Thermal and Statistical Physics

371 Pages·2020·47.243 MB·English

by  R.B. Singh

THERMAL
AND
STATISTICAL
PHYSICS
R.B. Singh
Heaodft hPeh ysDiecpsa rtment
U.N.G..CP ollPeagder,a una
(AffilitaDot. eDd.U Un.i veGrosriatkyh,p ur)
Kushi(nUa.gPa.r)
PUBLISFHOIORNN GEW ORLD
NEWA GEI NTERNATI(OPLN)IA MLI TPEUDB,L ISHERS
NeDwe l•Bh ain g•aC lhoern•eCn oaci•h G iunw a•h adIte irl abad
y
Jala•nK dohlak•Lra u tcak •nM ouwm b•Ra ain chi
Visuisat wt ww.ngeepuwblais.ch·oemr s
Preface
Therpmhaylsa ilckssno,o awshn e aanttd h ermodiycsno anmsiiacdsaset rreadd ibtriaoonnfca hl
physainicdbss e itnagut guohn td ergsrtauddsueiannpttcaesmes a tny ye ars.t hBieun tt raofdtuecrt ion
oft hryeeead resgc roeuesr osmete,o poifsc tsa tpihsythsiaicbvcaeselae dnd tetodh c eo umrastee rial
fort hecslea sSsteast.ip shtyisucisaacebslss tcroanccotefq p utasn mteucmh asnuicacshqs u antum
staetneeslr,eg vyde elnsso,if t ysd teagteenspe,hr aasscpeya g,ca em,ms ap ace, ensemble, partition
funcettwicho.in ac rqheu intetewso t udoeufnn tdse rgsrtauddLueianmtkteeems, o. o sft. ttehaec hers
feedli fficiunrl etcyo mmaes nudiittnaegtbx otlt he es steu dAelntthsot.uh gehrm,ea nsaytr aen dard
treabtyei msiense nto nta hsueut bhbjouerttcsh t e ir ctoolnoat reagnntetdh meaairtree arriseao l s
arrantghemadot so tft hset udfeintnthdse msienul nvceosm foprotsaiibtnlsi eeo lne tcotpioinfcg s
theoiwirnn teArlesaslo ta .rf grea ctsitoundc eaonnftan sfo fto rd tohweitsnoetg h ebhioirog khs
priTchepesr .e seindste sbiotgomonke e edtr etqhuei roeufmn ednetrsgs rtaudduIeha nattbvesee .e n
vecrayr iesnf eulle tchtteoi pnligac ysti,hn segei qru aenntdchs eet oyfpl ree sesnot asttthiuaodtne nt
manyo atfr aoifld e arnneicwno gn cReepatlsti.hzm eie nnsgtt aoalftu en dergsrtauddeuevanettresy
attehmabpset me na dtepo retshemena tt eirmnio aseltl emeannetdaa srdiyil gye fosrtmiT.bot l hei s
enads uffniucmibeoenfert x amhpalvbeees ea nd dTehdo.u Ihg ahvm ea dmeyb eesftf iontr hti s
atteomntp hsteu bwjheicpltle a ntnhliean ygoo ftu htte e axnttd h seu bmjaetclttc e arn,gn uoets s as
toh owf aIrh avceo muept ot heex pectoafet sitoenesm eds crheotaledaaercrslhs,ee, ar rsn,e d
physaincsdit sutdsTe hnehtyas vt.ejo u dmgywe o rk carnipdta iscsac lotlnhyse ticrrru icttiicvies ms
eitthmoee or rt toh peu blissoth hmeayrtf s u teunrdee abveto oeun rl aarncgdo er mriescttaa nkde s
poltihstehe i xnst u acw ha tyh iatt bemcooramenem dso roeb jectfo-rot rhsiteeue nndst.t ed
Ia mt hantkmofy cu oll lefaagmumieelsmy,b a enrtdsh p eu blifsothrhe ecriosro pedruartiinogn
wriotfit nhmgea nusacnriditc psot m posing Taoenr dirh s up mraTinhn.et rieInhf goo.ptr ehei a nt
futtuhrreee adoeftr hbsio so wki hlellm epi nc orreacnttyyi pnogg rearprhoirc aolr conceptual
mistakmei gwhhhative cesh c ampyae tdt ednutripiornno-gr o efagda inpndr inting.
Int heen Ida ,w atihte rwehsipcohnb soteodh kri afswr sol me arnsecdh oalnsadtr usd ents.
- R.SBi.n gh
Contents
Preface
V
PART-T1h erPmhayls ics
12-53
CHAPT1E RK ineTthiecoo rfGy a ses
32-8
1.I1n troduction 3
1.F2u ndamAesnstuamlpo tfKi ionnTesht eioocfr I yd eGaals es 3
1.M3o lecFulluaxr 4
1.4 PorfGe asss ure 6
1.I5n terporfTe etmapteiroant ure 7
1.D6e ducotfGi aLosan w s 7
1.A7v ogaLdarwo 's 8
1.D8a ltLoanw' s 8
1.G9r ahaLmao'wfs D iffusion 8
II.O M axweLlalow'f Ds i stroifb uMtoilSoepnce ueldasr 9
1.1S1h aopfCe u rRveep resSepneDteiidsn tgr Fiubnucttiioonn l3
1.1E2f foefTc etm peroanSt puereed DiFsutnrcitbiuotnion 14
1.1M3o st PSrpoebAeavdbe,lr eSa pgeaeen dRd o oMte aSnq uSapreee d 14
1.1E4x periVmeernitfaoilfMc aaxtwieoDlnil s'tsr Liabwution 16
II. M5a xwell-BEonletrDzgimysa tnrni bution 17
1.1De6g rsoe fFe reedom l7
1.1T7h eoorfEe qmu ipaorfEt nietrigoyn 19
1.18 ApopfTl hiecoaortfEei qmou ni paorfEt ni�tSripgoeync H iefoaiftGc a ses 19
1.1P9o lyaGtaosmic 20
SolEvxeadm ples 21
QuestainPodrn osb lems 27
CHAPT2E RT ransPphoernto mena 2-9-43
2.M1e aFnr Peaet h
29
2.S2u rvEiqvuaalat niMdoe naF nr Peaet h 31
2.M3e aDni stCaonvcebery aeM do leicnaug lievD einr eacfttLieaoCrsno t l lisio3n2
2.T4r anPshpeonrotm ena 34
SolEvxeadm ples 40
QuestainPodrn osb lems 42
viii
Contents
CHAPTE3R E quatoifSo tnaf toeGr a ses
4½�
3.I1n troduction
3.E2q uaotfia onIn d eGaals 44
3.B3e havoifRo euaGrla ses 44
3.A4n drEexwpse rionmC eanrtb on Dioxide 45
47
3.C5r itSitcaatle
48
3.T6w o-PRheagsieo n
49
37. I ntermoFloerccuelsar
50
3.v8a dne Wra aElqsu a-otfiS otnate
52
3.v9a dne Wra aIlsso therms
54
3.1C0ri tiCcoanls tants
55
3.1A1l ternDaetriivvefa otCrir ointC iocnaslt ants
57
3.1L2i mitaoftv iadonen Wrsa aElqsu ation
58
1•
3.1L3a wo fC orrespSotnadtiensg
59
3.1D4e termionfCa rtiitoinc al Constants
59
3.1S5o mOet hEeqru atoifSo tnast e
60
3.1V6i rEiqaula otfiS otna tes-KaOmnmneEerqslu iantgiho n
62
3.17 Boyle oTfaev madpnee Wrra aatlusr eG as 62
SolEvxeadm ples 63
QuestainoPdnr so blems 67
CHAPTE4R Z eroLtahwo fT hermodynParmeilcismC:io nnacreyp ts 69-80
4.I1n troduction
69
4.T2h ermodSyynsatmaeinmcSd u rroundings
69
4.T3h ermodVyanramiiacb les
70
4.E4x tenasnIidnv tee nVasriivaeb les
70
71
4.T5h erEmqauli liZberrioLutamhwo: fT hermodynamics
4.T6h ermodyEnqaumiilci brium 73
4.T7h ermodPyrnoacmeiscs 74
4.R8e verasniIdbr lree versible Processes
74
4.E9q uaotfiS otna te 75
76
4.1C0o effiocfEi xepnatn ·s(iEoxnpansivity)
76
4.1C1o mpressibility
4.1R2e laBteitownPe aernDt eirailv atives 77
78
SolEvxeadm ples
80
QuestainPodrn osb lems
CHAPTESR F irLsatwo fT hermodynamics st-96
5. 1I nteErnnaelr gy .8 1
5.H2e at SI
5.W3o rk SI
Contentisx
5.W4o rDko nienS omOet hPerro cesses
82
5.W5o rDke peonnPd ast h 83
5.C6y cPlriocc ess
84
5.F7i rLsatwo fT hermodynamics 84
5.H8e aCta pacity 85
5.E9n erEgqyu aatniDdoi nff eroefHn ecaet Capacities 86
5.1A0d iabTartaincs foromfaa nIt dieGoaanls 88
5.1W1o rDko nienR everIssiobtlhEeex rpmaanolsfI i doeGnaa ls 90
5.1W2o rDko nienR everAsdiibalbEeax tpiacno sfai nIo dneG aals 90
5.1W3o rDko nienR everEsxipbalnoesfV i aoDnne W ra als Gas 91
5.1V4a riaotfTi eomnp erwaittHuher ieg ht-ALdaipasbea tRiact e 91
5.1T5o t(aElx oarcP te rfDeicftf)e rential 93
SolEvxeadm ples 94
QuestainPodrn osb lems 95
CHAPTE6R H eaEtn gianneSdse coLnadwo fT hermodynamics 971-19
6.I1n troduction 97
6.H2e aEtn gine 98
6.E3f ficoifHe enaEctny g ine 99
6.C4a rnIodte'Hasela E tn gine 100
6.R5e versoifCb airlEninotgtyi ne 103
6.C6a rnoRte frigerator 103
67. H eat Pump 104
6.C8a rnTohte orem 105
6.T9h ermodoyrAn basmoiSlccu atolefTe e mperature 106
6.1C0l asius-LCaltaHepeneaEtytq r uoan(t Fiiorns tH eLaEatqt ueantti on) 109
6.1S1p ecHiefiaoctfS aturVaatpeodu r L(aSteHecenoaEtntq d u ation) 111
SolEvxeadm ples 113
QuestainPodrn osb lems 118
CHAPTE7R E ntropy
12104-3
7. 1D efinition 120
7.P2r inocfEi nptlreIo npcyr ease 124
7.E3n traonpUdyn avaiElnaebrlgey 125
7.C4h anignEen trionHp eyaC to nduocrit niP orno ceEsqsu aolfio zfTa etmipoeenr a1t2u6r
7.C5a lcuolfCa htainoignnEe n troofapS yy stienRm e verPsriobclees s 127
7.I6n crienEa nster ionIp ryr evPerrosciebslsee s 129
7.E7f ficoifCe anrcCnyyo ctfl reoT m-D Si agram 130
7. 8E ntroofap nIy d eGaals 131
7. 9S tatiIsnttiecrapolrf Ee nttartoipoyn- aEnnDdti rsoopryd er 132
SolEvxeadm ples 134
QuestainPodrn osb lems 141
x Contents
CHAPTE8R T hermodyRnealmaitci ons
144-183
8.M1a xweTlhle'i;sm odyRnealmatiico ns 144
8.T2d Esq uations 174
8.3 Energy Equation 153
8.H4e aCta paEcqiutayt ions 155
8.J5o ule-TohrJo omusloen- EKffeelcvti n
161
8.T6h ermodyonfMa amginceSsty isctM eamg neto-ECfafleocrti c
166
8.T7h ermodyFnuanmcitci ons
169
8.T8h iLradwo fT hermodyNneammsiHtce'sasT t h eorem 137
SolEvxeadm ples 174
QuestainPodrn osb lems 180
CHAPTE9R P roduocftL ioowTn e mperaantLdui rqeu efoafGc atsieosn
184-197
9.I1n troduction 184
9. 2T echnioqfPu reosd uLcoiwTn egm perature 184
9.A3d iabDaetmiacg netization
186
9. 4L iquefoafGc atsieosn
190
9.M5a ttaetVr e r.Lyo wT emperature 193
9.S6u rpceonductivity
196
Questions 197
CHAPTER ConducotfHi eoant
10 1892-20
10.I1n troduction
198
10.C2o nducatnCidoo nnd uctivity
198
10.V3a riaanbSdlt ee aSdtya te
199
10.I4s othSeurrmfaacle 199
10.5 CooefTf hfeircCmioaenlnd tu ctivity
199
10.T6h erRmeasli stance 200
107. R ectiFllionowefH a eraF to:u rEiqeura tion 200
10.D8e termionfAa btsiooClnou ntdeu cotfaiM veittBayal r -FoMrebteh'osd 203
10.A9n gstrPoemr'iFsol doiMwce thfoodDr e termionfTa hteiroCmnoa nld vuicttyi 206
209
10.T1h0r Deiem ensFilooonwfHa ela t
210
10.R1a1d Filaolow fH eaDte:t ermionfKa otfBi aoCdno nductor
211
10.R1a2d Filaolow fH eaitnC ylinSdhreilcla l
231
10.D1e3t ermionfTa hteirComonan ld ucotfRi uvbibtGeyir v ientn h Feo romfT ube
241
10.D1e4t ermionfKa otfBi aoCdno ndu(cAtsobre Lsetaeon sCd)h :a rMlettohno d
215
10.15 FoofrI mcoaentt hiSeou nr foafacL ea ke
261
10.I1n6g Heanu Esxzp eriment
271
SolEvxeadm ples
219
QuestainPodrn osb lems
Contenxtis
CHAPTE1R1 TheRramdaila tion
221-253
11.I1n troduction 221
11.S2o urocfTe hse rRmaadli ation 221
11.R3a diation- ThDeertemcotpoirl e 222
11.N4a tuorfTe h enRnaadli aatniSdoo nmo efi tPsr operties 223
11.S5o mFeu ndamDeenftianli tions 224
11.E6n erFglyuI xn,t eannsRdia tdyi Eamnitt tance 225
11.R7a diaitnaiH oonl lEonwc losure 225
11.A8nI de(aPle rBfelcatBc)ok d y 226
11.F9e ry'sB oBdlya ck 226
11.W1i0e nB'lsaB cokd y 227
11.K1i1r chshL oafwf 227
11.R1e2l ationR aBdeitEawmneitet ntR ao nfacS eu rfaancEden erDgeyn sui ty 228
11.13 Radiation Pressure 229
11.S1t4e fan-BLoalwt zmann 232
11.S1o5l Caorn st(aS)n t 233
0
11.T1e6m _epratoufSr uen 234
11.D1i7s triobfEu nteiriognBny l aBcokd Rya diation 235
11.W1i8e nD'iss plaLcaewm ent 237
11.19 Norma(lS tMaonWddaeivsnei gsna )B ox 240
11.R2a0y leigLha-wJ eans 242
11.P2l1a nRcakd'isa Ltaiwo n 244
11.D2e2d ucotfSi toenf Laanwfr' osm P lanck's Law 246
11.D2e3d ucotfWi ioennD 'iss plaLcaewm ent 247
11.24 EnMeormgeyn toaufPnm hd o ton 248
SolvEexda mples 248
QuestainoPdnr so blems 252
PART-S2t atiPshtyisciacls
255-360
CHAPTE1R P relimCionnacreyp ts
257-270
11. I ntroduction 257
1.M2a xwell-BoltSztmaatnins t(iMc-sB) 257
1.B3o se-Ei(nBs-StEte)ai tni stics 257
1.F4e rmi-(DFi-rSDat)ca tistics 258
1.S5p ecifiocfta htSeit oaontfA e S ystem 258
1.D6e nsoifSt tya tes 260
1.M7a cros(cMoapciSrcto a)t e c262
1.M8i cros(cMoipcSirtcoa )t e 262
CHAPTE2R i> haSspea ce 271-275
2.P1h aSspea ce 271
2.·D2 e nsoifSt tya itnPe hsa Sspea ce 273
xii Contents
CHAPT3E RE nsemFbolrem uloafSt tiaotni Msetcihcaanli cs 27-6288
3.E1n se(m ble
267
3.D2e nsoifDt iys triibnyu -tSipoanc e
277
3.P3r inocfiE pqluaeaP lr iPorroib ability
277
3.E4r go·Hdyipcothesis
278
3.5 LioTuhveiolrleem' s
278
3.S6t atiEsqtuiiclailb rium
281
37. E nsemFbolrem ulaSttiaotni sotfi cal Mechanics
228
3.A8v erEangeero gfPy a rticle
278
3.T9h Eeq uipaTrhteiotrieomn
2874
CHAPTE4R T hermodyFnuanmcitci ons 28299-3
4.E1n tropy
289
4.E2n trionTp eyr omfsP robability
290
4.E3n trionTp eyr omfPs a rtFiutnicotni on
291
4.F4r eEen ergy
291
4.H5e lmhForleEtenz e rignTye romfPs a rtFiutnicotni on
292
4.T6h ermodFyunnacmtiiincTo enrsom fPs a rtFiutnicotni on
293
CHAPT5E RD istriLbauwtsi on 294-309
5.M1a xwell-BDoilsttzrmiabnunt ion
294
5.H2e aCta paocfai ntI yd eGaals 299
5.M3a xwell's Speed Distribution 299
5.F4e rmi-SDtiartaics tics 303
5.B5o se-ESitnasttiesitni cs 306
CHAPTE6R A pplicoafQt uiaonntsSu tma tistics 310-328
6.A1p plicoafFt eiromnis-S Dtiartaics tics 310
6.E2l ectHreoaCntai pca city 316
6.T3h ermEimoinsi(scRi iocnh ardsoEnq-uDautsihomna)n n 317
6.P4r opeorfIt dieBeaoslsS ey stem 320
6.E5n erogfBy - GEa s
323
6.B6l ackR aBdoidayPt liaonRnca:kd 'isaL taiwo n 323
6.C7o mparoifMs -oBBn,- aEn Fd- SDt atistics 324
6.V8a liCdriittyfoe rrC iloans Rseigciamle
326
CHAPTE7R P artiFtuinocnt ion 329-351
7I.C anonPiacratFliu tnicotni on 329
7.C2l assicaFlu nPcaotrfaiSt oyinst tiCeoomnn taNiD niisntgi ngPuairsthiacbll3e03es
7.T3h ermodFyunnacmtoiifMco o nnso atGoamsic
323
7.G4i bPbasr adox 323
7.I5n distinogfPu airsthaiancbSdliy elmsim teoytfW r ayv Feu nctions 335
Contexniitis
7. 6P artFiutnicoftnoiI ron nd istiPnagrutiischlaebsl e 336
7.M7o lecPualratrFi utnicotni on 3-�.
7. 8P artFiutnicoatnni Tdoh ne rmodPyrnoapmeoirfMct o ineosa tIodmeGiaacls 338
7. 9H elmhForleEtenz e rFg y 340
-
7. 1R0o t'a tPiaorntaFiultn icotni on 341
7. 1V1i braPtairotnFiautlni cotni on 342
7.1G2r aCnadn onEincsaelma bnGldre a Pnadr tFiutnicotni on 344
7. 1S3t atiPsrtoipceoarfaTlt h ieersm odSyynsatimenTim ec r omfGs r aPnadr tFiutnico3tn4i 6o n
7.1G4r aPnodt e<I>n tial 347
7.1I5d eGaalfs r oGmr aPnadr tFiutnicotni on 347
7.1O6c cupNautmibooenfar nE nerSgtyafr toemG raPnadr tFiutnicotni on: 349
Fermi-aDnBidor saec- EDiinssttreiibnu tion
CHAPTE8R_A pplicoafPt airotnisF tuinocnt ion 35326-0
8.S1p ecHiefiactS oolfi ds 352
8.P2h onon Concept 357
8.P3l anRcakd'isaL taiwPo:an r tFiutnicoMtnei tohno d 358
INDEX 36316-4