585:
degenerate particles; however, adding heat does not increase the speed of most of the electrons, because they are stuck in fully occupied quantum states. Pressure is increased only by the mass of the particles, which increases the gravitational force pulling the particles closer together. Therefore, the phenomenon is the opposite of that normally found in matter where if the mass of the matter is increased, the object becomes bigger. In degenerate gas, when the mass is increased, the particles become spaced closer together due to gravity (and the pressure is increased), so the object becomes smaller. Degenerate gas can be compressed to very high densities, typical values being in the range of 10,000 kilograms per cubic centimeter.
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occupy states of higher energy even at low temperatures. Degenerate gases strongly resist further compression because the electrons cannot move to already filled lower energy levels due to the Pauli exclusion principle. Since electrons cannot give up energy by moving to lower energy states, no thermal energy can be extracted. The momentum of the fermions in the fermion gas nevertheless generates pressure, termed "degeneracy pressure".
2160:
2184:
2136:
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2148:
492:
that temperature has a negligible effect on the total pressure. The adjacent figure shows the thermal pressure (red line) and total pressure (blue line) in a Fermi gas, with the difference between the two being the degeneracy pressure. As the temperature falls, the density and the degeneracy pressure increase, until the degeneracy pressure contributes most of the total pressure.
715:. However, because protons are much more massive than electrons, the same momentum represents a much smaller velocity for protons than for electrons. As a result, in matter with approximately equal numbers of protons and electrons, proton degeneracy pressure is much smaller than electron degeneracy pressure, and proton degeneracy is usually modelled as a correction to the
541:
quantum states are filled up to the Fermi energy. Most stars are supported against their own gravitation by normal thermal gas pressure, while in white dwarf stars the supporting force comes from the degeneracy pressure of the electron gas in their interior. In neutron stars, the degenerate particles are neutrons.
682:
at a given energy. This phenomenon is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs. The pressure increase is caused by the fact that the compactness of a neutron star causes gravitational forces to be much higher than in a less compact body
584:
of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light. Instead of temperature, the pressure in a degenerate gas depends only on the speed of the
579:
are luminous not because they are generating energy but rather because they have trapped a large amount of heat which is gradually radiated away. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. When gas becomes
784:
for neutron-degenerate objects. Whether quark-degenerate matter forms at all in these situations depends on the equations of state of both neutron-degenerate matter and quark-degenerate matter, both of which are poorly known. Quark stars are considered to be an intermediate category between neutron
170:
model. Examples include electrons in metals and in white dwarf stars and neutrons in neutron stars. The electrons are confined by
Coulomb attraction to positive ion cores; the neutrons are confined by gravitation attraction. The fermions, forced in to higher levels by the Pauli principle, exert
92:
remains non-zero even at absolute zero temperature. Adding particles or reducing the volume forces the particles into higher-energy quantum states. In this situation, a compression force is required, and is made manifest as a resisting pressure. The key feature is that this degeneracy pressure does
605:
and with realistic
Coulomb corrections, the corresponding mass limit is around 1.38 solar masses. The limit may also change with the chemical composition of the object, as it affects the ratio of mass to number of electrons present. The object's rotation, which counteracts the gravitational force,
540:
such as electrons, protons, and neutrons rather than molecules of ordinary matter. The electron gas in ordinary metals and in the interior of white dwarfs are two examples. Following the Pauli exclusion principle, there can be only one fermion occupying each quantum state. In a degenerate gas, all
563:
In an ordinary fermion gas in which thermal effects dominate, most of the available electron energy levels are unfilled and the electrons are free to move to these states. As particle density is increased, electrons progressively fill the lower energy states and additional electrons are forced to
516:
electrons alone as a degenerate gas, while the majority of the electrons are regarded as occupying bound quantum states. This solid state contrasts with degenerate matter that forms the body of a white dwarf, where most of the electrons would be treated as occupying free particle momentum states.
491:
All matter experiences both normal thermal pressure and degeneracy pressure, but in commonly encountered gases, thermal pressure dominates so much that degeneracy pressure can be ignored. Likewise, degenerate matter still has normal thermal pressure; the degeneracy pressure dominates to the point
800:
and as the low temperature ground state limit for states of matter. The electron degeneracy pressure occurs in the ground state systems which are non-degenerate in energy levels. The term "degeneracy" derives from work on the specific heat of gases that pre-dates the use of the term in quantum
127:
were almost completely ionised and closely packed. Fowler described white dwarfs as composed of a gas of particles that became degenerate at low temperature; he also pointed out that ordinary atoms are broadly similar in regards to the filling of energy levels by fermions. Milne proposed that
667:, usually either as a result of a merger or by feeding off of a close binary partner. Above the Chandrasekhar limit, the gravitational pressure at the core exceeds the electron degeneracy pressure, and electrons begin to combine with protons to produce neutrons (via inverse
710:
Sufficiently dense matter containing protons experiences proton degeneracy pressure, in a manner similar to the electron degeneracy pressure in electron-degenerate matter: protons confined to a sufficiently small volume have a large uncertainty in their momentum due to the
162:. The Pauli principle allows only one fermion in each quantum state and the confinement ensures that energy of these states increases as they are filled. The lowest states fill up and fermions are forced to occupy high energy states even at low temperature.
495:
While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy. Given a sufficiently drastic increase in temperature (such as during a red giant star's
87:
prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. This
600:
for objects with typical compositions expected for white dwarf stars (carbon and oxygen with two baryons per electron). This mass cut-off is appropriate only for a star supported by ideal electron degeneracy pressure under
Newtonian gravity; in
392:
503:
Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of
544:
A fermion gas in which all quantum states below a given energy level are filled is called a fully degenerate fermion gas. The difference between this energy level and the lowest energy level is known as the Fermi energy.
165:
While the Pauli principle and Fermi-Dirac distribution applies to all matter, the interesting cases for degenerate matter involve systems of many fermions. These cases can be understood with the help of the
614:
that run out of fuel. During this shrinking, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a
575:, largely helium and carbon nuclei, floating in a sea of electrons, which have been stripped from the nuclei. Degenerate gas is an almost perfect conductor of heat and does not obey ordinary gas laws.
462:
244:
675:). The result is an extremely compact star composed of "nuclear matter", which is predominantly a degenerate neutron gas with a small admixture of degenerate proton and electron gases.
927:
Andrew G. Truscott, Kevin E. Strecker, William I. McAlexander, Guthrie
Partridge, and Randall G. Hulet, "Observation of Fermi Pressure in a Gas of Trapped Atoms", Science, 2 March 2001
280:
641:, which are partially supported by the pressure from a degenerate neutron gas. Neutron stars are formed either directly from the supernova of stars with masses between 10 and 25
1332:
Hanle, Paul A. "The Coming of Age of Erwin Schrödinger: His
Quantum Statistics of Ideal Gases". Archive for History of Exact Sciences, vol. 17, no. 2, 1977, pp. 165â92. JSTOR,
93:
not depend on the temperature but only on the density of the fermions. Degeneracy pressure keeps dense stars in equilibrium, independent of the thermal structure of the star.
769:. The equations of state for the various proposed forms of quark-degenerate matter vary widely, and are usually also poorly defined, due to the difficulty of modelling
79:, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called
1350:
776:
Quark-degenerate matter may occur in the cores of neutron stars, depending on the equations of state of neutron-degenerate matter. It may also occur in hypothetical
866:
applied Fermi's model to the puzzle of the stability of white dwarf stars. This approach was extended to relativistic models by later studies and with the work of
678:
Neutrons in a degenerate neutron gas are spaced much more closely than electrons in an electron-degenerate gas because the more massive neutron has a much shorter
1143:
Rotondo, Michael; Rueda, Jorge A.; Ruffini, Remo; Xue, She-Sheng (2011). "Relativistic
Feynman-Metropolis-Teller theory for white dwarfs in general relativity".
832:, the effect at low temperatures came to be called "gas degeneracy". A fully degenerate gas has no volume dependence on pressure when temperature approaches
277:
temperature. At relatively low densities, the pressure of a fully degenerate gas can be derived by treating the system as an ideal Fermi gas, in this way
567:
Under high densities, matter becomes a degenerate gas when all electrons are stripped from their parent atoms. The core of a star, once hydrogen burning
273:
is the volume, the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at
580:
super-compressed, particles position right up against each other to produce degenerate gas that behaves more like a solid. In degenerate gases the
398:
is the mass of the individual particles making up the gas. At very high densities, where most of the particles are forced into quantum states with
1439:
405:
1605:
17:
1426:
An english translation of the original work of Enrico Fermi on the quantization of the monoatomic ideal gas, is given in this paper
781:
691:
196:
1551:
1082:
1537:
816:
at very low temperature as "degeneration"; he attributed this to quantum effects. In subsequent work in various papers on
399:
1397:
741:
is expected to occur. Several variations of this hypothesis have been proposed that represent quark-degenerate states.
96:
A degenerate mass whose fermions have velocities close to the speed of light (particle kinetic energy larger than its
2216:
1113:
847:
developed a semi-classical model for electrons in a metal. The model treated the electrons as a gas. Later in 1927,
2111:
1872:
1942:
1867:
1598:
1046:
995:
859:
model for metals. Sommerfeld called the low temperature region with quantum effects a "wholly degenerate gas".
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1882:
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with similar mass. The result is a star with a diameter on the order of a thousandth that of a white dwarf.
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1937:
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883:
593:
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35:
2102:
867:
2231:
2221:
1591:
155:
84:
45:
468:
is another proportionality constant depending on the properties of the particles making up the gas.
111:, stellar objects composed of degenerate matter, was originally developed in a joint effort between
2089:
1988:
1618:
797:
175:
31:
1578:
1983:
758:
1486:
2226:
2008:
1998:
1748:
1743:
1249:
Annala, Eemeli; Gorda, Tyler; Kurkela, Aleksi; NÀttilÀ, Joonas; Vuorinen, Aleksi (2020-06-01).
852:
817:
141:
65:
174:
The allocation or distribution of fermions into quantum states ranked by energy is called the
1309:
1038:
1031:
712:
387:{\displaystyle P={\frac {(3\pi ^{2})^{2/3}\hbar ^{2}}{5m}}\left({\frac {N}{V}}\right)^{5/3},}
1927:
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1215:
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8:
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also changes the limit for any particular object. Celestial objects below this limit are
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954:
761:
materials are degenerate gases of quarks in which quarks pair up in a manner similar to
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to this electron gas model, computing the specific heat of metals; the result became
848:
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525:
30:
This article is about a state of matter. For multiple states with equal energy, see
2140:
2128:
2034:
1657:
1543:
1498:
1451:
1440:"Propaganda in Science: Sommerfeld and the Spread of the Electron Theory of Metals"
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Lecture 17: Stellar
Evolution. Discusses degenerate gases in models of stars
1414:
Zannoni, Alberto (1999). "On the
Quantization of the Monoatomic Ideal Gas".
596:
cannot support the object against collapse. The limit is approximately 1.44
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1957:
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1947:
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61:
53:
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There is an upper limit to the mass of an electron-degenerate object, the
1993:
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1799:
1420:
1073:
Taylor, John Robert; Zafiratos, Chris D.; Dubson, Michael Andrew (2004).
762:
699:
679:
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607:
576:
558:
191:
57:
1471:
520:
Exotic examples of degenerate matter include neutron degenerate matter,
1932:
1907:
1834:
1804:
1738:
1717:
1377:
1333:
1108:
section 15.3 â R Kippenhahn & A. Weigert, 1990, 3rd printing 1994.
825:
777:
754:
738:
728:
668:
649:
620:
597:
128:
degenerate matter is found in most of the nuclei of stars, not only in
2195:
178:. Degenerate matter exhibits the results of Fermi-Dirac distribution.
1455:
856:
813:
686:
The properties of neutron matter set an upper limit to the mass of a
637:
Neutron degeneracy is analogous to electron degeneracy and exists in
480:
187:
167:
76:
69:
1667:
2069:
1897:
1267:
750:
537:
484:
1210:
1157:
500:), matter can become non-degenerate without reducing its density.
2029:
1917:
1852:
1769:
1764:
737:
At densities greater than those supported by neutron degeneracy,
147:
146:
Degenerate matter exhibits quantum mechanical properties when a
1638:
745:
is a degenerate gas of quarks that is often assumed to contain
512:
of metals derives their physical properties by considering the
508:
and the screening of nuclei from each other by electrons. The
124:
1647:
1633:
571:
reactions stops, becomes a collection of positively charged
1068:
1066:
611:
265:
is the number of particles (typically atoms or molecules),
2147:
1444:
Historical
Studies in the Physical and Biological Sciences
1251:"Evidence for quark-matter cores in massive neutron stars"
619:(primarily supported by neutron degeneracy pressure) or a
1643:
1248:
1077:(2 ed.). Upper Saddle River, NJ: Pearson Education.
572:
1196:
Potekhin, A. Y. (2011). "The
Physics of Neutron Stars".
1189:
1063:
610:
stars, formed by the gradual shrinking of the cores of
1142:
988:
A History of Astronomy : from 1890 to the Present
64:, where thermal pressure alone is not enough to avoid
2100:
1072:
457:{\displaystyle P=K\left({\frac {N}{V}}\right)^{4/3},}
408:
283:
199:
154:. These properties result from a combination of the
1030:
456:
386:
238:
75:Degenerate matter is usually modelled as an ideal
1037:. New York: Holt, Rinehart and Winston. pp.
943:Monthly Notices of the Royal Astronomical Society
2208:
1484:
1017:
1015:
1535:
1351:"Zur Quantelung des idealen einatomigen Gases"
780:, formed by the collapse of objects above the
1599:
1021:
1012:
239:{\displaystyle P=k_{\rm {B}}{\frac {NT}{V}},}
909:
123:. Eddington had suggested that the atoms in
1613:
1075:Modern physics for scientists and engineers
1606:
1592:
56:to refer to dense stellar objects such as
1419:
1284:
1266:
1209:
1156:
962:
921:
171:pressure preventing further compression.
68:. The term also applies to metals in the
1195:
796:uses the word 'degenerate' in two ways:
470:
190:, whose pressure is proportional to its
52:at low temperature. The term is used in
1485:Koester, D; Chanmugam, G (1990-07-01).
1413:
917:http://apod.nasa.gov/apod/ap100228.html
536:Degenerate gases are gases composed of
14:
2209:
1437:
985:
936:
548:
181:
27:Type of dense exotic matter in physics
1587:
1345:
782:TolmanâOppenheimerâVolkoff mass limit
626:
1334:http://www.jstor.org/stable/41133485
1307:
892: â Theoretical model in physics
705:
475:Pressure vs temperature curves of a
722:
531:
24:
1242:
656:acquiring a mass in excess of the
212:
25:
2243:
1572:
898:â High-pressure phase of hydrogen
2194:
2182:
2170:
2158:
2146:
2134:
2122:
2110:
1666:
851:applied the Pauli principle via
713:Heisenberg uncertainty principle
692:TolmanâOppenheimerâVolkoff limit
487:), for a given particle density.
1536:Cohen-Tanoudji, Claude (2011).
1478:
1431:
1407:
1339:
1326:
1301:
1106:Stellar Structure and Evolution
808:described the reduction of the
719:of electron-degenerate matter.
1491:Reports on Progress in Physics
1487:"Physics of white dwarf stars"
1438:Eckert, Michael (1987-01-01).
1228:10.3367/UFNe.0180.201012c.1279
1136:
1118:
1099:
979:
930:
310:
293:
150:system temperature approaches
102:relativistic degenerate matter
13:
1:
2055:Macroscopic quantum phenomena
1529:
2065:Order and disorder (physics)
986:David., Leverington (1995).
937:Fowler, R. H. (1926-12-10).
902:
694:, which is analogous to the
594:electron degeneracy pressure
555:Electron degeneracy pressure
7:
1308:Cain, Fraser (2016-07-25).
990:. London: Springer London.
877:
402:, the pressure is given by
10:
2248:
1539:Advances in Atomic Physics
1503:10.1088/0034-4885/53/7/001
1175:10.1103/PhysRevD.84.084007
868:Subrahmanyan Chandrasekhar
788:
726:
630:
552:
139:
135:
29:
2017:
1971:
1843:
1757:
1731:
1675:
1664:
1626:
1286:10.1038/s41567-020-0914-9
749:in addition to the usual
479:and quantum ideal gases (
156:Pauli exclusion principle
85:Pauli exclusion principle
46:Pauli exclusion principle
18:Neutron-degenerate matter
2217:Concepts in astrophysics
2090:Thermo-dielectric effect
1989:Enthalpy of vaporization
1683:BoseâEinstein condensate
1336:. Accessed 27 July 2023.
1130:Encyclopaedia Britannica
886:â Degenerate bosonic gas
884:BoseâEinstein condensate
872:model for star stability
798:degenerate energy levels
528:and white dwarf matter.
176:Fermi-Dirac distribution
32:Degenerate energy levels
1984:Enthalpy of sublimation
1310:"What are Quark Stars?"
785:stars and black holes.
623:may be formed instead.
48:significantly alters a
1999:Latent internal energy
1749:Color-glass condensate
1358:Zeitschrift fĂŒr Physik
964:10.1093/mnras/87.2.114
853:Fermi-Dirac statistics
818:quantum thermodynamics
488:
458:
388:
240:
142:Fermi-Dirac statistics
66:gravitational collapse
34:. For other uses, see
1809:Magnetically ordered
1126:"Chandrasekhar limit"
474:
459:
400:relativistic energies
389:
269:is temperature, and
241:
1688:Fermionic condensate
870:became the accepted
759:Color superconductor
406:
281:
197:
1903:Chemical ionization
1795:Programmable matter
1785:Quantum spin liquid
1653:Supercritical fluid
1370:1926ZPhy...36..902F
1277:2020NatPh..16..907A
1220:2010PhyU...53.1235Y
1167:2011PhRvD..84h4007R
1033:Solid state physics
955:1926MNRAS..87..114F
890:Fermi liquid theory
658:Chandrasekhar limit
627:Neutron degeneracy
590:Chandrasekhar limit
549:Electron degeneracy
510:free electron model
477:classical ideal gas
186:Unlike a classical
182:Degeneracy pressure
160:quantum confinement
90:degeneracy pressure
2050:Leidenfrost effect
1979:Enthalpy of fusion
1744:Quarkâgluon plasma
1378:10.1007/BF01400221
1364:(11â12): 902â912.
717:equations of state
603:general relativity
489:
454:
384:
259:Boltzmann constant
236:
2098:
2097:
2080:Superheated vapor
2075:Superconductivity
2045:Equation of state
1893:Flash evaporation
1845:Phase transitions
1830:String-net liquid
1723:Photonic molecule
1693:Degenerate matter
1553:978-981-277-496-5
1204:(12): 1235â1256.
1145:Physical Review D
1084:978-0-13-805715-2
1027:Mermin, N. David.
1023:Neil W., Ashcroft
939:"On Dense Matter"
896:Metallic hydrogen
849:Arnold Sommerfeld
830:Erwin Schrödinger
794:Quantum mechanics
706:Proton degeneracy
526:metallic hydrogen
431:
361:
346:
231:
42:Degenerate matter
16:(Redirected from
2239:
2232:Phases of matter
2222:Degenerate stars
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2035:Compressed fluid
1670:
1615:States of matter
1608:
1601:
1594:
1585:
1584:
1568:
1566:
1565:
1556:. Archived from
1544:World Scientific
1523:
1522:
1482:
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1475:
1456:10.2307/27757582
1435:
1429:
1428:
1423:
1421:cond-mat/9912229
1411:
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1396:. Archived from
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919:
913:
845:Llewellyn Thomas
723:Quark degeneracy
673:electron capture
582:kinetic energies
532:Degenerate gases
463:
461:
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455:
450:
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445:
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113:Arthur Eddington
109:degenerate stars
98:rest mass energy
44:occurs when the
21:
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2159:
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2135:
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2109:
2101:
2099:
2094:
2025:Baryonic matter
2013:
1967:
1938:Saturated fluid
1878:Crystallization
1839:
1813:Antiferromagnet
1753:
1727:
1671:
1662:
1622:
1612:
1575:
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1546:. p. 791.
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1198:Physics-Uspekhi
1194:
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1085:
1071:
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1049:
1020:
1013:
998:
984:
980:
935:
931:
926:
922:
914:
910:
905:
880:
864:Ralph H. Fowler
843:and separately
822:Albert Einstein
791:
767:superconductors
735:
727:Main articles:
725:
708:
666:
647:
635:
629:
592:, beyond which
561:
553:Main articles:
551:
534:
441:
437:
423:
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418:
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404:
403:
371:
367:
353:
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220:
218:
211:
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194:
184:
144:
138:
107:The concept of
72:approximation.
50:state of matter
39:
28:
23:
22:
15:
12:
11:
5:
2245:
2235:
2234:
2229:
2224:
2219:
2204:
2203:
2191:
2179:
2167:
2155:
2143:
2131:
2119:
2096:
2095:
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2087:
2082:
2077:
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2067:
2062:
2057:
2052:
2047:
2042:
2037:
2032:
2027:
2021:
2019:
2015:
2014:
2012:
2011:
2006:
2004:Trouton's rule
2001:
1996:
1991:
1986:
1981:
1975:
1973:
1969:
1968:
1966:
1965:
1960:
1955:
1950:
1945:
1940:
1935:
1930:
1925:
1920:
1915:
1910:
1905:
1900:
1895:
1890:
1885:
1880:
1875:
1873:Critical point
1870:
1865:
1860:
1855:
1849:
1847:
1841:
1840:
1838:
1837:
1832:
1827:
1826:
1825:
1820:
1815:
1807:
1802:
1797:
1792:
1787:
1782:
1777:
1775:Liquid crystal
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1761:
1759:
1755:
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1746:
1741:
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1733:
1729:
1728:
1726:
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1720:
1715:
1710:
1708:Strange matter
1705:
1703:Rydberg matter
1700:
1695:
1690:
1685:
1679:
1677:
1673:
1672:
1665:
1663:
1661:
1660:
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1624:
1623:
1611:
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1596:
1588:
1582:
1581:
1574:
1573:External links
1571:
1570:
1569:
1552:
1531:
1528:
1525:
1524:
1497:(7): 837â915.
1477:
1450:(2): 191â233.
1430:
1406:
1403:on 2019-04-06.
1349:(1926-11-01).
1338:
1325:
1314:Universe Today
1300:
1261:(9): 907â910.
1255:Nature Physics
1241:
1188:
1135:
1117:
1098:
1083:
1062:
1047:
1011:
996:
978:
949:(2): 114â122.
929:
920:
907:
906:
904:
901:
900:
899:
893:
887:
879:
876:
839:Early in 1927
806:Walther Nernst
790:
787:
773:interactions.
765:in electrical
763:Cooper pairing
747:strange quarks
743:Strange matter
724:
721:
707:
704:
671:, also termed
664:
645:
631:Main article:
628:
625:
569:nuclear fusion
550:
547:
533:
530:
522:strange matter
453:
448:
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140:Main article:
137:
134:
81:quantum states
26:
9:
6:
4:
3:
2:
2244:
2233:
2230:
2228:
2227:Exotic matter
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2197:
2192:
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2060:Mpemba effect
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2041:
2040:Cooling curve
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2016:
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1963:Vitrification
1961:
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1949:
1946:
1944:
1941:
1939:
1936:
1934:
1931:
1929:
1928:Recombination
1926:
1924:
1923:Melting point
1921:
1919:
1916:
1914:
1911:
1909:
1906:
1904:
1901:
1899:
1896:
1894:
1891:
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1868:Critical line
1866:
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1858:Boiling point
1856:
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1790:Exotic matter
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1597:
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1577:
1576:
1560:on 2012-05-11
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1360:(in German).
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1154:
1151:(8): 084007.
1150:
1146:
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1131:
1127:
1121:
1115:
1114:0-387-58013-1
1111:
1107:
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1016:
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873:
869:
865:
862:Also in 1927
860:
858:
854:
850:
846:
842:
837:
835:
834:absolute zero
831:
827:
823:
819:
815:
811:
810:specific heat
807:
802:
799:
795:
786:
783:
779:
774:
772:
768:
764:
760:
756:
752:
748:
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740:
734:
730:
720:
718:
714:
703:
701:
697:
696:Chandrasekhar
693:
689:
684:
681:
676:
674:
670:
663:
660:of 1.44
659:
655:
651:
644:
640:
639:neutron stars
634:
624:
622:
618:
613:
609:
604:
599:
595:
591:
586:
583:
578:
574:
570:
565:
560:
556:
546:
542:
539:
529:
527:
523:
518:
515:
511:
507:
506:atomic nuclei
501:
499:
493:
486:
482:
478:
473:
469:
467:
451:
446:
442:
438:
433:
428:
425:
420:
415:
412:
409:
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397:
381:
376:
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363:
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355:
350:
342:
339:
332:
328:
322:
318:
314:
304:
300:
296:
287:
284:
276:
275:absolute zero
272:
268:
264:
260:
253:
250:is pressure,
249:
233:
228:
224:
221:
207:
203:
200:
193:
189:
179:
177:
172:
169:
163:
161:
157:
153:
152:absolute zero
149:
143:
133:
131:
130:compact stars
126:
122:
118:
114:
110:
105:
103:
99:
94:
91:
86:
82:
78:
73:
71:
67:
63:
62:neutron stars
59:
55:
51:
47:
43:
37:
33:
19:
2189:Solar System
2085:Superheating
1958:Vaporization
1953:Triple point
1948:Supercooling
1913:Lambda point
1863:Condensation
1780:Time crystal
1758:Other states
1698:Quantum Hall
1692:
1562:. Retrieved
1558:the original
1538:
1494:
1490:
1480:
1447:
1443:
1433:
1425:
1409:
1398:the original
1361:
1357:
1341:
1328:
1317:. Retrieved
1313:
1303:
1258:
1254:
1244:
1201:
1197:
1191:
1148:
1144:
1138:
1129:
1120:
1105:
1101:
1074:
1032:
987:
981:
946:
942:
932:
923:
911:
861:
841:Enrico Fermi
838:
803:
792:
775:
771:strong force
739:quark matter
736:
733:Strange star
709:
688:neutron star
685:
677:
661:
654:white dwarfs
650:solar masses
642:
636:
633:Neutron star
617:neutron star
598:solar masses
587:
577:White dwarfs
566:
562:
543:
535:
519:
502:
498:helium flash
494:
490:
465:
395:
270:
266:
262:
251:
247:
185:
173:
164:
145:
121:Arthur Milne
117:Ralph Fowler
108:
106:
101:
100:) is called
95:
89:
74:
58:white dwarfs
54:astrophysics
41:
40:
2177:Outer space
2165:Spaceflight
1994:Latent heat
1943:Sublimation
1888:Evaporation
1823:Ferromagnet
1818:Ferrimagnet
1800:Dark matter
1732:High energy
801:mechanics.
778:quark stars
700:white dwarf
608:white dwarf
559:White dwarf
192:temperature
2211:Categories
2009:Volatility
1972:Quantities
1933:Regelation
1908:Ionization
1883:Deposition
1835:Superglass
1805:Antimatter
1739:QCD matter
1718:Supersolid
1713:Superfluid
1676:Low energy
1564:2012-01-31
1530:References
1319:2021-01-15
1268:1903.09121
1093:1319408575
1048:0030839939
997:1447121244
826:Max Planck
729:Quark star
698:limit for
680:wavelength
669:beta decay
621:black hole
514:conduction
36:Degeneracy
2141:Astronomy
2129:Chemistry
1519:250915046
1511:0034-4885
1464:0890-9997
1394:123334672
1386:0044-3328
1347:Fermi, E.
1295:1745-2481
1236:119231427
1211:1102.5735
1183:119120610
1158:1012.0154
1006:840277483
973:0035-8711
903:Citations
857:Fermi gas
828:, and by
652:), or by
481:Fermi gas
329:ℏ
301:π
188:ideal gas
168:Fermi gas
77:Fermi gas
70:Fermi gas
2070:Spinodal
2018:Concepts
1898:Freezing
1472:27757582
1029:(1976).
878:See also
804:In 1914
757:quarks.
538:fermions
485:Bose gas
125:Sirius B
2201:Science
2117:Physics
2103:Portals
2030:Binodal
1918:Melting
1853:Boiling
1770:Crystal
1765:Colloid
1366:Bibcode
1273:Bibcode
1216:Bibcode
1163:Bibcode
951:Bibcode
789:History
702:stars.
257:is the
148:fermion
136:Concept
1658:Plasma
1639:Liquid
1550:
1517:
1509:
1470:
1462:
1392:
1384:
1293:
1234:
1181:
1112:
1091:
1081:
1057:934604
1055:
1045:
1004:
994:
971:
690:, the
464:where
394:where
246:where
83:. The
2153:Stars
1648:Vapor
1634:Solid
1627:State
1515:S2CID
1468:JSTOR
1416:arXiv
1401:(PDF)
1390:S2CID
1354:(PDF)
1263:arXiv
1232:S2CID
1206:arXiv
1179:S2CID
1153:arXiv
824:, by
814:gases
612:stars
1619:list
1548:ISBN
1507:ISSN
1460:ISSN
1382:ISSN
1291:ISSN
1110:ISBN
1089:OCLC
1079:ISBN
1053:OCLC
1043:ISBN
1002:OCLC
992:ISBN
969:ISSN
915:see
755:down
753:and
731:and
573:ions
557:and
158:and
119:and
60:and
1644:Gas
1499:doi
1452:doi
1374:doi
1281:doi
1224:doi
1171:doi
959:doi
820:by
812:of
2213::
1646:/
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1513:.
1505:.
1495:53
1493:.
1489:.
1466:.
1458:.
1448:17
1446:.
1442:.
1424:.
1388:.
1380:.
1372:.
1362:36
1356:.
1312:.
1289:.
1279:.
1271:.
1259:16
1257:.
1253:.
1230:.
1222:.
1214:.
1202:53
1200:.
1177:.
1169:.
1161:.
1149:84
1147:.
1128:.
1087:.
1065:^
1051:.
1041:.
1039:39
1025:;
1014:^
1000:.
967:.
957:.
947:87
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941:.
874:.
836:.
751:up
524:,
483:,
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115:,
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1521:.
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1454::
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1297:.
1283::
1275::
1265::
1238:.
1226::
1218::
1208::
1185:.
1173::
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1155::
1132:.
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1059:.
1008:.
975:.
961::
953::
665:â
662:M
648:(
646:â
643:M
466:K
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439:4
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410:P
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288:=
285:P
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255:B
252:k
248:P
234:,
229:V
225:T
222:N
213:B
208:k
204:=
201:P
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.