2687:. For two given macroscopically specified states of a system, there is a mathematically defined quantity called the 'difference of information entropy between them'. This defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the initial macroscopically specified state from the final macroscopically specified state. Equivalently, in a thermodynamic process, energy spreads.
2712:
42:
1612:
3669:
1837:, and ultimately dates back to theories of heat in antiquity. The laws of thermodynamics are the result of progress made in this field over the nineteenth and early twentieth centuries. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by
2323:
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's
1864:
with entropy increases. Gradually, this resolved itself and a zeroth law was later added to allow for a self-consistent definition of temperature. Additional laws have been suggested, but have not achieved the generality of the four accepted laws, and are generally not discussed in standard textbooks.
1863:
over the period 1906–1912. While the numbering of the laws is universal today, various textbooks throughout the 20th century have numbered the laws differently. In some fields, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt
2322:
is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces acting between the system and its surroundings. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.
2669:
While reversible processes are a useful and convenient theoretical limiting case, all natural processes are irreversible. A prime example of this irreversibility is the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies,
2495:
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is
1888:
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law". Some statements go further, so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually
2508:
indicates the irreversibility of natural processes, and in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, especially of temperature. It can be formulated in a variety of interesting and important ways. One of the simplest is the
Clausius
3072:
1725:
Traditionally, thermodynamics has recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law. A more fundamental statement was later labelled as the zeroth law after the first three laws had been established.
2528:
of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same
2715:
a) Single possible configuration for a system at absolute zero, i.e., only one microstate is accessible. b) At temperatures greater than absolute zero, multiple microstates are accessible due to atomic vibration (exaggerated in the
2315:
1331:
2921:
2410:
2732:) the residual entropy of a system is typically close to zero. However, it reaches zero only when the system has a unique ground state (i.e., the state with the minimum thermal energy has only one configuration, or
3317:
Contemporary
Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August
3150:
2676:
may also be viewed as a physical measure concerning the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. Such details are often referred to as
2796:
2149:
2533:
The second law is applicable to a wide variety of processes, both reversible and irreversible. According to the second law, in a reversible heat transfer, an element of heat transferred,
2042:
2490:
2161:, which says that energy can be neither created nor destroyed, but can only change form. A particular consequence of this is that the total energy of an isolated system does not change.
1896:
in the 1930s, long after the first, second, and third laws were widely recognized. The law allows the definition of temperature in a non-circular way without reference to entropy, its
1892:
These concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century. The name 'zeroth law' was invented by
2664:
1737:
and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
2183:
1166:
1111:
1056:
863:
816:
731:
684:
596:
549:
2860:
2554:
1641:
767:
635:
1001:
2737:
1342:
2597:
2333:
500:
2670:
initially of different temperatures, come into direct thermal connection, then heat immediately and spontaneously flows from the hotter body to the colder one.
2621:
2574:
1230:
839:
792:
707:
660:
572:
525:
2524:
with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the
2432:
is a form of energy transfer. Heat transfer is the natural process of moving energy to or from a system, other than by work or the transfer of matter. In a
1806:
464:
2180:. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.
1802:
1320:
3067:{\displaystyle {\frac {\mathrm {d} J_{k}}{\mathrm {d} F_{i}}}{\bigg |}_{F_{i}=0}~=~{\frac {\mathrm {d} J_{i}}{\mathrm {d} F_{k}}}{\bigg |}_{F_{k}=0}}
2330:
When matter is transferred into a system, the internal energy and potential energy associated with it are transferred into the new combined system.
1842:
1353:
2168:
and its relationship to temperature. If a system has a definite temperature, then its total energy has three distinguishable components, termed
3548:
3478:
923:
2904:
1897:
1634:
1221:
457:
335:
890:
2824:= 1 as all the atoms are identical for a pure substance, and as a result all orders are identical as there is only one combination) and
273:
3627:
3613:
3094:
2733:
1405:
1379:
900:
354:
3655:
3641:
3425:
3391:
3370:
3349:
3325:
3274:
3253:
3225:
1852:
306:
2081:
1783:
never decreases. A common corollary of the statement is that heat does not spontaneously pass from a colder body to a warmer body.
1458:
1985:
3673:
3195:
929:
328:
2753:
2744:
with fewer microstates are less probable. In general, entropy is related to the number of possible microstates according to the
2439:
3689:
1627:
2875:
2324:
1558:
90:
2874:
have been considered the fourth law of thermodynamics. They describe the relation between thermodynamic flows and forces in
1838:
1453:
1533:
1306:
283:
1884:
If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
3453:
2871:
2505:
1873:
1768:
1730:
918:
121:
111:
2736:). Microstates are used here to describe the probability of a system being in a specific state, as each microstate is
2696:
2051:
When two initially isolated systems are combined into a new system, then the total internal energy of the new system,
1969:
1915:
1787:
1741:
126:
116:
2915:(related to their related intrinsic parameters, such as temperature and pressure), the Onsager theorem states that
2682:
1824:
1448:
1410:
1374:
86:
1876:
provides for the foundation of temperature as an empirical parameter in thermodynamic systems and establishes the
2887:
2879:
2521:
1880:
between the temperatures of multiple bodies in thermal equilibrium. The law may be stated in the following form:
1818:
1683:
1203:
951:
397:
210:
200:
2418:
denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and
3694:
3577:
3164:
1615:
1443:
1240:
943:
882:
418:
407:
73:
1930:
is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.
2158:
1919:
1761:
1548:
1468:
1265:
349:
78:
1938:(i.e. there is no transfer of matter into or out of the system), the first law states that the change in
3190:
2883:
2319:
1772:
1745:
1691:
1687:
1483:
1060:
373:
219:
68:
3179:
2629:
3500:
1834:
1780:
1679:
1563:
1488:
1478:
278:
152:
140:
2745:
1909:
1877:
1856:
1734:
1508:
1503:
1270:
292:
258:
253:
166:
3174:
2813:
1830:
1597:
1260:
1208:
1121:
1066:
1011:
440:
424:
311:
263:
248:
238:
47:
41:
2711:
1255:
845:
798:
713:
666:
578:
531:
3651:
3637:
3623:
3609:
3554:
3544:
3516:
3474:
3421:
3387:
3366:
3345:
3321:
3270:
3249:
3221:
2827:
2741:
2720:
At absolute zero temperature, the system is in the state with the minimum thermal energy, the
2536:
1922:, adapted for thermodynamic processes. In general, the conservation law states that the total
1663:
1592:
1553:
1543:
1115:
913:
749:
741:
614:
243:
233:
175:
2878:, under the assumption that thermodynamic variables can be defined locally in a condition of
1801:
The first and second laws prohibit two kinds of perpetual motion machines, respectively: the
3508:
2725:
2173:
1703:
1513:
1498:
1438:
1433:
1250:
1245:
971:
895:
363:
228:
3543:. Steve Campbell, Institute of Physics. San Rafael, CA: Morgan & Claypool Publishers.
3540:
Quantum thermodynamics : an introduction to the thermodynamics of quantum information
2433:
2177:
2165:
1939:
1927:
1893:
1848:
1757:
1463:
1311:
965:
606:
429:
190:
157:
3303:, edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.
2576:), both of the system and of the sources or destination of the heat, with the increment (
1790:
states that a system's entropy approaches a constant value as the temperature approaches
3504:
3444:, original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.
2579:
482:
2891:
2606:
2559:
2169:
1860:
1707:
1659:
1518:
1288:
824:
777:
692:
645:
557:
510:
388:
268:
205:
195:
63:
33:
17:
3683:
3437:
2704:
2520:
When two initially isolated systems in separate but nearby regions of space, each in
1935:
1791:
1699:
1587:
905:
474:
435:
147:
3572:
2310:{\displaystyle E_{\rm {total}}=KE_{\rm {system}}+PE_{\rm {system}}+U_{\rm {system}}}
3601:
3491:
Wendt, Richard P. (1974). "Simplified transport theory for electrolyte solutions".
3337:
3312:
2724:. The constant value (not necessarily zero) of entropy at this point is called the
2721:
2436:
system, the internal energy can only be changed by the transfer of energy as heat:
1711:
1538:
1523:
1473:
956:
2047:
For processes that include the transfer of matter, a further statement is needed.
2820:
the number of microstates. At absolute zero there is only 1 microstate possible (
2509:
statement, that heat does not spontaneously pass from a colder to a hotter body.
2060:, will be equal to the sum of the internal energies of the two initial systems,
1859:(or Nernst's postulate), which is now known as the third law, was formulated by
1667:
1493:
301:
3558:
1702:
that form a basis of precluding the possibility of certain phenomena, such as
1582:
1528:
3520:
2703:
A system's entropy approaches a constant value as its temperature approaches
3185:
180:
3538:
3340:(1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in
2405:{\displaystyle \left(u\,\Delta M\right)_{\rm {in}}=\Delta U_{\rm {system}}}
1855:, what are now known as the first and second laws were established. Later,
3668:
3320:, edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam,
3169:
1719:
1296:
1213:
1005:
413:
185:
3365:, (first edition 1968), third edition 1983, Cambridge University Press,
2327:. Work added to the system increases the potential energy of the system.
1798:), the entropy of a system at absolute zero is typically close to zero.
2673:
2600:
2525:
2513:
1776:
1715:
1675:
402:
3512:
3471:
A Farewell to
Entropy: Statistical Thermodynamics Based on Information
1952:) is equal to the difference between the heat supplied to the system (
3442:
Elements of
Classical Thermodynamics for Advanced Students of Physics
2516:
of a thermodynamic system. In terms of this quantity it implies that
1923:
1753:
1671:
1829:
The history of thermodynamics is fundamentally interwoven with the
2729:
2728:
of the system. With the exception of non-crystalline solids (e.g.
2710:
1809:
which spontaneously converts thermal energy into mechanical work.
1795:
3634:
Thermodynamics. An
Advanced Treatment for Chemists and Physicists
3218:
Thermodynamics. An
Advanced Treatment for Chemists and Physicists
3460:, Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.
3145:{\displaystyle J_{i}={\frac {\mathrm {d} X_{i}}{\mathrm {d} t}}}
2429:
1889:
arrange bodies in a real number sequence from colder to hotter.
1749:
1695:
378:
2176:(energy resulting from an externally imposed force field), and
3420:, translated by E.S. Halberstadt, Wiley–Interscience, London,
3407:, Cambridge University Press, London, pp. 30, 34ff, 46f, 83.
1847:. By 1860, as formalized in the works of scientists such as
1744:
states that, when energy passes into or out of a system (as
2903:(energy, mass, entropy, number of particles and so on) and
1900:. Such a temperature definition is said to be 'empirical'.
2791:{\displaystyle S=k_{\mathrm {B} }\,\mathrm {ln} \,\Omega }
3240:
3238:
3236:
3234:
2681:
on a microscopic or molecular scale, and less often as
1698:, and establish relationships between them. They state
3097:
2924:
2830:
2756:
2632:
2609:
2582:
2562:
2539:
2442:
2336:
2186:
2172:(energy due to the motion of the system as a whole),
2084:
1988:
1124:
1069:
1014:
974:
848:
827:
801:
780:
752:
716:
695:
669:
648:
617:
581:
560:
534:
513:
485:
3144:
3066:
2854:
2790:
2658:
2615:
2591:
2568:
2548:
2512:It implies the existence of a quantity called the
2484:
2404:
2309:
2143:
2036:
1805:which produces work with no energy input, and the
1160:
1105:
1050:
995:
857:
833:
810:
786:
761:
725:
701:
678:
654:
629:
590:
566:
543:
519:
494:
3386:, American Institute of Physics Press, New York,
3212:
3210:
3088:index every parameter and its related force, and
3040:
2966:
1794:. With the exception of non-crystalline solids (
3248:, second edition, W.H. Freeman, San Francisco,
2701:
2518:
2049:
1932:
1882:
1718:in general and are applicable in other natural
2740:to have the same probability of occurring, so
2154:The First Law encompasses several principles:
3220:, seventh edition, North Holland, Amsterdam,
2144:{\displaystyle U_{\rm {system}}=U_{1}+U_{2}.}
1635:
8:
3499:(10). American Chemical Society (ACS): 646.
2037:{\displaystyle \Delta U_{\rm {system}}=Q-W.}
3315:(1978). The concepts of thermodynamics, in
1807:perpetual motion machine of the second kind
1686:. The laws also use various parameters for
2599:) of the system's conjugate variable, its
2485:{\displaystyle \Delta U_{\rm {system}}=Q.}
1968:the system on its surroundings. (Note, an
1803:perpetual motion machine of the first kind
1642:
1628:
1191:
343:
162:
40:
29:
3344:, edited by J. Serrin, Springer, Berlin,
3131:
3123:
3114:
3111:
3102:
3096:
3050:
3045:
3039:
3038:
3028:
3019:
3011:
3002:
2999:
2976:
2971:
2965:
2964:
2954:
2945:
2937:
2928:
2925:
2923:
2829:
2784:
2776:
2775:
2768:
2767:
2755:
2652:
2645:
2631:
2608:
2581:
2561:
2538:
2451:
2450:
2441:
2380:
2379:
2359:
2358:
2346:
2335:
2285:
2284:
2255:
2254:
2222:
2221:
2192:
2191:
2185:
2132:
2119:
2090:
2089:
2083:
1997:
1996:
1987:
1972:, not used in this article, is to define
1123:
1068:
1013:
973:
847:
826:
800:
779:
751:
715:
694:
668:
647:
616:
580:
559:
533:
512:
484:
3618:Goldstein, Martin & Inge F. (1993).
3458:Thermodynamics and Statistical Mechanics
3405:The Concepts of Classical Thermodynamics
3297:Thermodynamics and Statistical Mechanics
3206:
2894:). Given a set of extensive parameters
2425:denotes the amount of transferred mass.
1844:Reflections on the Motive Power of Fire
1388:
1365:
1319:
1279:
1229:
1194:
387:
362:
291:
218:
165:
32:
3182:(Parody of the laws of thermodynamics)
1760:changes in accordance with the law of
3532:
3530:
2556:, is the product of the temperature (
27:Observational basis of thermodynamics
7:
3155:are called the thermodynamic flows.
2882:. These relations are derived from
3342:New Perspectives in Thermodynamics
3132:
3115:
3020:
3003:
2946:
2929:
2785:
2780:
2777:
2769:
2467:
2464:
2461:
2458:
2455:
2452:
2443:
2396:
2393:
2390:
2387:
2384:
2381:
2372:
2363:
2360:
2347:
2301:
2298:
2295:
2292:
2289:
2286:
2271:
2268:
2265:
2262:
2259:
2256:
2238:
2235:
2232:
2229:
2226:
2223:
2205:
2202:
2199:
2196:
2193:
2106:
2103:
2100:
2097:
2094:
2091:
2013:
2010:
2007:
2004:
2001:
1998:
1989:
849:
802:
717:
670:
582:
535:
355:Intensive and extensive properties
25:
3620:The Refrigerator and the Universe
3606:Four Laws That Drive the Universe
3573:"Lars Onsager – American chemist"
2659:{\displaystyle \delta Q=T\,dS\,.}
1982:the system by its surroundings):
1710:, they are important fundamental
3667:
3473:, World Scientific, New Jersey,
3196:Table of thermodynamic equations
1611:
1610:
930:Table of thermodynamic equations
3301:Lectures on Theoretical Physics
3244:Kittel, C. Kroemer, H. (1980).
1406:Maxwell's thermodynamic surface
2876:non-equilibrium thermodynamics
2843:
2837:
2805:is the entropy of the system,
2325:gravitational potential energy
1706:. In addition to their use in
1140:
1128:
1085:
1073:
1030:
1018:
990:
978:
1:
3493:Journal of Chemical Education
3286:Guggenheim (1985), p. 8.
1307:Mechanical equivalent of heat
3295:Sommerfeld, A. (1951/1955).
2890:(in the absence of external
2872:Onsager reciprocal relations
2506:second law of thermodynamics
1874:zeroth law of thermodynamics
1769:second law of thermodynamics
1731:zeroth law of thermodynamics
919:Onsager reciprocal relations
3537:Deffner, Sebastian (2019).
2697:third law of thermodynamics
1918:is a version of the law of
1916:first law of thermodynamics
1788:third law of thermodynamics
1742: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}
3711:
3648:Equilibrium Thermodynamics
3384:A Survey of Thermodynamics
3363:Equilibrium Thermodynamics
3361:Adkins, C.J. (1968/1983).
3267:Equilibrium Thermodynamics
1907:
1825:Timeline of thermodynamics
1822:
1816:
858:{\displaystyle \partial T}
811:{\displaystyle \partial V}
726:{\displaystyle \partial p}
679:{\displaystyle \partial V}
591:{\displaystyle \partial T}
544:{\displaystyle \partial S}
3632:Guggenheim, E.A. (1985).
3216:Guggenheim, E.A. (1985).
2888:microscopic reversibility
2522:thermodynamic equilibrium
1970:alternate sign convention
1819:History of thermodynamics
1771:states that in a natural
1684:thermodynamic equilibrium
1332:An Inquiry Concerning the
3578:Encyclopaedia Britannica
3418:Classical Thermodynamics
2855:{\displaystyle \ln(1)=0}
2549:{\displaystyle \delta Q}
1662:which define a group of
1345:Heterogeneous Substances
762:{\displaystyle \alpha =}
630:{\displaystyle \beta =-}
3622:. Harvard Univ. Press.
3403:Buchdahl, H.A. (1966),
3269:, McGraw-Hill, London,
3165:Chemical thermodynamics
2886:under the principle of
1688:thermodynamic processes
3690:Laws of thermodynamics
3674:Laws of thermodynamics
3646:Adkins, C. J., (1968)
3146:
3068:
2856:
2792:
2717:
2709:
2660:
2617:
2593:
2570:
2550:
2531:
2486:
2406:
2311:
2159:Conservation of energy
2152:
2145:
2045:
2038:
1920:conservation of energy
1886:
1762:conservation of energy
1656:laws of thermodynamics
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
18:Laws of Thermodynamics
3469:Ben-Naim, A. (2008).
3416:*MĂĽnster, A. (1970),
3265:Adkins, C.J. (1968).
3191:Statistical mechanics
3147:
3069:
2884:statistical mechanics
2857:
2793:
2714:
2661:
2618:
2594:
2571:
2551:
2487:
2407:
2312:
2146:
2039:
1781:thermodynamic systems
1773:thermodynamic process
1680:thermodynamic systems
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:
3676:at Wikimedia Commons
3095:
2922:
2905:thermodynamic forces
2828:
2754:
2630:
2607:
2580:
2560:
2537:
2440:
2334:
2184:
2082:
1986:
1841:in 1824 in his book
1835:history of chemistry
1678:, that characterize
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:
3636:, seventh edition.
3505:1974JChEd..51..646W
3382:Bailyn, M. (1994).
2746:Boltzmann principle
2684:dispersal of energy
1910:Thermodynamic cycle
1878:transitive relation
1779:of the interacting
1735:thermal equilibrium
1664:physical quantities
1334:Source ... Friction
1266:Loschmidt's paradox
458:Material properties
336:Conjugate variables
3180:Ginsberg's theorem
3175:Entropy production
3142:
3064:
2852:
2814:Boltzmann constant
2788:
2742:macroscopic states
2718:
2699:can be stated as:
2656:
2613:
2592:{\displaystyle dS}
2589:
2566:
2546:
2482:
2402:
2307:
2141:
2034:
1898:conjugate variable
1831:history of physics
1692:thermodynamic work
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
3672:Media related to
3550:978-1-64327-658-8
3513:10.1021/ed051p646
3479:978-981-270-706-2
3140:
3035:
2998:
2992:
2961:
2880:local equilibrium
2866:Onsager relations
2616:{\displaystyle S}
2569:{\displaystyle T}
1978:as the work done
1775:, the sum of the
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
3702:
3671:
3590:
3589:
3587:
3586:
3569:
3563:
3562:
3534:
3525:
3524:
3488:
3482:
3467:
3461:
3451:
3445:
3435:
3429:
3414:
3408:
3401:
3395:
3380:
3374:
3359:
3353:
3335:
3329:
3310:
3304:
3293:
3287:
3284:
3278:
3263:
3257:
3242:
3229:
3214:
3151:
3149:
3148:
3143:
3141:
3139:
3135:
3129:
3128:
3127:
3118:
3112:
3107:
3106:
3087:
3073:
3071:
3070:
3065:
3063:
3062:
3055:
3054:
3044:
3043:
3036:
3034:
3033:
3032:
3023:
3017:
3016:
3015:
3006:
3000:
2996:
2990:
2989:
2988:
2981:
2980:
2970:
2969:
2962:
2960:
2959:
2958:
2949:
2943:
2942:
2941:
2932:
2926:
2914:
2902:
2861:
2859:
2858:
2853:
2797:
2795:
2794:
2789:
2783:
2774:
2773:
2772:
2726:residual entropy
2665:
2663:
2662:
2657:
2622:
2620:
2619:
2614:
2598:
2596:
2595:
2590:
2575:
2573:
2572:
2567:
2555:
2553:
2552:
2547:
2491:
2489:
2488:
2483:
2472:
2471:
2470:
2424:
2417:
2411:
2409:
2408:
2403:
2401:
2400:
2399:
2368:
2367:
2366:
2357:
2353:
2316:
2314:
2313:
2308:
2306:
2305:
2304:
2276:
2275:
2274:
2243:
2242:
2241:
2210:
2209:
2208:
2174:potential energy
2150:
2148:
2147:
2142:
2137:
2136:
2124:
2123:
2111:
2110:
2109:
2077:
2068:
2059:
2043:
2041:
2040:
2035:
2018:
2017:
2016:
1977:
1963:
1958:) and the work (
1957:
1951:
1857:Nernst's theorem
1756:), the system's
1704:perpetual motion
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:
3710:
3709:
3705:
3704:
3703:
3701:
3700:
3699:
3695:Scientific laws
3680:
3679:
3664:
3598:
3596:Further reading
3593:
3584:
3582:
3571:
3570:
3566:
3551:
3536:
3535:
3528:
3490:
3489:
3485:
3468:
3464:
3452:
3448:
3436:
3432:
3415:
3411:
3402:
3398:
3381:
3377:
3360:
3356:
3336:
3332:
3311:
3307:
3294:
3290:
3285:
3281:
3264:
3260:
3246:Thermal Physics
3243:
3232:
3215:
3208:
3204:
3161:
3130:
3119:
3113:
3098:
3093:
3092:
3078:
3046:
3037:
3024:
3018:
3007:
3001:
2972:
2963:
2950:
2944:
2933:
2927:
2920:
2919:
2912:
2907:
2900:
2895:
2892:magnetic fields
2868:
2826:
2825:
2811:
2763:
2752:
2751:
2693:
2628:
2627:
2605:
2604:
2578:
2577:
2558:
2557:
2535:
2534:
2502:
2446:
2438:
2437:
2419:
2413:
2375:
2342:
2338:
2337:
2332:
2331:
2280:
2250:
2217:
2187:
2182:
2181:
2178:internal energy
2166:internal energy
2164:The concept of
2128:
2115:
2085:
2080:
2079:
2076:
2070:
2067:
2061:
2058:
2052:
1992:
1984:
1983:
1973:
1959:
1953:
1950:
1943:
1942:of the system (
1940:internal energy
1928:isolated system
1912:
1906:
1894:Ralph H. Fowler
1870:
1853:William Thomson
1849:Rudolf Clausius
1827:
1821:
1815:
1758:internal energy
1700:empirical facts
1660:scientific laws
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:
3708:
3706:
3698:
3697:
3692:
3682:
3681:
3678:
3677:
3663:
3662:External links
3660:
3659:
3658:
3650:. McGraw-Hill
3644:
3630:
3628:978-0674753259
3616:
3614:978-0199232369
3608:. OUP Oxford.
3597:
3594:
3592:
3591:
3564:
3549:
3526:
3483:
3462:
3446:
3430:
3409:
3396:
3375:
3354:
3330:
3305:
3288:
3279:
3258:
3230:
3205:
3203:
3200:
3199:
3198:
3193:
3188:
3183:
3177:
3172:
3167:
3160:
3157:
3153:
3152:
3138:
3134:
3126:
3122:
3117:
3110:
3105:
3101:
3075:
3074:
3061:
3058:
3053:
3049:
3042:
3031:
3027:
3022:
3014:
3010:
3005:
2995:
2987:
2984:
2979:
2975:
2968:
2957:
2953:
2948:
2940:
2936:
2931:
2910:
2898:
2867:
2864:
2851:
2848:
2845:
2842:
2839:
2836:
2833:
2809:
2799:
2798:
2787:
2782:
2779:
2771:
2766:
2762:
2759:
2692:
2689:
2667:
2666:
2655:
2651:
2648:
2644:
2641:
2638:
2635:
2612:
2588:
2585:
2565:
2545:
2542:
2501:
2498:
2493:
2492:
2481:
2478:
2475:
2469:
2466:
2463:
2460:
2457:
2454:
2449:
2445:
2426:
2398:
2395:
2392:
2389:
2386:
2383:
2378:
2374:
2371:
2365:
2362:
2356:
2352:
2349:
2345:
2341:
2328:
2317:
2303:
2300:
2297:
2294:
2291:
2288:
2283:
2279:
2273:
2270:
2267:
2264:
2261:
2258:
2253:
2249:
2246:
2240:
2237:
2234:
2231:
2228:
2225:
2220:
2216:
2213:
2207:
2204:
2201:
2198:
2195:
2190:
2170:kinetic energy
2162:
2140:
2135:
2131:
2127:
2122:
2118:
2114:
2108:
2105:
2102:
2099:
2096:
2093:
2088:
2074:
2065:
2056:
2033:
2030:
2027:
2024:
2021:
2015:
2012:
2009:
2006:
2003:
2000:
1995:
1991:
1948:
1905:
1902:
1869:
1866:
1861:Walther Nernst
1817:Main article:
1814:
1811:
1708:thermodynamics
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:
3707:
3696:
3693:
3691:
3688:
3687:
3685:
3675:
3670:
3666:
3665:
3661:
3657:
3656:0-07-084057-1
3653:
3649:
3645:
3643:
3642:0-444-86951-4
3639:
3635:
3631:
3629:
3625:
3621:
3617:
3615:
3611:
3607:
3603:
3602:Atkins, Peter
3600:
3599:
3595:
3580:
3579:
3574:
3568:
3565:
3560:
3556:
3552:
3546:
3542:
3541:
3533:
3531:
3527:
3522:
3518:
3514:
3510:
3506:
3502:
3498:
3494:
3487:
3484:
3480:
3476:
3472:
3466:
3463:
3459:
3455:
3450:
3447:
3443:
3440:(1957/1966).
3439:
3438:Pippard, A.B.
3434:
3431:
3427:
3426:0-471-62430-6
3423:
3419:
3413:
3410:
3406:
3400:
3397:
3393:
3392:0-88318-797-3
3389:
3385:
3379:
3376:
3372:
3371:0-521-25445-0
3368:
3364:
3358:
3355:
3351:
3350:3-540-15931-2
3347:
3343:
3339:
3334:
3331:
3328:, pp. 411–51.
3327:
3326:0-444-85166-6
3323:
3319:
3314:
3309:
3306:
3302:
3298:
3292:
3289:
3283:
3280:
3276:
3275:0-07-084057-1
3272:
3268:
3262:
3259:
3255:
3254:0-7167-1088-9
3251:
3247:
3241:
3239:
3237:
3235:
3231:
3227:
3226:0-444-86951-4
3223:
3219:
3213:
3211:
3207:
3201:
3197:
3194:
3192:
3189:
3187:
3184:
3181:
3178:
3176:
3173:
3171:
3168:
3166:
3163:
3162:
3158:
3156:
3136:
3124:
3120:
3108:
3103:
3099:
3091:
3090:
3089:
3085:
3081:
3059:
3056:
3051:
3047:
3029:
3025:
3012:
3008:
2993:
2985:
2982:
2977:
2973:
2955:
2951:
2938:
2934:
2918:
2917:
2916:
2913:
2906:
2901:
2893:
2889:
2885:
2881:
2877:
2873:
2865:
2863:
2849:
2846:
2840:
2834:
2831:
2823:
2819:
2815:
2808:
2804:
2764:
2760:
2757:
2750:
2749:
2748:
2747:
2743:
2739:
2735:
2731:
2727:
2723:
2713:
2708:
2706:
2705:absolute zero
2700:
2698:
2690:
2688:
2686:
2685:
2680:
2675:
2671:
2653:
2649:
2646:
2642:
2639:
2636:
2633:
2626:
2625:
2624:
2610:
2602:
2586:
2583:
2563:
2543:
2540:
2530:
2527:
2523:
2517:
2515:
2510:
2507:
2499:
2497:
2479:
2476:
2473:
2447:
2435:
2431:
2427:
2423:
2416:
2376:
2369:
2354:
2350:
2343:
2339:
2329:
2326:
2321:
2318:
2281:
2277:
2251:
2247:
2244:
2218:
2214:
2211:
2188:
2179:
2175:
2171:
2167:
2163:
2160:
2157:
2156:
2155:
2151:
2138:
2133:
2129:
2125:
2120:
2116:
2112:
2086:
2073:
2064:
2055:
2048:
2044:
2031:
2028:
2025:
2022:
2019:
1993:
1981:
1976:
1971:
1967:
1962:
1956:
1947:
1941:
1937:
1936:closed system
1931:
1929:
1925:
1921:
1917:
1911:
1903:
1901:
1899:
1895:
1890:
1885:
1881:
1879:
1875:
1867:
1865:
1862:
1858:
1854:
1850:
1846:
1845:
1840:
1836:
1832:
1826:
1820:
1812:
1810:
1808:
1804:
1799:
1797:
1793:
1792:absolute zero
1789:
1784:
1782:
1778:
1774:
1770:
1765:
1763:
1759:
1755:
1751:
1747:
1743:
1738:
1736:
1732:
1727:
1723:
1721:
1717:
1713:
1709:
1705:
1701:
1697:
1693:
1689:
1685:
1681:
1677:
1673:
1669:
1665:
1661:
1658:are a set of
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:
3647:
3633:
3619:
3605:
3583:. Retrieved
3576:
3567:
3539:
3496:
3492:
3486:
3470:
3465:
3457:
3454:Wilson, H.A.
3449:
3441:
3433:
3417:
3412:
3404:
3399:
3383:
3378:
3373:, pp. 18–20.
3362:
3357:
3341:
3333:
3316:
3308:
3300:
3299:, vol. 5 of
3296:
3291:
3282:
3266:
3261:
3245:
3217:
3154:
3083:
3079:
3076:
2908:
2896:
2869:
2821:
2817:
2806:
2802:
2800:
2722:ground state
2719:
2702:
2694:
2683:
2678:
2672:
2668:
2532:
2519:
2511:
2503:
2496:impossible.
2494:
2428:The flow of
2421:
2414:
2153:
2071:
2062:
2053:
2050:
2046:
1979:
1974:
1965:
1960:
1954:
1945:
1933:
1913:
1891:
1887:
1883:
1871:
1843:
1828:
1800:
1785:
1766:
1739:
1728:
1724:
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
103:
89: /
3581:(biography)
3086:= 1,2,3,...
1839:Sadi Carnot
1668:temperature
1271:Synergetics
952:Free energy
398:Temperature
259:Quasistatic
254:Isenthalpic
211:Instruments
201:Equilibrium
153:Open system
87:Equilibrium
69:Statistical
3684:Categories
3585:2021-03-10
3559:1112388794
3338:Serrin, J.
3313:Serrin, J.
3202:References
2734:microstate
2500:Second law
2434:diathermal
1908:See also:
1868:Zeroth law
1823:See also:
1690:, such as
1666:, such as
1583:Nucleation
1427:Scientists
1231:Philosophy
944:Potentials
307:Heat pumps
264:Polytropic
249:Isentropic
239:Isothermal
3521:0021-9584
3186:H-theorem
2835:
2786:Ω
2691:Third law
2634:δ
2541:δ
2526:entropies
2444:Δ
2373:Δ
2348:Δ
2026:−
1990:Δ
1904:First law
1777:entropies
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
3604:(2007).
3456:(1966).
3428:, p. 22.
3394:, p. 26.
3170:Enthalpy
3159:See also
2716:figure).
2679:disorder
1833:and the
1733:defines
1720:sciences
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
3501:Bibcode
2812:is the
2738:assumed
2674:Entropy
2601:entropy
2529:values.
2514:entropy
1964:) done
1813:History
1796:glasses
1716:physics
1676: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
3654:
3640:
3626:
3612:
3557:
3547:
3519:
3477:
3424:
3390:
3369:
3348:
3324:
3273:
3252:
3224:
3077:where
2997:
2991:
2816:, and
2801:where
2412:where
2057:system
1949:system
1926:of an
1924:energy
1754:matter
1674:, and
1672:energy
1529:Planck
1519:Nernst
1494:Kelvin
1454:Carnot
744:
609:
477:
419:Volume
334:Note:
293:Cycles
122:Second
112:Zeroth
2730:glass
1934:In a
1752:, or
1577:Other
1544:Stahl
1499:Lewis
1489:Joule
1479:Gibbs
1474:Duhem
167:State
127:Third
117:First
3652:ISBN
3638:ISBN
3624:ISBN
3610:ISBN
3555:OCLC
3545:ISBN
3517:ISSN
3475:ISBN
3422:ISBN
3388:ISBN
3367:ISBN
3346:ISBN
3322:ISBN
3318:1977
3271:ISBN
3250:ISBN
3222:ISBN
2870:The
2695:The
2504:The
2430:heat
2320:Work
2069:and
1914:The
1872:The
1851:and
1786:The
1767:The
1750:heat
1746:work
1740:The
1729:The
1712:laws
1696:heat
1694:and
1654:The
1549:Tait
379:Heat
374:Work
104:Laws
3509:doi
2623:):
1714:of
1682:in
1392:Art
338:in
3686::
3575:.
3553:.
3529:^
3515:.
3507:.
3497:51
3495:.
3233:^
3209:^
3082:,
2862:.
2832:ln
2078::
1980:on
1966:by
1764:.
1748:,
1722:.
1670:,
3588:.
3561:.
3523:.
3511::
3503::
3481:.
3352:.
3277:.
3256:.
3228:.
3137:t
3133:d
3125:i
3121:X
3116:d
3109:=
3104:i
3100:J
3084:k
3080:i
3060:0
3057:=
3052:k
3048:F
3041:|
3030:k
3026:F
3021:d
3013:i
3009:J
3004:d
2994:=
2986:0
2983:=
2978:i
2974:F
2967:|
2956:i
2952:F
2947:d
2939:k
2935:J
2930:d
2911:i
2909:F
2899:i
2897:X
2850:0
2847:=
2844:)
2841:1
2838:(
2822:Ω
2818:Ω
2810:B
2807:k
2803:S
2781:n
2778:l
2770:B
2765:k
2761:=
2758:S
2707:.
2654:.
2650:S
2647:d
2643:T
2640:=
2637:Q
2611:S
2603:(
2587:S
2584:d
2564:T
2544:Q
2480:.
2477:Q
2474:=
2468:m
2465:e
2462:t
2459:s
2456:y
2453:s
2448:U
2422:M
2420:Δ
2415:u
2397:m
2394:e
2391:t
2388:s
2385:y
2382:s
2377:U
2370:=
2364:n
2361:i
2355:)
2351:M
2344:u
2340:(
2302:m
2299:e
2296:t
2293:s
2290:y
2287:s
2282:U
2278:+
2272:m
2269:e
2266:t
2263:s
2260:y
2257:s
2252:E
2248:P
2245:+
2239:m
2236:e
2233:t
2230:s
2227:y
2224:s
2219:E
2215:K
2212:=
2206:l
2203:a
2200:t
2197:o
2194:t
2189:E
2139:.
2134:2
2130:U
2126:+
2121:1
2117:U
2113:=
2107:m
2104:e
2101:t
2098:s
2095:y
2092:s
2087:U
2075:2
2072:U
2066:1
2063:U
2054:U
2032:.
2029:W
2023:Q
2020:=
2014:m
2011:e
2008:t
2005:s
2002:y
1999:s
1994:U
1975:W
1961:W
1955:Q
1946:U
1944:Δ
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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