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1、Problems&SolutionsforStatisticalPhysicsofParticlesUpdatedJuly2008byMehranKardarDepartmentofPhysicsMassachusettsInstituteofTechnologyCambridge,Massachusetts02139,USATableofContentsI.Thermodynamics............................1II.Probability..............................25III.K
2、ineticTheoryofGases........................38IV.ClassicalStatisticalMechanics.....................72V.InteractingParticles..........................93VI.QuantumStatisticalMechanics....................121VII.IdealQuantumGases........................138ProblemsforChapterI-Ther
3、modynamics1.Surfacetension:ThermodynamicpropertiesoftheinterfacebetweentwophasesaredescribedbyastatefunctioncalledthesurfacetensionS.ItisdefinedintermsoftheworkrequiredtoincreasethesurfaceareabyanamountdAthroughdW¯=SdA.(a)Byconsideringtheworkdoneagainstsurfacetensioninaninfini
4、tesimalchangeinradius,showthatthepressureinsideasphericaldropofwaterofradiusRislargerthanoutsidepressureby2S/R.WhatistheairpressureinsideasoapbubbleofradiusR?•Theworkdonebyawaterdropletontheoutsideworld,neededtoincreasetheradiusfromRtoR+∆Ris∆W=(P−P)·4πR2·∆R,owherePisthepress
5、ureinsidethedropandPoistheatmosphericpressure.Inequilibrium,thisshouldbeequaltotheincreaseinthesurfaceenergyS∆A=S·8πR·∆R,whereSisthesurfacetension,and∆Wtotal=0,=⇒∆Wpressure=−∆Wsurface,resultingin22S(P−Po)·4πR·∆R=S·8πR·∆R,=⇒(P−Po)=.RInasoapbubble,therearetwoair-soapsurfaceswi
6、thalmostequalradiiofcurvatures,and2SPfilm−Po=Pinterior−Pfilm=,Rleadingto4SPinterior−Po=.RHence,theairpressureinsidethebubbleislargerthanatmosphericpressureby4S/R.(b)Awaterdropletcondensesonasolidsurface.TherearethreesurfacetensionsinvolvedSaw,Ssw,andSsa,wherea,s,andwrefertoair
7、,solidandwaterrespectively.Calculatetheangleofcontact,andfindtheconditionfortheappearanceofawaterfilm(completewetting).•Whensteamcondensesonasolidsurface,watereitherformsadroplet,orspreadsonthesurface.Therearetwowaystoconsiderthisproblem:Method1:Energyassociatedwiththeinterfac
8、es1Inequilibrium,thetotalenergyassociatedwiththethreeinterfacesshouldbemini
