《thermal physics》普林斯顿大学

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1、PHYSICSDEPARTMENT,PRINCETONUNIVERSITYPHYSICS301FINALEXAMINATIONJanuary17,2000,8:30{11:30am,JadwinA06Thisexamcontainsveproblems.Workanythreeoftheveproblems.Allproblemscountequallyalthoughsomeareharderthanothers.Doalltheworkyouwantgradedintheseparateexambooks.Indicateclearlywh

2、ichthreeproblemsyouhaveworkedandwantgraded.Iwillonlygradethreeproblems.Ifyouhandinmorethanthreeproblemswithoutindicatingwhichthreearetobegraded,Iwillgradetherstthree,only!Writelegibly.IfIcan'treadit,itdoesn'tcount!Putyournameonallexambooksthatyouhandin.(Onlyoneshouldbenecessa

3、ry!!!)Ontherstexambook,rewriteandsignthehonorpledge:IpledgemyhonorthatIhavenotviolatedtheHonorCodeduringthisexamination.Copyrightc2000,EdwardJ.GrothPhysics301FinalExam17-Jan-2000Page2PhysicalConstantsandConversionFactorsc=2:9981010cms−1;h=1:05410−27ergs;k=1:38010−16ergK−1

4、;e=4:80310−10statcoulomb;23−1N0=6:02510moleculesmole;m−28g;electron=9:10810m−24proton=1:67210g;m−24neutron=1:67510g;m−24g;amu=1:66010=9:27310−21ergGauss−1;BG=6:67310−8cm3s−2g−1:1atm=1:013106dynecm−2;1eV=1:60210−12erg;1cal=4:186107erg:Copyrightc2000,EdwardJ.GrothPhy

5、sics301FinalExam17-Jan-2000Page31.ConsideralineofN+1pins".Aspincanpointupordownandthespinsarelabeled0;1;2;:::;Ninorderalongtheline.Supposethatwhentwoadjacentspinspointinthesamedirection,theycontribute−Jtotheenergyofthesystemandwhentheypointinoppositedirections,theircontributio

6、nis+J>0.Non-adjacentspinshavenointeractions.(a)Whatarethepossibleenergiesofthissystemandhowmanystatesaretherewitheachenergy?Hint:youmaynditeasiertospecifyastateanddothecalculationsintermsofthenumberofsamedirectionandoppositedirectionpairsratherthanthenumberofupanddownspins.(b

7、)Thesystemisinthermalequilibriumwithaheatbathattemperature.Whatisthepartitionfunction?Aclosedformexpressionisdesired.(c)Thesystemisstillinequilibriumattemperature.Determineitsaverageenergyandentropy.Copyrightc2000,EdwardJ.GrothPhysics301FinalExam17-Jan-2000Page42.Inbiologica

8、lsystems,allsortsofinterestinginteractionsoccur.Forexample,it