42:
1612:
3463:
For ordinary materials, the bulk compressibility (sum of the linear compressibilities on the three axes) is positive, that is, an increase in pressure squeezes the material to a smaller volume. This condition is required for mechanical stability. However, under very specific conditions, materials can
3449:
In transition regions, where this pressure dependent dissociation is incomplete, both beta (the volume/pressure differential ratio) and the differential, constant pressure heat capacity greatly increases. For moderate pressures, above 10,000 K the gas further dissociates into free electrons and
3422:
Many effects are often mentioned in conjunction with the term "compressibility", but regularly have little to do with the compressible nature of air. From a strictly aerodynamic point of view, the term should refer only to those side-effects arising as a result of the changes in airflow from an
3454:
for the resulting plasma can similarly be computed for a mole of initial air, producing values between 2 and 4 for partially or singly ionized gas. Each dissociation absorbs a great deal of energy in a reversible process and this greatly reduces the thermodynamic temperature of hypersonic gas
2811:
3446:, defined for an initial 30 gram moles of air, rather than track the varying mean molecular weight, millisecond by millisecond. This pressure dependent transition occurs for atmospheric oxygen in the 2,500–4,000 K temperature range, and in the 5,000–10,000 K range for nitrogen.
2557:
2001:
1904:
2085:
1331:
2381:
3352:). The void space can be full of liquid or gas. Geologic materials reduce in volume only when the void spaces are reduced, which expel the liquid or gas from the voids. This can happen over a period of time, resulting in
2662:
2169:
2462:
1775:
3455:
decelerated near the aerospace object. Ions or free radicals transported to the object surface by diffusion may release this extra (nonthermal) energy if the surface catalyzes the slower recombination process.
1797:
of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. The reciprocal of compressibility at fixed temperature is called the isothermal
2643:
2231:
2903:
3009:
3389:
The degree of compressibility of a fluid has strong implications for its dynamics. Most notably, the propagation of sound is dependent on the compressibility of the medium.
2468:
1166:
1111:
1056:
3074:
863:
816:
731:
684:
596:
549:
1641:
767:
635:
3423:
incompressible fluid (similar in effect to water) to a compressible fluid (acting as a gas) as the speed of sound is approached. There are two effects in particular,
1712:
2271:
1001:
2949:
1925:
1828:
1342:
2026:
500:
1230:
839:
792:
707:
660:
572:
525:
3442:
similarly dissociates to 2 N. Since this occurs dynamically as air flows over the aerospace object, it is convenient to alter the compressibility factor
3020:
The deviation from ideal gas behavior tends to become particularly significant (or, equivalently, the compressibility factor strays far from unity) near the
3415:, a host of new aerodynamic effects become important in the design of aircraft. These effects, often several of them at a time, made it very difficult for
464:
1810:
The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is
3434:
One complication occurs in hypersonic aerodynamics, where dissociation causes an increase in the "notional" molar volume because a mole of oxygen, as O
2806:{\displaystyle \beta _{T}={\frac {(\partial \rho /\partial \mu )_{V,T}}{\rho ^{2}}}={\frac {\langle (\Delta N)^{2}\rangle /V}{k_{\rm {B}}T\rho ^{2}}},}
2309:
1320:
1353:
2109:
2387:
3648:
923:
1724:
1634:
1221:
457:
335:
890:
273:
1405:
1379:
900:
354:
3934:
3705:
306:
1458:
2575:
929:
328:
3488:
3021:
1627:
3944:
1558:
90:
1453:
3570:
2595:
1533:
1306:
283:
2646:
2184:
918:
121:
111:
3384:
126:
116:
3336:
to quantify the ability of a soil or rock to reduce in volume under applied pressure. This concept is important for
2656:
shows that the isothermal compressibility is also related to the relative size of fluctuations in particle density:
1448:
1410:
1374:
86:
1203:
951:
397:
210:
200:
3360:
2832:
2274:
3939:
3661:
Fine, Rana A.; Millero, F. J. (1973). "Compressibility of water as a function of temperature and pressure".
2858:
1786:
1615:
1443:
1240:
943:
882:
418:
407:
73:
3885:
Moore, B.; Jaglinski, T.; Stone, D. S.; Lakes, R. S. (2006). "Negative incremental bulk modulus in foams".
2969:
2848:
2286:
1548:
1468:
1265:
349:
103:
78:
3025:
2653:
1675:
1483:
1060:
373:
219:
68:
2955:, all measured independently of one another. In the case of an ideal gas, the compressibility factor
3894:
3857:
3810:
3769:
3730:
3670:
3595:
3586:
Domenico, P. A.; Mifflin, M. D. (1965). "Water from low permeability sediments and land subsidence".
2277:
relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid.
1563:
1488:
1478:
278:
152:
140:
2552:{\displaystyle {\frac {1}{\beta _{S}}}={\frac {1}{\beta _{T}}}+{\frac {\Lambda ^{2}T}{\rho c_{v}}},}
3721:
Munn, R. W. (1971). "Role of the elastic constants in negative thermal expansion of axial solids".
2567:
2100:
1508:
1503:
1270:
292:
258:
253:
166:
3910:
3826:
2821:
2175:
1811:
1597:
1260:
1208:
1121:
1066:
1011:
440:
424:
311:
263:
248:
238:
47:
41:
3052:
1255:
845:
798:
713:
666:
578:
531:
3701:
3644:
3611:
3311:
3029:
1592:
1553:
1543:
1115:
913:
749:
741:
614:
243:
233:
175:
3514:
1697:
3902:
3865:
3818:
3798:
3777:
3738:
3678:
3603:
3337:
3230:
2256:
1996:{\displaystyle \beta _{S}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial p}}\right)_{S},}
1899:{\displaystyle \beta _{T}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial p}}\right)_{T},}
1794:
1691:
1513:
1498:
1438:
1433:
1250:
1245:
971:
895:
363:
228:
27:
Measure of the relative volume change of a fluid or solid as a response to a pressure change
3539:
2927:
2080:{\displaystyle \beta ={\frac {1}{\rho }}\left({\frac {\partial \rho }{\partial p}}\right).}
3372:
2020:
of a material is inversely proportional to its volume, it can be shown that in both cases
1659:
1463:
1311:
965:
429:
190:
157:
3898:
3861:
3814:
3773:
3734:
3674:
3599:
482:
3494:
3412:
2828:
2096:
1655:
1518:
1288:
824:
777:
692:
645:
557:
510:
388:
268:
205:
195:
63:
33:
3928:
3830:
3483:
3428:
3329:
3214:
3024:, or in the case of high pressure or low temperature. In these cases, a generalized
2960:
1587:
905:
474:
435:
147:
3914:
3742:
3416:
3404:
3398:
3363:
in the design of certain structural foundations. For example, the construction of
2952:
2242:
1799:
1538:
1523:
1473:
956:
3870:
3845:
3639:
3473:
3341:
2921:
2376:{\displaystyle {\frac {\beta _{T}}{\beta _{S}}}={\frac {c_{p}}{c_{v}}}=\gamma ,}
2010:
is entropy. For a solid, the distinction between the two is usually negligible.
1913:
indicates that the partial differential is to be taken at constant temperature.
1493:
301:
3348:. Geologic materials are made up of two portions: solids and voids (or same as
3906:
3407:. At low speeds, the compressibility of air is not significant in relation to
3353:
2296:
2292:
1815:
1582:
1528:
3607:
3478:
3424:
3364:
3295:
2840:
2300:
180:
17:
3822:
3782:
3757:
3032:
better suited to the problem must be utilized to produce accurate results.
2164:{\displaystyle c^{2}=\left({\frac {\partial p}{\partial \rho }}\right)_{S}}
3408:
3371:
poses a considerable design constraint, and often leads to use of driven
3349:
2913:
2836:
2457:{\displaystyle \beta _{S}=\beta _{T}-{\frac {\alpha ^{2}T}{\rho c_{p}}},}
1687:
1296:
1213:
1005:
413:
185:
3419:
era aircraft to reach speeds much beyond 800 km/h (500 mph).
3368:
3345:
2014:
402:
3682:
3615:
3017:
can, in general, be either greater or less than unity for a real gas.
1770:{\displaystyle \beta =-{\frac {1}{V}}{\frac {\partial V}{\partial p}}}
3758:"Negative compressibility, negative Poisson's ratio, and stability"
3700:. American Institute of Aeronautics and Astronautics. p. 313.
1683:
1679:
378:
2178:, that the isentropic compressibility can be expressed as:
3367:
structures over underlying layers of highly compressible
2652:
In an extensive thermodynamic system, the application of
1793:
is pressure. The choice to define compressibility as the
3039:
3055:
2972:
2930:
2861:
2665:
2598:
2471:
2390:
2312:
2259:
2187:
2112:
2029:
1928:
1831:
1727:
1700:
1124:
1069:
1014:
974:
848:
827:
801:
780:
752:
716:
695:
669:
648:
617:
581:
560:
534:
513:
485:
2638:{\displaystyle \Lambda =(\partial P/\partial T)_{V}}
3633:
3631:
3629:
3627:
3625:
3068:
3003:
2943:
2897:
2805:
2637:
2551:
2456:
2375:
2265:
2226:{\displaystyle \beta _{S}={\frac {1}{\rho c^{2}}}}
2225:
2163:
2079:
1995:
1898:
1769:
1706:
1694:) change. In its simple form, the compressibility
1160:
1105:
1050:
995:
857:
833:
810:
786:
761:
725:
701:
678:
654:
629:
590:
566:
543:
519:
494:
3411:design, but as the airflow nears and exceeds the
2241:The inverse of the compressibility is called the
1678:of the instantaneous relative volume change of a
3464:exhibit a compressibility that can be negative.
3385:Navier–Stokes equations § Compressible flow
3515:"Coefficient of compressibility - AMS Glossary"
1670:or, if the temperature is held constant, the
1635:
8:
3563:
3561:
2759:
2737:
2295:compressibility is generally related to the
3846:"Materials with Negative Compressibilities"
3438:, becomes 2 moles of monatomic oxygen and N
2827:The term "compressibility" is also used in
3403:Compressibility is an important factor in
1642:
1628:
1191:
343:
162:
40:
29:
3869:
3781:
3756:Lakes, Rod; Wojciechowski, K. W. (2008).
3723:Journal of Physics C: Solid State Physics
3060:
3054:
2993:
2979:
2971:
2935:
2929:
2878:
2868:
2860:
2791:
2777:
2776:
2762:
2753:
2734:
2723:
2706:
2691:
2679:
2670:
2664:
2629:
2614:
2597:
2537:
2519:
2512:
2501:
2492:
2481:
2472:
2470:
2442:
2424:
2417:
2408:
2395:
2389:
2356:
2346:
2340:
2329:
2319:
2313:
2311:
2258:
2214:
2201:
2192:
2186:
2155:
2131:
2117:
2111:
2050:
2036:
2028:
1984:
1960:
1945:
1933:
1927:
1887:
1863:
1848:
1836:
1830:
1747:
1737:
1726:
1699:
1123:
1068:
1013:
973:
847:
826:
800:
779:
751:
715:
694:
668:
647:
616:
580:
559:
533:
512:
484:
3540:"Isothermal compressibility of gases -"
3506:
1388:
1365:
1319:
1279:
1229:
1194:
387:
362:
291:
218:
165:
32:
3797:Gatt, Ruben; Grima, Joseph N. (2008).
3640:University Physics with Modern Physics
2898:{\displaystyle Z={\frac {pV_{m}}{RT}}}
2303:) compressibility by a few relations:
3004:{\displaystyle p={\frac {RT}{V_{m}}}}
7:
3041:Vertical, drained compressibilities
2959:is equal to unity, and the familiar
1718:in some fields) may be expressed as
3575:. Pergamon. pp. 54–55 and 342.
3491:, associated with supersonic flight
3637:Hugh D. Young; Roger A. Freedman.
2778:
2743:
2696:
2685:
2619:
2608:
2599:
2516:
2142:
2134:
2061:
2053:
1971:
1963:
1874:
1866:
1758:
1750:
849:
802:
717:
670:
582:
535:
355:Intensive and extensive properties
25:
3698:Dynamics of Atmospheric Re-entry
3375:or other innovative techniques.
2576:coefficient of thermal expansion
1611:
1610:
930:Table of thermodynamic equations
3268:Water at 25 °C (undrained)
1406:Maxwell's thermodynamic surface
3887:Philosophical Magazine Letters
3359:It is an important concept in
2831:to describe deviations of the
2750:
2740:
2703:
2682:
2626:
2605:
1668:coefficient of compressibility
1140:
1128:
1085:
1073:
1030:
1018:
990:
978:
1:
3871:10.1126/science.281.5374.143a
3571:Course of Theoretical Physics
2592:is the particle density, and
1307:Mechanical equivalent of heat
2839:from those expected from an
2647:thermal pressure coefficient
1919:compressibility is defined:
1822:compressibility is defined:
919:Onsager reciprocal relations
3663:Journal of Chemical Physics
3489:Prandtl–Glauert singularity
3399:Aerodynamics § History
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}
3961:
3799:"Negative compressibility"
3573:Vol 5: Statistical Physics
3396:
3382:
3069:{\displaystyle \beta _{T}}
2284:
2091:Relation to speed of sound
1672:isothermal compressibility
858:{\displaystyle \partial T}
811:{\displaystyle \partial V}
726:{\displaystyle \partial p}
679:{\displaystyle \partial V}
591:{\displaystyle \partial T}
544:{\displaystyle \partial S}
3907:10.1080/09500830600957340
3844:Kornblatt, J. A. (1998).
3803:Physica Status Solidi RRL
3743:10.1088/0022-3719/5/5/005
3568:Landau; Lifshitz (1980).
2174:It follows, by replacing
1332:An Inquiry Concerning the
3935:Thermodynamic properties
3696:Regan, Frank J. (1993).
3643:. Addison-Wesley; 2012.
3588:Water Resources Research
3459:Negative compressibility
3361:geotechnical engineering
2833:thermodynamic properties
2275:compressibility equation
2237:Relation to bulk modulus
1345:Heterogeneous Substances
762:{\displaystyle \alpha =}
630:{\displaystyle \beta =-}
3762:Physica Status Solidi B
3608:10.1029/WR001i004p00563
1707:{\displaystyle \kappa }
3823:10.1002/pssr.200802101
3783:10.1002/pssb.200777708
3070:
3005:
2945:
2899:
2849:compressibility factor
2807:
2639:
2553:
2458:
2377:
2287:Compressibility factor
2267:
2266:{\displaystyle \beta }
2227:
2165:
2081:
1997:
1900:
1771:
1708:
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
3945:Mechanical quantities
3344:reserves in confined
3071:
3026:compressibility chart
3006:
2946:
2944:{\displaystyle V_{m}}
2900:
2808:
2654:statistical mechanics
2640:
2554:
2459:
2378:
2268:
2228:
2166:
2082:
1998:
1901:
1772:
1709:
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:
3519:Glossary.AMetSoc.org
3053:
2970:
2928:
2859:
2663:
2596:
2469:
2388:
2310:
2257:
2185:
2110:
2027:
1926:
1909:where the subscript
1829:
1725:
1698:
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:
3899:2006PMagL..86..651M
3862:1998Sci...281..143K
3815:2008PSSRR...2..236G
3774:2008PSSBR.245..545L
3735:1972JPhC....5..535M
3675:1973JChPh..59.5529F
3600:1965WRR.....1..563D
3192:Dense, sandy gravel
3042:
2568:heat capacity ratio
2176:partial derivatives
2101:classical mechanics
1686:as a response to a
1666:(also known as the
1334:Source ... Friction
1266:Loschmidt's paradox
458:Material properties
336:Conjugate variables
3856:(5374): 143a–143.
3340:, when estimating
3066:
3040:
3028:or an alternative
3001:
2941:
2895:
2822:chemical potential
2803:
2635:
2574:is the volumetric
2549:
2454:
2373:
2263:
2223:
2161:
2077:
1993:
1896:
1767:
1704:
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
3683:10.1063/1.1679903
3669:(10): 5529–5536.
3649:978-0-321-69686-1
3326:
3325:
3030:equation of state
2999:
2893:
2798:
2729:
2544:
2507:
2487:
2449:
2362:
2335:
2221:
2149:
2068:
2044:
1978:
1953:
1881:
1856:
1765:
1745:
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
3952:
3919:
3918:
3882:
3876:
3875:
3873:
3841:
3835:
3834:
3794:
3788:
3787:
3785:
3753:
3747:
3746:
3718:
3712:
3711:
3693:
3687:
3686:
3658:
3652:
3635:
3620:
3619:
3583:
3577:
3576:
3565:
3556:
3555:
3553:
3551:
3536:
3530:
3529:
3527:
3525:
3511:
3453:
3445:
3338:specific storage
3322:
3320:
3306:
3304:
3290:
3288:
3274:
3263:
3261:
3255:
3253:
3241:
3239:
3231:Carbon disulfide
3225:
3223:
3209:
3207:
3201:
3199:
3187:
3185:
3179:
3177:
3165:
3163:
3157:
3155:
3143:
3141:
3135:
3133:
3126:Medium-hard clay
3121:
3119:
3113:
3111:
3099:
3097:
3091:
3089:
3075:
3073:
3072:
3067:
3065:
3064:
3043:
3016:
3010:
3008:
3007:
3002:
3000:
2998:
2997:
2988:
2980:
2958:
2950:
2948:
2947:
2942:
2940:
2939:
2919:
2911:
2904:
2902:
2901:
2896:
2894:
2892:
2884:
2883:
2882:
2869:
2819:
2812:
2810:
2809:
2804:
2799:
2797:
2796:
2795:
2783:
2782:
2781:
2770:
2766:
2758:
2757:
2735:
2730:
2728:
2727:
2718:
2717:
2716:
2695:
2680:
2675:
2674:
2644:
2642:
2641:
2636:
2634:
2633:
2618:
2591:
2573:
2565:
2558:
2556:
2555:
2550:
2545:
2543:
2542:
2541:
2528:
2524:
2523:
2513:
2508:
2506:
2505:
2493:
2488:
2486:
2485:
2473:
2463:
2461:
2460:
2455:
2450:
2448:
2447:
2446:
2433:
2429:
2428:
2418:
2413:
2412:
2400:
2399:
2382:
2380:
2379:
2374:
2363:
2361:
2360:
2351:
2350:
2341:
2336:
2334:
2333:
2324:
2323:
2314:
2272:
2270:
2269:
2264:
2252:
2248:
2245:, often denoted
2232:
2230:
2229:
2224:
2222:
2220:
2219:
2218:
2202:
2197:
2196:
2170:
2168:
2167:
2162:
2160:
2159:
2154:
2150:
2148:
2140:
2132:
2122:
2121:
2086:
2084:
2083:
2078:
2073:
2069:
2067:
2059:
2051:
2045:
2037:
2019:
2009:
2002:
2000:
1999:
1994:
1989:
1988:
1983:
1979:
1977:
1969:
1961:
1954:
1946:
1938:
1937:
1912:
1905:
1903:
1902:
1897:
1892:
1891:
1886:
1882:
1880:
1872:
1864:
1857:
1849:
1841:
1840:
1792:
1784:
1776:
1774:
1773:
1768:
1766:
1764:
1756:
1748:
1746:
1738:
1717:
1713:
1711:
1710:
1705:
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:
3960:
3959:
3955:
3954:
3953:
3951:
3950:
3949:
3925:
3924:
3923:
3922:
3884:
3883:
3879:
3843:
3842:
3838:
3796:
3795:
3791:
3755:
3754:
3750:
3720:
3719:
3715:
3708:
3695:
3694:
3690:
3660:
3659:
3655:
3636:
3623:
3585:
3584:
3580:
3567:
3566:
3559:
3549:
3547:
3538:
3537:
3533:
3523:
3521:
3513:
3512:
3508:
3503:
3470:
3461:
3451:
3443:
3441:
3437:
3401:
3395:
3387:
3381:
3334:compressibility
3318:
3316:
3302:
3300:
3286:
3284:
3272:
3259:
3257:
3251:
3249:
3237:
3235:
3221:
3219:
3205:
3203:
3197:
3195:
3183:
3181:
3175:
3173:
3161:
3159:
3153:
3151:
3139:
3137:
3131:
3129:
3117:
3115:
3109:
3107:
3095:
3093:
3087:
3085:
3056:
3051:
3050:
3038:
3014:
2989:
2981:
2968:
2967:
2956:
2931:
2926:
2925:
2917:
2909:
2885:
2874:
2870:
2857:
2856:
2817:
2787:
2772:
2771:
2749:
2736:
2719:
2702:
2681:
2666:
2661:
2660:
2625:
2594:
2593:
2579:
2571:
2563:
2533:
2529:
2515:
2514:
2497:
2477:
2467:
2466:
2438:
2434:
2420:
2419:
2404:
2391:
2386:
2385:
2352:
2342:
2325:
2315:
2308:
2307:
2289:
2283:
2255:
2254:
2250:
2246:
2239:
2210:
2206:
2188:
2183:
2182:
2141:
2133:
2127:
2126:
2113:
2108:
2107:
2093:
2060:
2052:
2046:
2025:
2024:
2017:
2007:
1970:
1962:
1956:
1955:
1929:
1924:
1923:
1910:
1873:
1865:
1859:
1858:
1832:
1827:
1826:
1818:. Accordingly,
1808:
1790:
1782:
1757:
1749:
1723:
1722:
1715:
1696:
1695:
1664:compressibility
1660:fluid mechanics
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:
3958:
3956:
3948:
3947:
3942:
3940:Fluid dynamics
3937:
3927:
3926:
3921:
3920:
3877:
3836:
3789:
3748:
3729:(5): 535–542.
3713:
3706:
3688:
3653:
3621:
3594:(4): 563–576.
3578:
3557:
3531:
3505:
3504:
3502:
3499:
3498:
3497:
3495:Shear strength
3492:
3486:
3481:
3476:
3469:
3466:
3460:
3457:
3439:
3435:
3413:speed of sound
3397:Main article:
3394:
3391:
3383:Main article:
3380:
3379:Fluid dynamics
3377:
3330:Earth sciences
3324:
3323:
3314:
3308:
3307:
3298:
3292:
3291:
3281:
3277:
3276:
3269:
3265:
3264:
3247:
3246:Rock, fissured
3243:
3242:
3233:
3227:
3226:
3217:
3211:
3210:
3193:
3189:
3188:
3171:
3167:
3166:
3149:
3145:
3144:
3127:
3123:
3122:
3105:
3101:
3100:
3083:
3079:
3078:
3063:
3059:
3047:
3037:
3034:
3022:critical point
3012:
3011:
2996:
2992:
2987:
2984:
2978:
2975:
2963:is recovered:
2938:
2934:
2906:
2905:
2891:
2888:
2881:
2877:
2873:
2867:
2864:
2852:is defined as
2829:thermodynamics
2814:
2813:
2802:
2794:
2790:
2786:
2780:
2775:
2769:
2765:
2761:
2756:
2752:
2748:
2745:
2742:
2739:
2733:
2726:
2722:
2715:
2712:
2709:
2705:
2701:
2698:
2694:
2690:
2687:
2684:
2678:
2673:
2669:
2632:
2628:
2624:
2621:
2617:
2613:
2610:
2607:
2604:
2601:
2560:
2559:
2548:
2540:
2536:
2532:
2527:
2522:
2518:
2511:
2504:
2500:
2496:
2491:
2484:
2480:
2476:
2464:
2453:
2445:
2441:
2437:
2432:
2427:
2423:
2416:
2411:
2407:
2403:
2398:
2394:
2383:
2372:
2369:
2366:
2359:
2355:
2349:
2345:
2339:
2332:
2328:
2322:
2318:
2285:Main article:
2282:
2281:Thermodynamics
2279:
2262:
2238:
2235:
2234:
2233:
2217:
2213:
2209:
2205:
2200:
2195:
2191:
2172:
2171:
2158:
2153:
2147:
2144:
2139:
2136:
2130:
2125:
2120:
2116:
2099:is defined in
2097:speed of sound
2092:
2089:
2088:
2087:
2076:
2072:
2066:
2063:
2058:
2055:
2049:
2043:
2040:
2035:
2032:
2004:
2003:
1992:
1987:
1982:
1976:
1973:
1968:
1965:
1959:
1952:
1949:
1944:
1941:
1936:
1932:
1907:
1906:
1895:
1890:
1885:
1879:
1876:
1871:
1868:
1862:
1855:
1852:
1847:
1844:
1839:
1835:
1807:
1804:
1779:
1778:
1763:
1760:
1755:
1752:
1744:
1741:
1736:
1733:
1730:
1703:
1656: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:
3957:
3946:
3943:
3941:
3938:
3936:
3933:
3932:
3930:
3916:
3912:
3908:
3904:
3900:
3896:
3892:
3888:
3881:
3878:
3872:
3867:
3863:
3859:
3855:
3851:
3847:
3840:
3837:
3832:
3828:
3824:
3820:
3816:
3812:
3808:
3804:
3800:
3793:
3790:
3784:
3779:
3775:
3771:
3767:
3763:
3759:
3752:
3749:
3744:
3740:
3736:
3732:
3728:
3724:
3717:
3714:
3709:
3707:1-56347-048-9
3703:
3699:
3692:
3689:
3684:
3680:
3676:
3672:
3668:
3664:
3657:
3654:
3650:
3646:
3642:
3641:
3634:
3632:
3630:
3628:
3626:
3622:
3617:
3613:
3609:
3605:
3601:
3597:
3593:
3589:
3582:
3579:
3574:
3572:
3564:
3562:
3558:
3546:. 3 June 2015
3545:
3544:Petrowiki.org
3541:
3535:
3532:
3520:
3516:
3510:
3507:
3500:
3496:
3493:
3490:
3487:
3485:
3484:Poisson ratio
3482:
3480:
3477:
3475:
3472:
3471:
3467:
3465:
3458:
3456:
3447:
3432:
3430:
3429:critical mach
3426:
3420:
3418:
3414:
3410:
3406:
3400:
3392:
3390:
3386:
3378:
3376:
3374:
3370:
3366:
3362:
3357:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3315:
3313:
3310:
3309:
3299:
3297:
3294:
3293:
3282:
3279:
3278:
3270:
3267:
3266:
3248:
3245:
3244:
3234:
3232:
3229:
3228:
3218:
3216:
3215:Ethyl alcohol
3213:
3212:
3194:
3191:
3190:
3172:
3169:
3168:
3150:
3147:
3146:
3128:
3125:
3124:
3106:
3103:
3102:
3084:
3081:
3080:
3076:
3061:
3057:
3048:
3045:
3044:
3036:Earth science
3035:
3033:
3031:
3027:
3023:
3018:
2994:
2990:
2985:
2982:
2976:
2973:
2966:
2965:
2964:
2962:
2961:ideal gas law
2954:
2936:
2932:
2923:
2915:
2889:
2886:
2879:
2875:
2871:
2865:
2862:
2855:
2854:
2853:
2851:
2850:
2844:
2842:
2838:
2834:
2830:
2825:
2823:
2800:
2792:
2788:
2784:
2773:
2767:
2763:
2754:
2746:
2731:
2724:
2720:
2713:
2710:
2707:
2699:
2692:
2688:
2676:
2671:
2667:
2659:
2658:
2657:
2655:
2650:
2648:
2630:
2622:
2615:
2611:
2602:
2590:
2586:
2582:
2577:
2569:
2546:
2538:
2534:
2530:
2525:
2520:
2509:
2502:
2498:
2494:
2489:
2482:
2478:
2474:
2465:
2451:
2443:
2439:
2435:
2430:
2425:
2421:
2414:
2409:
2405:
2401:
2396:
2392:
2384:
2370:
2367:
2364:
2357:
2353:
2347:
2343:
2337:
2330:
2326:
2320:
2316:
2306:
2305:
2304:
2302:
2298:
2294:
2288:
2280:
2278:
2276:
2260:
2244:
2236:
2215:
2211:
2207:
2203:
2198:
2193:
2189:
2181:
2180:
2179:
2177:
2156:
2151:
2145:
2137:
2128:
2123:
2118:
2114:
2106:
2105:
2104:
2102:
2098:
2090:
2074:
2070:
2064:
2056:
2047:
2041:
2038:
2033:
2030:
2023:
2022:
2021:
2016:
2011:
1990:
1985:
1980:
1974:
1966:
1957:
1950:
1947:
1942:
1939:
1934:
1930:
1922:
1921:
1920:
1918:
1914:
1893:
1888:
1883:
1877:
1869:
1860:
1853:
1850:
1845:
1842:
1837:
1833:
1825:
1824:
1823:
1821:
1817:
1813:
1805:
1803:
1801:
1796:
1788:
1761:
1753:
1742:
1739:
1734:
1731:
1728:
1721:
1720:
1719:
1701:
1693:
1689:
1685:
1681:
1677:
1673:
1669:
1665:
1661:
1657:
1645:
1640:
1638:
1633:
1631:
1626:
1625:
1623:
1622:
1617:
1609:
1608:
1607:
1606:
1599:
1596:
1594:
1591:
1589:
1588:Self-assembly
1586:
1584:
1581:
1580:
1574:
1573:
1565:
1562:
1560:
1559:van der Waals
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1484:von Helmholtz
1482:
1480:
1477:
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1387:
1381:
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1027:
1024:
1021:
1015:
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1004:
987:
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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:
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795:
781:
774:
773:
770:
756:
753:
746:
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739:
720:
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673:
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642:
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638:
624:
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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:
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67:
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3548:. Retrieved
3543:
3534:
3522:. Retrieved
3518:
3509:
3462:
3448:
3433:
3421:
3417:World War II
3405:aerodynamics
3402:
3393:Aerodynamics
3388:
3358:
3333:
3327:
3082:Plastic clay
3077:(m/N or Pa)
3049:
3019:
3013:
2953:molar volume
2916:of the gas,
2907:
2847:
2845:
2826:
2815:
2651:
2588:
2584:
2580:
2561:
2290:
2243:bulk modulus
2240:
2173:
2094:
2012:
2005:
1916:
1915:
1908:
1819:
1809:
1800:bulk modulus
1780:
1671:
1667:
1663:
1653:
1449:Carathéodory
1380:Heat engines
1352:
1341:
1330:
1312:Motive power
1297:
957:Free entropy
928:
606:
428:
427: /
417:
416: /
408:introduction
401:
400: /
339:
302:Heat engines
89: /
18:Compressible
3893:(10): 651.
3474:Mach number
3342:groundwater
3280:Rock, sound
2922:temperature
2249:(sometimes
1271:Synergetics
952:Free energy
398:Temperature
259:Quasistatic
254:Isenthalpic
211:Instruments
201:Equilibrium
153:Open system
87:Equilibrium
69:Statistical
3929:Categories
3809:(5): 236.
3768:(3): 545.
3501:References
3354:settlement
3170:Dense sand
3148:Loose sand
3104:Stiff clay
2297:isentropic
2293:isothermal
2013:Since the
1917:Isentropic
1820:isothermal
1816:isothermal
1812:isentropic
1806:Definition
1583:Nucleation
1427:Scientists
1231:Philosophy
944:Potentials
307:Heat pumps
264:Polytropic
249:Isentropic
239:Isothermal
3831:216142598
3651:. p. 356.
3479:Mach tuck
3425:wave drag
3365:high-rise
3296:Glycerine
3058:β
2841:ideal gas
2789:ρ
2760:⟩
2744:Δ
2738:⟨
2721:ρ
2700:μ
2697:∂
2689:ρ
2686:∂
2668:β
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2609:∂
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2273:).). The
2261:β
2208:ρ
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2057:ρ
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2031:β
1972:∂
1964:∂
1943:−
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1875:∂
1867:∂
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1759:∂
1751:∂
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1729:β
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1702:κ
1690:(or mean
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
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536:∂
244:Adiabatic
234:Isochoric
220:Processes
181:Ideal gas
64:Classical
3915:41596692
3468:See also
3409:aircraft
3350:porosity
3346:aquifers
3046:Material
2914:pressure
2837:real gas
1795:negative
1688:pressure
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
3895:Bibcode
3858:Bibcode
3850:Science
3811:Bibcode
3770:Bibcode
3731:Bibcode
3671:Bibcode
3616:5917760
3596:Bibcode
3369:bay mud
3312:Mercury
2951:is its
2920:is its
2912:is the
2820:is the
2645:is the
2566:is the
2015:density
1676:measure
1674:) is a
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
3913:
3829:
3704:
3647:
3614:
3450:ions.
2924:, and
2908:where
2816:where
2562:where
2006:where
1787:volume
1781:where
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1662:, the
1529:Planck
1519:Nernst
1494:Kelvin
1454:Carnot
744:
609:
477:
419:Volume
334:Note:
293:Cycles
122:Second
112:Zeroth
3911:S2CID
3827:S2CID
3550:3 May
3524:3 May
3373:piles
3283:<
2835:of a
1684:solid
1680:fluid
1577:Other
1544:Stahl
1499:Lewis
1489:Joule
1479:Gibbs
1474:Duhem
167:State
127:Third
117:First
3702:ISBN
3645:ISBN
3612:OSTI
3552:2017
3526:2017
3427:and
3332:use
3328:The
2846:The
2299:(or
2291:The
2103:as:
2095:The
1789:and
1658:and
1549:Tait
379:Heat
374:Work
104:Laws
3903:doi
3866:doi
3854:281
3819:doi
3778:doi
3766:245
3739:doi
3679:doi
3604:doi
3317:3.7
3301:2.1
3285:3.3
3275:10
3271:4.6
3258:3.3
3250:6.9
3236:9.3
3220:1.1
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3182:1.3
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