Statistical Physics, Second Revised and Enlarged Edition
88 Fermi–Diracgases functiong(ε)∝ε^1 /^2 andμfallsslightly.Usingthe results ofAppendixCitcan be shown that for this case μ(T)=μ( ...
Properties ofan ideal Fermi–Dirac gas 89 AboveT=0, whilstyetinthedegeneratelimitTTTTF,theintegral(8.7) canbe evaluated using th ...
90 Fermi–Diracgases Pressure P. The pressureisalso readily deducedfromU.Infactit remains true that for a gas of massive particle ...
Application to metals 91 region. Afullcalculation ofSorofFisfairlycomplicated,andwillnotbe attempted here. (There is nopartition ...
92 Fermi–Diracgases g↓() g↑() F B B +B B Fig. 8. 4 Calculatingthemagnetization ofaspin-^12 FDgas atT=0. Thele ...
Application to helium-3 93 Liquid 35 Solid 29 0 0. 32 K T Gas P (atm) Fig. 8. 5 Thephasediagramfor^3 He(notdrawn to scale). move ...
94 Fermi–Diracgases is usuallypositive. A negativedP/dTcan occurin two situations. Occasionally it happensthatthesolidcontractso ...
Summary 95 8.4 Summary This chapter discusses the properties of an ideal Fermi–Dirac gas. Quantum statistics rather than MB st ...
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9 Bose–Einsteingases Thischapterdiscusses the properties ofanidealBose–Einstein (BE)gas, which without anyinteractions neverthel ...
98 Bose–Einsteingases apossibilityina‘friendly’boson system since thereisnoexclusion principle. Hence we must haveB>1 to desc ...
Properties ofan ideal Bose–Einstein gas 99 thedenominator ofequation (9.4)isnegligible, andthefunctionF(B)reduces simply to 1/B. ...
100 Bose–Einsteingases Equation (9. 6 ) has radicallydifferent solutions above and belowTTTB.Abovethis temperature, the second t ...
Application to helium- 4 101 T T TTTB TTTB CV 3 2 NkkkB 3 U = 2 NkkkBT UUU, P UUT5/2 (a)(b) Fig. 9. 3 The variation with tempe ...
102 Bose–Einsteingases Liquid^4 He remainsfluidto thelowest temperatures atpressuresbelow about 25 atm, for reasons discussed in ...
Application to helium- 4 103 S T TTT Fig. 9. 6 The variation ofentropy withtemperatureforliquid^4 He, showing a verticaltangent ...
104 Bose–Einsteingases oftheflow tube. The source reservoir warms upasitisdepletedofsuperfluidwhereas the receiving reservoir co ...
Phoneybosons 105 density,wealso needtoknow, (i)how manystates there areinthefrequencyrangeof interest, and (ii) how the frequenc ...
106 Bose–Einsteingases TT = 1.25TTT 0 TT=TTT 0 TT = 0.8TTT 0 0 1 23456 7 (units of kkkBTTT 0 /h) u() Fig. 9. 7 The spectraldis ...
Phoneybosons 107 inthis case, andtherefore (followingtheargument ofsection 8.1.3)P=U/ 3 V. The radiation pressure is simply one- ...
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