
2667:
2644:
2642:
2641:
2636:
2634:
2633:
2615:
2614:
2596:
2595:
2577:
2576:
2558:
2557:
2556:
2539:
2536:
2468:gasoline engines
2361:
2359:
2358:
2353:
2345:
2340:
2332:
2308:
2306:
2305:
2300:
2292:
2291:
2259:
2257:
2256:
2251:
2224:
2222:
2221:
2216:
2189:
2187:
2186:
2181:
2154:
2152:
2151:
2146:
2119:
2117:
2116:
2111:
2060:
2058:
2057:
2052:
2050:
2049:
2031:
2030:
2005:
2002:
1987:
1985:
1984:
1979:
1969:
1955:
1952:
1882:heat pump cycles
1859:
1857:
1856:
1851:
1849:
1848:
1826:
1824:
1823:
1818:
1816:
1815:
1796:
1794:
1793:
1788:
1773:
1771:
1770:
1765:
1757:
1756:
1738:
1737:
1653:transfer of heat
1633:
1626:
1619:
1603:
1602:
1310:Key publications
1291:
1290:("living force")
1240:Brownian ratchet
1235:Entropy and life
1230:Entropy and time
1181:
1180:
1156:
1154:
1153:
1148:
1101:
1099:
1098:
1093:
1046:
1044:
1043:
1038:
991:
989:
988:
983:
885:Clausius theorem
880:Carnot's theorem
853:
851:
850:
845:
829:
827:
826:
821:
806:
804:
803:
798:
782:
780:
779:
774:
761:
760:
757:
755:
754:
749:
721:
719:
718:
713:
697:
695:
694:
689:
674:
672:
671:
666:
650:
648:
647:
642:
629:
628:
625:
623:
622:
617:
586:
584:
583:
578:
562:
560:
559:
554:
539:
537:
536:
531:
515:
513:
512:
507:
494:
493:
490:
488:
487:
482:
460:
459:
333:
332:
152:
151:
33:
19:
18:
5747:
5746:
5742:
5741:
5740:
5738:
5737:
5736:
5702:
5701:
5700:
5695:
5632:
5606:
5538:
5527:
5517:Organic Rankine
5491:
5445:
5442:hot air engines
5439:
5428:
5421:
5416:
5386:
5358:
5356:Further reading
5353:
5352:
5339:
5330:
5323:
5301:
5297:
5292:
5270:
5227:
5223:
5219:
5217:
5200:
5197:
5196:
5161:
5157:
5155:
5144:
5141:
5140:
5101:
5097:
5093:
5091:
5085:
5080:
5068:
5065:
5064:
5025:
5022:
5021:
5003:
4981:
4977:
4975:
4972:
4971:
4954:
4950:
4948:
4945:
4944:
4916:
4910:
4874:
4870:
4861:
4857:
4856:
4850:
4846:
4844:
4827:
4824:
4823:
4793:
4789:
4780:
4776:
4775:
4769:
4765:
4763:
4740:
4737:
4736:
4707:
4703:
4702:
4700:
4697:
4696:
4678:
4674:
4673:
4671:
4668:
4667:
4645:
4641:
4635:
4631:
4629:
4615:
4612:
4611:
4585:
4579:
4573:of the cycle).
4538:
4534:
4513:
4509:
4507:
4504:
4503:
4468:
4464:
4443:
4439:
4418:
4414:
4409:
4406:
4405:
4385:
4381:
4372:
4368:
4356:
4352:
4343:
4339:
4324:
4320:
4311:
4307:
4298:
4294:
4282:
4278:
4269:
4265:
4256:
4252:
4240:
4236:
4227:
4223:
4214:
4210:
4198:
4194:
4185:
4181:
4172:
4168:
4147:
4143:
4141:
4138:
4137:
4111:
4107:
4090:
4087:
4086:
4064:
4061:
4060:
4037:
4033:
4025:
4022:
4021:
3993:
3990:
3989:
3963:
3959:
3948:
3945:
3944:
3927:
3923:
3921:
3918:
3917:
3891:
3887:
3881:
3876:
3861:
3858:
3857:
3838:
3835:
3834:
3833:to final state
3818:
3815:
3814:
3794:
3791:
3790:
3774:
3771:
3770:
3736:
3581:
3577:
3464:
3322:Expansion, 3→4
3271:(constant heat)
3258:
3172:
3132:
3126:
3098:
3094:
3079:
3075:
3059:
3058:
3054:
3048:
3046:
3043:
3042:
3019:
3015:
3006:
3002:
2997:
2974:
2970:
2969:
2962:
2958:
2957:
2938:
2934:
2932:
2929:
2928:
2911:
2888:
2884:
2883:
2876:
2872:
2871:
2852:
2848:
2846:
2843:
2842:
2824:
2820:
2811:
2807:
2802:
2779:
2775:
2774:
2767:
2763:
2762:
2743:
2739:
2737:
2734:
2733:
2716:
2693:
2689:
2688:
2681:
2677:
2676:
2657:
2653:
2651:
2648:
2647:
2623:
2619:
2604:
2600:
2585:
2581:
2566:
2562:
2546:
2545:
2541:
2535:
2533:
2530:
2529:
2523:mechanical work
2504:hot air engines
2502:, which models
2494:, which models
2486:, which models
2474:, which models
2466:, which models
2445:
2431:
2369:
2333:
2331:
2320:
2317:
2316:
2286:
2282:
2277:
2274:
2273:
2236:
2233:
2232:
2201:
2198:
2197:
2166:
2163:
2162:
2131:
2128:
2127:
2096:
2093:
2092:
2082:
2039:
2035:
2023:
2019:
2001:
1999:
1996:
1995:
1951:
1949:
1946:
1945:
1907:
1886:mechanical work
1874:
1838:
1834:
1832:
1829:
1828:
1808:
1804:
1802:
1799:
1798:
1782:
1779:
1778:
1746:
1742:
1730:
1726:
1715:
1712:
1711:
1661:state variables
1637:
1592:
1591:
1567:
1559:
1558:
1557:
1417:
1409:
1408:
1387:
1373:
1348:
1344:
1337:
1333:
1326:
1322:
1289:
1282:
1264:
1245:Maxwell's demon
1207:
1178:
1177:
1161:
1160:
1159:
1112:
1109:
1108:
1107:
1057:
1054:
1053:
1052:
1002:
999:
998:
997:
962:
959:
958:
957:
955:Internal energy
950:
935:
925:
924:
899:
874:
864:
863:
862:
836:
833:
832:
815:
812:
811:
789:
786:
785:
768:
765:
764:
740:
737:
736:
704:
701:
700:
683:
680:
679:
657:
654:
653:
636:
633:
632:
605:
602:
601:
596:Compressibility
569:
566:
565:
548:
545:
544:
522:
519:
518:
501:
498:
497:
473:
470:
469:
449:
439:
438:
419:Particle number
372:
331:
320:
310:
309:
268:Irreversibility
180:State of matter
147:Isolated system
132:
122:
121:
120:
95:
85:
84:
80:Non-equilibrium
72:
47:
39:
17:
12:
11:
5:
5745:
5735:
5734:
5732:Thermodynamics
5729:
5724:
5719:
5714:
5697:
5696:
5694:
5693:
5688:
5683:
5678:
5673:
5668:
5663:
5658:
5653:
5648:
5642:
5640:
5634:
5633:
5631:
5630:
5625:
5620:
5614:
5612:
5608:
5607:
5605:
5604:
5599:
5594:
5589:
5584:
5579:
5574:
5569:
5564:
5559:
5554:
5549:
5543:
5541:
5533:
5532:
5529:
5528:
5526:
5525:
5520:
5510:
5505:
5499:
5497:
5493:
5492:
5490:
5489:
5484:
5479:
5474:
5469:
5464:
5459:
5454:
5448:
5446:
5437:
5431:
5423:
5422:
5415:
5414:
5407:
5400:
5392:
5385:
5384:External links
5382:
5381:
5380:
5377:
5370:
5357:
5354:
5351:
5350:
5328:
5321:
5294:
5293:
5291:
5288:
5287:
5286:
5281:
5276:
5269:
5266:
5262:
5261:
5250:
5247:
5242:
5236:
5233:
5230:
5226:
5222:
5216:
5213:
5210:
5207:
5204:
5190:
5189:
5175:
5170:
5167:
5164:
5160:
5154:
5151:
5148:
5130:
5129:
5116:
5110:
5107:
5104:
5100:
5096:
5088:
5083:
5079:
5075:
5072:
5054:
5053:
5041:
5038:
5035:
5032:
5029:
5011:state function
5002:
4999:
4984:
4980:
4957:
4953:
4936:
4935:
4928:
4914:Stirling cycle
4912:Main article:
4909:
4908:Stirling cycle
4906:
4902:Ericsson cycle
4898:Stirling cycle
4894:
4893:
4877:
4873:
4869:
4864:
4860:
4853:
4849:
4843:
4840:
4837:
4834:
4813:
4812:
4796:
4792:
4788:
4783:
4779:
4772:
4768:
4762:
4759:
4756:
4753:
4750:
4747:
4710:
4706:
4681:
4677:
4664:
4663:
4648:
4644:
4638:
4634:
4628:
4625:
4622:
4619:
4581:Main article:
4578:
4575:
4553:
4550:
4547:
4544:
4541:
4537:
4533:
4528:
4525:
4522:
4519:
4516:
4512:
4491:
4488:
4483:
4480:
4477:
4474:
4471:
4467:
4463:
4458:
4455:
4452:
4449:
4446:
4442:
4438:
4433:
4430:
4427:
4424:
4421:
4417:
4413:
4393:
4388:
4384:
4380:
4375:
4371:
4367:
4364:
4359:
4355:
4351:
4346:
4342:
4338:
4335:
4332:
4327:
4323:
4319:
4314:
4310:
4306:
4301:
4297:
4293:
4290:
4285:
4281:
4277:
4272:
4268:
4264:
4259:
4255:
4251:
4248:
4243:
4239:
4235:
4230:
4226:
4222:
4217:
4213:
4209:
4206:
4201:
4197:
4193:
4188:
4184:
4180:
4175:
4171:
4167:
4162:
4159:
4156:
4153:
4150:
4146:
4122:
4119:
4114:
4110:
4106:
4103:
4100:
4097:
4094:
4074:
4071:
4068:
4048:
4045:
4040:
4036:
4032:
4029:
4009:
4006:
4003:
4000:
3997:
3974:
3971:
3966:
3962:
3958:
3955:
3952:
3930:
3926:
3916:Assuming that
3914:
3913:
3902:
3899:
3894:
3890:
3884:
3879:
3875:
3871:
3868:
3865:
3842:
3822:
3798:
3778:
3763:
3762:
3755:
3735:
3732:
3729:
3728:
3723:
3720:
3717:
3714:
3711:
3705:
3704:
3698:
3695:
3692:
3689:
3687:
3681:
3680:
3667:
3664:
3661:
3658:
3655:
3649:
3648:
3643:
3640:
3637:
3634:
3631:
3625:
3624:
3602:
3599:
3596:
3593:
3590:
3584:
3583:
3579:
3575:
3572:
3569:
3566:
3563:
3560:
3554:
3553:
3545:
3544:
3542:
3539:
3536:
3533:
3530:
3524:
3523:
3517:
3514:
3511:
3508:
3505:
3499:
3498:
3493:
3490:
3487:
3484:
3481:
3475:
3474:
3472:
3469:
3466:
3461:
3458:
3452:
3451:
3449:
3446:
3443:
3440:
3437:
3431:
3430:
3425:
3422:
3419:
3416:
3413:
3407:
3406:
3403:
3400:
3397:
3394:
3391:
3385:
3384:
3379:
3376:
3373:
3370:
3367:
3361:
3360:
3357:
3354:
3351:
3348:
3345:
3339:
3338:
3330:
3329:
3326:
3323:
3320:
3317:
3314:
3303:
3302:
3296:
3290:
3284:
3278:
3272:
3257:
3254:
3247:
3246:
3243:
3240:
3236:
3235:
3228:
3221:
3208:Stirling cycle
3186:
3185:
3171:
3168:
3138:for household
3128:Main article:
3125:
3122:
3121:
3120:
3107:
3104:
3101:
3097:
3093:
3088:
3085:
3082:
3078:
3074:
3068:
3065:
3062:
3057:
3036:
3035:
3022:
3018:
3014:
3009:
3005:
2994:
2991:
2988:
2984:
2977:
2973:
2965:
2961:
2956:
2952:
2947:
2944:
2941:
2937:
2926:
2908:
2905:
2902:
2898:
2891:
2887:
2879:
2875:
2870:
2866:
2861:
2858:
2855:
2851:
2840:
2827:
2823:
2819:
2814:
2810:
2799:
2796:
2793:
2789:
2782:
2778:
2770:
2766:
2761:
2757:
2752:
2749:
2746:
2742:
2731:
2713:
2710:
2707:
2703:
2696:
2692:
2684:
2680:
2675:
2671:
2666:
2663:
2660:
2656:
2645:
2632:
2629:
2626:
2622:
2618:
2613:
2610:
2607:
2603:
2599:
2594:
2591:
2588:
2584:
2580:
2575:
2572:
2569:
2565:
2561:
2555:
2552:
2549:
2544:
2508:Ericsson cycle
2500:Stirling cycle
2496:steam turbines
2476:diesel engines
2453:motor vehicles
2449:electric power
2441:Main article:
2430:
2427:
2426:
2425:
2422:
2419:
2412:
2368:
2365:
2364:
2363:
2351:
2348:
2343:
2339:
2336:
2330:
2327:
2324:
2310:
2298:
2295:
2290:
2285:
2281:
2267:
2261:
2249:
2246:
2243:
2240:
2226:
2214:
2211:
2208:
2205:
2191:
2179:
2176:
2173:
2170:
2156:
2144:
2141:
2138:
2135:
2121:
2109:
2106:
2103:
2100:
2081:
2078:
2062:
2061:
2048:
2045:
2042:
2038:
2034:
2029:
2026:
2022:
2018:
2015:
2012:
2009:
1989:
1988:
1977:
1974:
1968:
1965:
1962:
1959:
1906:
1903:
1873:
1870:
1862:thermodynamics
1847:
1844:
1841:
1837:
1814:
1811:
1807:
1786:
1775:
1774:
1763:
1760:
1755:
1752:
1749:
1745:
1741:
1736:
1733:
1729:
1725:
1722:
1719:
1686:state function
1639:
1638:
1636:
1635:
1628:
1621:
1613:
1610:
1609:
1608:
1607:
1594:
1593:
1590:
1589:
1584:
1579:
1574:
1568:
1565:
1564:
1561:
1560:
1556:
1555:
1550:
1545:
1540:
1535:
1530:
1525:
1520:
1515:
1510:
1505:
1500:
1495:
1490:
1485:
1480:
1475:
1470:
1465:
1460:
1455:
1450:
1445:
1440:
1435:
1430:
1425:
1419:
1418:
1415:
1414:
1411:
1410:
1405:
1404:
1403:
1402:
1397:
1389:
1388:
1386:
1385:
1382:
1378:
1375:
1374:
1372:
1371:
1366:
1364:Thermodynamics
1360:
1357:
1356:
1352:
1351:
1350:
1349:
1340:
1338:
1329:
1327:
1318:
1313:
1312:
1306:
1305:
1304:
1303:
1298:
1293:
1281:
1280:
1278:Caloric theory
1274:
1271:
1270:
1266:
1265:
1263:
1262:
1257:
1252:
1247:
1242:
1237:
1232:
1226:
1223:
1222:
1216:
1215:
1214:
1213:
1206:
1205:
1200:
1195:
1189:
1186:
1185:
1179:
1176:
1175:
1172:
1168:
1167:
1166:
1163:
1162:
1158:
1157:
1146:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1116:
1102:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1047:
1036:
1033:
1030:
1027:
1024:
1021:
1018:
1015:
1012:
1009:
1006:
992:
981:
978:
975:
972:
969:
966:
951:
949:
948:
943:
937:
936:
931:
930:
927:
926:
923:
922:
915:
910:
905:
898:
897:
892:
887:
882:
876:
875:
870:
869:
866:
865:
859:
858:
855:
854:
843:
840:
830:
819:
808:
807:
796:
793:
783:
772:
758:
747:
744:
734:
727:
726:
723:
722:
711:
708:
698:
687:
676:
675:
664:
661:
651:
640:
626:
615:
612:
609:
599:
592:
591:
588:
587:
576:
573:
563:
552:
541:
540:
529:
526:
516:
505:
491:
480:
477:
467:
458:
457:
456:
450:
445:
444:
441:
440:
435:
434:
433:
432:
427:
422:
411:
400:
381:
380:
374:
373:
371:
370:
365:
359:
356:
355:
349:
348:
347:
346:
341:
322:
321:
316:
315:
312:
311:
306:
305:
304:
303:
298:
293:
285:
284:
278:
277:
276:
275:
270:
265:
260:
258:Free expansion
255:
250:
245:
240:
235:
230:
225:
220:
212:
211:
205:
204:
203:
202:
197:
195:Control volume
192:
187:
185:Phase (matter)
182:
177:
172:
167:
159:
158:
150:
149:
144:
139:
133:
128:
127:
124:
123:
119:
118:
113:
108:
103:
97:
96:
91:
90:
87:
86:
83:
82:
71:
70:
65:
60:
55:
49:
48:
45:
44:
41:
40:
35:The classical
34:
26:
25:
23:Thermodynamics
15:
9:
6:
4:
3:
2:
5744:
5733:
5730:
5728:
5725:
5723:
5720:
5718:
5715:
5713:
5710:
5709:
5707:
5692:
5689:
5687:
5684:
5682:
5679:
5677:
5674:
5672:
5669:
5667:
5666:Transcritical
5664:
5662:
5659:
5657:
5654:
5652:
5649:
5647:
5646:Hampson–Linde
5644:
5643:
5641:
5639:
5638:Refrigeration
5635:
5629:
5626:
5624:
5621:
5619:
5616:
5615:
5613:
5609:
5603:
5600:
5598:
5595:
5593:
5590:
5588:
5585:
5583:
5580:
5578:
5575:
5573:
5570:
5568:
5567:Gas-generator
5565:
5563:
5560:
5558:
5555:
5553:
5552:Brayton/Joule
5550:
5548:
5545:
5544:
5542:
5540:
5534:
5524:
5521:
5518:
5514:
5511:
5509:
5506:
5504:
5501:
5500:
5498:
5494:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5458:
5457:Brayton/Joule
5455:
5453:
5450:
5449:
5447:
5443:
5435:
5432:
5430:
5424:
5420:
5413:
5408:
5406:
5401:
5399:
5394:
5393:
5390:
5378:
5375:
5371:
5368:
5364:
5360:
5359:
5347:
5346:0-07-238332-1
5343:
5337:
5335:
5333:
5324:
5322:0-07-238332-1
5318:
5314:
5309:
5308:
5299:
5295:
5285:
5282:
5280:
5277:
5275:
5272:
5271:
5265:
5248:
5245:
5240:
5234:
5231:
5228:
5224:
5220:
5214:
5211:
5208:
5205:
5202:
5195:
5194:
5193:
5173:
5168:
5165:
5162:
5158:
5152:
5149:
5139:
5138:
5137:
5135:
5134:absolute zero
5114:
5108:
5105:
5102:
5098:
5094:
5086:
5081:
5077:
5073:
5070:
5063:
5062:
5061:
5059:
5039:
5036:
5033:
5030:
5027:
5020:
5019:
5018:
5016:
5012:
5008:
4998:
4982:
4978:
4955:
4951:
4942:
4933:
4929:
4926:
4922:
4921:
4920:
4915:
4905:
4903:
4899:
4875:
4871:
4867:
4862:
4858:
4851:
4847:
4841:
4838:
4835:
4832:
4822:
4821:
4820:
4818:
4794:
4790:
4786:
4781:
4777:
4770:
4766:
4760:
4757:
4754:
4751:
4748:
4745:
4735:
4734:
4733:
4731:
4727:
4708:
4704:
4679:
4675:
4646:
4642:
4636:
4632:
4626:
4623:
4620:
4617:
4610:
4609:
4608:
4606:
4602:
4598:
4594:
4590:
4584:
4574:
4572:
4567:
4551:
4548:
4545:
4542:
4539:
4535:
4531:
4526:
4523:
4520:
4517:
4514:
4510:
4489:
4486:
4481:
4478:
4475:
4472:
4469:
4465:
4461:
4456:
4453:
4450:
4447:
4444:
4440:
4436:
4431:
4428:
4425:
4422:
4419:
4415:
4386:
4382:
4378:
4373:
4369:
4357:
4353:
4349:
4344:
4340:
4333:
4325:
4321:
4317:
4312:
4308:
4299:
4295:
4291:
4283:
4279:
4275:
4270:
4266:
4257:
4253:
4249:
4241:
4237:
4233:
4228:
4224:
4215:
4211:
4207:
4199:
4195:
4191:
4186:
4182:
4173:
4169:
4165:
4160:
4157:
4154:
4151:
4148:
4144:
4134:
4120:
4112:
4108:
4104:
4101:
4095:
4092:
4072:
4069:
4066:
4046:
4038:
4034:
4030:
4027:
4007:
4001:
3998:
3995:
3986:
3972:
3964:
3960:
3956:
3953:
3943:is constant,
3928:
3924:
3900:
3897:
3892:
3888:
3882:
3877:
3873:
3869:
3866:
3856:
3855:
3854:
3840:
3820:
3812:
3796:
3776:
3768:
3760:
3756:
3753:
3749:
3748:
3747:
3740:
3727:
3724:
3721:
3718:
3715:
3712:
3710:
3707:
3706:
3702:
3699:
3696:
3693:
3690:
3688:
3686:
3683:
3682:
3679:
3675:
3671:
3668:
3665:
3662:
3659:
3656:
3654:
3651:
3650:
3647:
3646:Diesel engine
3644:
3641:
3638:
3635:
3632:
3630:
3627:
3626:
3622:
3618:
3614:
3610:
3606:
3603:
3600:
3597:
3594:
3591:
3589:
3586:
3585:
3573:
3570:
3567:
3564:
3561:
3559:
3556:
3555:
3551:
3546:
3543:
3540:
3537:
3534:
3531:
3529:
3526:
3525:
3522:
3518:
3515:
3512:
3509:
3506:
3504:
3501:
3500:
3497:
3494:
3491:
3488:
3485:
3482:
3480:
3477:
3476:
3473:
3470:
3467:
3462:
3459:
3457:
3454:
3453:
3450:
3447:
3444:
3441:
3438:
3436:
3433:
3432:
3429:
3428:Steam engines
3426:
3423:
3420:
3417:
3414:
3412:
3409:
3408:
3404:
3401:
3398:
3395:
3392:
3390:
3387:
3386:
3383:
3380:
3377:
3374:
3371:
3368:
3366:
3363:
3362:
3358:
3355:
3352:
3349:
3346:
3344:
3341:
3340:
3336:
3331:
3327:
3324:
3321:
3318:
3315:
3312:
3311:
3306:
3300:
3297:
3294:
3291:
3288:
3285:
3282:
3279:
3276:
3273:
3270:
3267:
3266:
3265:
3263:
3253:
3244:
3241:
3238:
3237:
3233:
3229:
3226:
3222:
3219:
3215:
3214:
3211:
3209:
3204:
3202:
3201:Brayton cycle
3198:
3194:
3180:
3176:
3175:
3167:
3165:
3164:liquify gases
3161:
3157:
3153:
3149:
3145:
3144:refrigerators
3141:
3137:
3131:
3105:
3099:
3095:
3091:
3086:
3080:
3076:
3072:
3055:
3041:
3040:
3039:
3020:
3016:
3012:
3007:
3003:
2992:
2989:
2986:
2982:
2975:
2971:
2963:
2959:
2954:
2950:
2945:
2939:
2935:
2927:
2906:
2903:
2900:
2896:
2889:
2885:
2877:
2873:
2868:
2864:
2859:
2853:
2849:
2841:
2825:
2821:
2817:
2812:
2808:
2797:
2794:
2791:
2787:
2780:
2776:
2768:
2764:
2759:
2755:
2750:
2744:
2740:
2732:
2711:
2708:
2705:
2701:
2694:
2690:
2682:
2678:
2673:
2669:
2664:
2658:
2654:
2646:
2630:
2624:
2620:
2616:
2611:
2605:
2601:
2597:
2592:
2586:
2582:
2578:
2573:
2567:
2563:
2559:
2542:
2528:
2527:
2526:
2524:
2515:
2511:
2509:
2505:
2501:
2497:
2493:
2492:Rankine cycle
2489:
2485:
2484:Brayton cycle
2481:
2477:
2473:
2469:
2465:
2461:
2456:
2454:
2450:
2444:
2435:
2423:
2420:
2417:
2413:
2410:
2406:
2402:
2398:
2394:
2390:
2386:
2385:
2384:
2382:
2373:
2349:
2346:
2341:
2337:
2334:
2328:
2325:
2322:
2314:
2311:
2296:
2293:
2288:
2283:
2279:
2271:
2268:
2265:
2262:
2247:
2244:
2241:
2238:
2230:
2227:
2212:
2209:
2206:
2203:
2195:
2192:
2177:
2174:
2171:
2168:
2160:
2157:
2142:
2139:
2136:
2133:
2125:
2122:
2107:
2104:
2101:
2098:
2090:
2087:
2086:
2085:
2077:
2075:
2071:
2066:
2046:
2043:
2040:
2036:
2032:
2027:
2024:
2020:
2016:
2013:
2010:
2007:
1994:
1993:
1992:
1975:
1972:
1966:
1963:
1960:
1957:
1944:
1943:
1942:
1940:
1936:
1932:
1928:
1924:
1920:
1911:
1902:
1900:
1896:
1892:
1887:
1883:
1879:
1872:Heat and work
1869:
1867:
1863:
1845:
1842:
1839:
1835:
1812:
1809:
1805:
1784:
1761:
1758:
1753:
1750:
1747:
1743:
1739:
1734:
1731:
1727:
1723:
1720:
1710:
1709:
1708:
1706:
1702:
1698:
1694:
1689:
1687:
1683:
1679:
1675:
1671:
1666:
1662:
1658:
1654:
1651:that involve
1650:
1646:
1634:
1629:
1627:
1622:
1620:
1615:
1614:
1612:
1611:
1606:
1598:
1597:
1596:
1595:
1588:
1585:
1583:
1580:
1578:
1577:Self-assembly
1575:
1573:
1570:
1569:
1563:
1562:
1554:
1551:
1549:
1548:van der Waals
1546:
1544:
1541:
1539:
1536:
1534:
1531:
1529:
1526:
1524:
1521:
1519:
1516:
1514:
1511:
1509:
1506:
1504:
1501:
1499:
1496:
1494:
1491:
1489:
1486:
1484:
1481:
1479:
1476:
1474:
1473:von Helmholtz
1471:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1431:
1429:
1426:
1424:
1421:
1420:
1413:
1412:
1401:
1398:
1396:
1393:
1392:
1391:
1390:
1383:
1380:
1379:
1377:
1376:
1370:
1367:
1365:
1362:
1361:
1359:
1358:
1354:
1353:
1347:
1346:
1339:
1336:
1335:
1328:
1325:
1324:
1317:
1316:
1315:
1314:
1311:
1308:
1307:
1302:
1299:
1297:
1294:
1292:
1288:
1284:
1283:
1279:
1276:
1275:
1273:
1272:
1268:
1267:
1261:
1258:
1256:
1253:
1251:
1248:
1246:
1243:
1241:
1238:
1236:
1233:
1231:
1228:
1227:
1225:
1224:
1221:
1218:
1217:
1212:
1209:
1208:
1204:
1201:
1199:
1196:
1194:
1191:
1190:
1188:
1187:
1183:
1182:
1173:
1170:
1169:
1165:
1164:
1144:
1141:
1138:
1135:
1132:
1126:
1123:
1120:
1114:
1106:
1103:
1089:
1086:
1083:
1080:
1077:
1071:
1068:
1065:
1059:
1051:
1048:
1034:
1031:
1028:
1025:
1022:
1016:
1013:
1010:
1004:
996:
993:
976:
973:
970:
964:
956:
953:
952:
947:
944:
942:
939:
938:
934:
929:
928:
921:
920:
916:
914:
911:
909:
906:
904:
901:
900:
896:
895:Ideal gas law
893:
891:
888:
886:
883:
881:
878:
877:
873:
868:
867:
841:
831:
817:
810:
809:
794:
784:
770:
763:
762:
759:
745:
742:
735:
732:
729:
728:
709:
699:
685:
678:
677:
662:
652:
638:
631:
630:
627:
613:
610:
607:
600:
597:
594:
593:
574:
564:
550:
543:
542:
527:
517:
503:
496:
495:
492:
478:
475:
468:
465:
462:
461:
455:
452:
451:
448:
443:
442:
431:
428:
426:
425:Vapor quality
423:
421:
420:
415:
412:
410:
409:
404:
401:
398:
394:
393:
388:
385:
384:
383:
382:
379:
376:
375:
369:
366:
364:
361:
360:
358:
357:
354:
351:
350:
345:
342:
340:
337:
336:
335:
334:
330:
326:
319:
314:
313:
302:
299:
297:
294:
292:
289:
288:
287:
286:
283:
280:
279:
274:
271:
269:
266:
264:
263:Reversibility
261:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
219:
216:
215:
214:
213:
210:
207:
206:
201:
198:
196:
193:
191:
188:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
162:
161:
160:
157:
154:
153:
148:
145:
143:
140:
138:
137:Closed system
135:
134:
131:
126:
125:
117:
114:
112:
109:
107:
104:
102:
99:
98:
94:
89:
88:
81:
77:
74:
73:
69:
66:
64:
61:
59:
56:
54:
51:
50:
43:
42:
38:
32:
28:
27:
24:
21:
20:
5523:Regenerative
5452:Bell Coleman
5418:
5373:
5366:
5362:
5306:
5298:
5263:
5191:
5131:
5055:
5014:
5006:
5004:
4940:
4937:
4931:
4924:
4917:
4895:
4817:refrigerator
4814:
4665:
4589:Carnot cycle
4586:
4583:Carnot cycle
4577:Carnot cycle
4568:
4135:
3987:
3915:
3764:
3758:
3751:
3745:
3343:Bell Coleman
3304:
3259:
3250:
3205:
3189:
3152:refrigerants
3133:
3037:
2520:
2488:gas turbines
2482:include the
2472:Diesel cycle
2457:
2446:
2429:Power cycles
2378:
2083:
2067:
2063:
1990:
1938:
1934:
1930:
1926:
1922:
1916:
1881:
1878:power cycles
1877:
1875:
1776:
1690:
1644:
1642:
1438:Carathéodory
1369:Heat engines
1341:
1330:
1319:
1301:Motive power
1286:
946:Free entropy
917:
417:
416: /
406:
405: /
397:introduction
390:
389: /
328:
291:Heat engines
281:
78: /
5691:Ionocaloric
5686:Vuilleumier
5508:Hygroscopic
3767:perfect gas
3734:Ideal cycle
3623:from 1833.
3519:Manson and
3435:Hygroscopic
3378:isothermal
3299:isenthalpic
3193:gas turbine
2443:Heat engine
2409:temperature
2264:Isenthalpic
2070:heat engine
1670:heat engine
1260:Synergetics
941:Free energy
387:Temperature
248:Quasistatic
243:Isenthalpic
200:Instruments
190:Equilibrium
142:Open system
76:Equilibrium
58:Statistical
5706:Categories
5656:Pulse tube
5628:Mixed/dual
5290:References
5279:Economizer
4925:isothermal
4815:and for a
4601:isothermal
4597:isentropic
4502:, we have
3722:isochoric
3719:isentropic
3713:isentropic
3701:Pulse jets
3670:Shcramjets
3663:isentropic
3657:isentropic
3642:isochoric
3571:isochoric
3568:isentropic
3562:isentropic
3513:isothermal
3507:isothermal
3492:isochoric
3489:isothermal
3483:isothermal
3471:isochoric
3465:and volume
3399:isothermal
3393:isothermal
3375:isentropic
3372:isothermal
3369:isentropic
3293:isentropic
3275:isothermal
3197:jet engine
3140:heat pumps
2506:, and the
2470:, and the
2464:Otto cycle
2389:Isentropic
2381:Otto Cycle
2313:Reversible
2270:Polytropic
2229:Isentropic
2124:Isothermal
1919:PV diagram
1572:Nucleation
1416:Scientists
1220:Philosophy
933:Potentials
296:Heat pumps
253:Polytropic
238:Isentropic
228:Isothermal
5651:Kleemenko
5537:Internal
5215:∮
5203:∮
5147:Δ
5078:∫
5028:∮
4934:processes
4932:isochoric
4927:processes
4868:−
4787:−
4730:heat pump
4627:−
4618:η
4462:−
4412:Δ
4379:−
4350:−
4318:−
4276:−
4234:−
4192:−
4118:Δ
4099:Δ
4044:Δ
4005:Δ
3970:Δ
3951:Δ
3874:∫
3864:Δ
3761:processes
3759:isochoric
3754:processes
3716:isochoric
3697:isobaric
3694:adiabatic
3691:isochoric
3666:isobaric
3660:isochoric
3639:adiabatic
3633:adiabatic
3609:turbojets
3601:isobaric
3598:adiabatic
3592:adiabatic
3565:isochoric
3541:isobaric
3538:adiabatic
3532:adiabatic
3510:isochoric
3486:isochoric
3468:adiabatic
3460:adiabatic
3448:isobaric
3445:adiabatic
3439:adiabatic
3424:isobaric
3421:adiabatic
3415:adiabatic
3402:isobaric
3356:isobaric
3353:adiabatic
3347:adiabatic
3287:isochoric
3269:adiabatic
3103:→
3084:→
2955:∫
2943:→
2869:∫
2857:→
2760:∫
2748:→
2674:∫
2662:→
2628:→
2609:→
2590:→
2571:→
2416:Isochoric
2393:adiabatic
2329:−
2239:δ
2204:δ
2194:Isochoric
2169:δ
2134:δ
2099:δ
2089:Adiabatic
2074:heat pump
2033:−
1964:∮
1740:−
1718:Δ
1707:applies:
1674:heat pump
1553:Waterston
1503:von Mayer
1458:de Donder
1448:Clapeyron
1428:Boltzmann
1423:Bernoulli
1384:Education
1355:Timelines
1139:−
1084:−
872:Equations
839:∂
792:∂
743:α
707:∂
660:∂
614:−
608:β
572:∂
525:∂
233:Adiabatic
223:Isochoric
209:Processes
170:Ideal gas
53:Classical
5618:Combined
5577:Humphrey
5562:Expander
5547:Atkinson
5482:Stoddard
5472:Stirling
5467:Ericsson
5427:External
5268:See also
3752:isobaric
3653:Humphrey
3636:isobaric
3595:isobaric
3558:Atkinson
3535:isobaric
3528:Stoddard
3479:Stirling
3442:isobaric
3418:isobaric
3396:isobaric
3389:Ericsson
3350:isobaric
3281:isobaric
2462:are the
2401:pressure
2159:Isobaric
1605:Category
1543:Thompson
1453:Clausius
1433:Bridgman
1287:Vis viva
1269:Theories
1203:Gas laws
995:Enthalpy
403:Pressure
218:Isobaric
175:Real gas
63:Chemical
46:Branches
5681:Siemens
5597:Scuderi
5513:Rankine
5274:Entropy
3617:-shafts
3605:Ramjets
3588:Brayton
3456:Scuderi
3411:Rankine
2397:entropy
1682:entropy
1528:Smeaton
1523:Rankine
1513:Onsager
1498:Maxwell
1493:Massieu
1198:Entropy
1193:General
1184:History
1174:Culture
1171:History
395: (
392:Entropy
329:italics
130:Systems
5587:Miller
5582:Lenoir
5557:Diesel
5503:Kalina
5487:Manson
5462:Carnot
5344:
5319:
4830:
4743:
4728:for a
4666:where
3685:Lenoir
3674:pulse-
3629:Diesel
3615:, and
3613:-props
3578:< V
3503:Manson
3365:Carnot
3328:Notes
3313:Cycle
3136:models
2498:, the
2490:, the
2405:volume
1970:
1929:) and
1897:, the
1665:system
1518:Planck
1508:Nernst
1483:Kelvin
1443:Carnot
733:
598:
466:
408:Volume
323:Note:
282:Cycles
111:Second
101:Zeroth
5611:Mixed
5009:is a
4732:is:
4085:and
2414:2→3:
2387:1→2:
1566:Other
1533:Stahl
1488:Lewis
1478:Joule
1468:Gibbs
1463:Duhem
156:State
116:Third
106:First
5623:HEHC
5592:Otto
5342:ISBN
5317:ISBN
4900:and
4587:The
4020:and
3709:Otto
3676:and
3142:and
2379:The
1880:and
1701:work
1699:and
1697:heat
1657:work
1655:and
1538:Tait
368:Heat
363:Work
93:Laws
5060:as
5005:If
4941:Q=W
4595:of
3195:or
3050:(4)
2537:(3)
2411:(T)
2003:(2)
1953:(1)
1893:or
1381:Art
327:in
5708::
5331:^
5315:.
5313:14
4566:.
4133:.
3769:,
3672:,
3611:,
3607:,
3582:.
3552::
3166:.
2391:/
2076:.
1688:.
1643:A
5519:)
5515:(
5444:)
5440:(
5411:e
5404:t
5397:v
5369:.
5348:.
5325:.
5249:0
5246:=
5241:T
5235:v
5232:e
5229:r
5225:Q
5221:d
5212:=
5209:S
5206:d
5188:.
5174:T
5169:v
5166:e
5163:r
5159:Q
5153:=
5150:S
5115:T
5109:v
5106:e
5103:r
5099:Q
5095:d
5087:T
5082:0
5074:=
5071:S
5052:.
5040:0
5037:=
5034:Z
5031:d
5015:Z
5007:Z
4983:C
4979:T
4956:H
4952:T
4876:L
4872:T
4863:H
4859:T
4852:L
4848:T
4842:=
4839:P
4836:O
4833:C
4795:L
4791:T
4782:H
4778:T
4771:L
4767:T
4761:+
4758:1
4755:=
4752:P
4749:O
4746:C
4709:H
4705:T
4680:L
4676:T
4647:H
4643:T
4637:L
4633:T
4624:1
4621:=
4552:e
4549:l
4546:c
4543:y
4540:c
4536:W
4532:=
4527:e
4524:l
4521:c
4518:y
4515:c
4511:Q
4490:0
4487:=
4482:e
4479:l
4476:c
4473:y
4470:c
4466:W
4457:e
4454:l
4451:c
4448:y
4445:c
4441:Q
4437:=
4432:e
4429:l
4426:c
4423:y
4420:c
4416:U
4392:)
4387:1
4383:v
4374:2
4370:v
4366:(
4363:)
4358:C
4354:p
4345:A
4341:p
4337:(
4334:=
4331:)
4326:2
4322:v
4313:1
4309:v
4305:(
4300:C
4296:p
4292:+
4289:)
4284:1
4280:v
4271:2
4267:v
4263:(
4258:A
4254:p
4250:=
4247:)
4242:3
4238:v
4229:4
4225:v
4221:(
4216:C
4212:p
4208:+
4205:)
4200:1
4196:v
4187:2
4183:v
4179:(
4174:A
4170:p
4166:=
4161:e
4158:l
4155:c
4152:y
4149:c
4145:W
4121:T
4113:v
4109:C
4105:=
4102:U
4096:=
4093:Q
4073:0
4070:=
4067:W
4047:T
4039:p
4035:C
4031:=
4028:Q
4008:v
4002:p
3999:=
3996:W
3973:T
3965:v
3961:C
3957:=
3954:U
3929:v
3925:C
3901:T
3898:d
3893:v
3889:C
3883:b
3878:a
3870:=
3867:U
3841:b
3821:a
3797:T
3777:U
3580:4
3576:1
3106:4
3100:3
3096:W
3092:+
3087:2
3081:1
3077:W
3073:=
3067:t
3064:e
3061:n
3056:W
3021:1
3017:V
3013:=
3008:4
3004:V
2993:,
2990:V
2987:d
2983:P
2976:1
2972:V
2964:4
2960:V
2951:=
2946:1
2940:4
2936:W
2907:,
2904:V
2901:d
2897:P
2890:4
2886:V
2878:3
2874:V
2865:=
2860:4
2854:3
2850:W
2826:3
2822:V
2818:=
2813:2
2809:V
2798:,
2795:V
2792:d
2788:P
2781:3
2777:V
2769:2
2765:V
2756:=
2751:3
2745:2
2741:W
2712:,
2709:V
2706:d
2702:P
2695:2
2691:V
2683:1
2679:V
2670:=
2665:2
2659:1
2655:W
2631:1
2625:4
2621:W
2617:+
2612:4
2606:3
2602:W
2598:+
2593:3
2587:2
2583:W
2579:+
2574:2
2568:1
2564:W
2560:=
2554:t
2551:e
2548:n
2543:W
2362:.
2350:0
2347:=
2342:T
2338:Q
2335:d
2326:S
2323:d
2309:.
2297:C
2294:=
2289:n
2284:V
2280:p
2248:0
2245:=
2242:S
2213:0
2210:=
2207:V
2178:0
2175:=
2172:P
2143:0
2140:=
2137:T
2108:0
2105:=
2102:Q
2047:t
2044:u
2041:o
2037:Q
2028:n
2025:i
2021:Q
2017:=
2014:Q
2011:=
2008:W
1976:V
1973:d
1967:P
1961:=
1958:W
1939:W
1935:V
1931:X
1927:P
1923:Y
1846:t
1843:u
1840:o
1836:E
1813:n
1810:i
1806:E
1785:U
1762:0
1759:=
1754:t
1751:u
1748:o
1744:E
1735:n
1732:i
1728:E
1724:=
1721:U
1632:e
1625:t
1618:v
1145:S
1142:T
1136:H
1133:=
1130:)
1127:p
1124:,
1121:T
1118:(
1115:G
1090:S
1087:T
1081:U
1078:=
1075:)
1072:V
1069:,
1066:T
1063:(
1060:A
1035:V
1032:p
1029:+
1026:U
1023:=
1020:)
1017:p
1014:,
1011:S
1008:(
1005:H
980:)
977:V
974:,
971:S
968:(
965:U
842:T
818:V
795:V
771:1
746:=
710:p
686:V
663:V
639:1
611:=
575:T
551:N
528:S
504:T
479:=
476:c
399:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
