Fundamentals of statistical and thermal physics

666 Pages·1965·58.22 MB·English

by  F Reif

Fundamentals of

and
eee

‘Virinl equation of wate, 19%, 422
Viscosity, SATS
cpettinient of, 478,
sf dilate woe, 478478
enlewation in tetas of x, 608, 518
indepeadeuce of pressure, 475477
igntous resull, S4585
tempemture dependienes, 477-478
‘Viewous few thrayeh tubes, 481

Worm
Aefisition uf, 102 .

ost

Worm
relation to absolute temparntnre, 106
‘Wave lunetion of free pactile, 35d
‘Wave vector, 333
‘Weise rnoleenlar field, 430
‘Wiedemman-Kraus law, 516
Wien’s diaplucarneot law
‘Wiener-Kbintchine re'stiona, S88-58f
‘Work, 0-70
done by pressure, 76-78
magnetic, 440-414

Zoruth law of thercaddyasinics, 102, 122
statistical

thermal physics

F. REIF
Professor of Physics
University of California, Berkeley

Euternational Siudene Bestion

MeGHAW-HITE, HOOK COMPANY
New Yack Se bonis Sux Preteen

Sandon Mesion Parana Syteey —Zurnto
ROCARUSHA COMPANY, LTD,

a> Tokye
Pundamentale ot statiatieal and thermal physics
INTERNATIONAL STUDENT EDITION

Exchalve tights by Kogukush Co,, Ltd, for mannfacture
and export from Jepin. ‘Thi book cannot be re-exporied
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1

Copyright ©1905 by MeGraw-Hill, Ine, All rights reserved.
‘This book, or parts Urerenf, may not be reproduced in
any form Wwithoul permission of the publishers, Lilwary
of Congress Catalog Card Number 63-22730,
Preface

-ymix noun ie devoted to a diseuesion of some of the hasie physical concopts and
metbods appropriate far the deazirtion af systemainvalving very many partic
les. 1€ is intended, in particulas, to present the disciplines of thermody-
namics, statiatieal rechanics, and kinetic theory fronr 8 unified aud modem
‘point of view. Accordingly, tbe proeentation departs from Ue historicul
Gevelapment. in which thermadynamice was the first of these disciplines lo
use asian independent abject. The history uf the deus conrerned with best,
Work, and the kinctic Uheory of matter is interesting snd instructive, but i
doa sob reprevent the eleareet ur ost ilfutiinating my of developing these
subjects. Uhave therefore abandoned thc historical approach in favor of ene
that empbasiare the essontia! unity of the subject matter and sccea to develop
physical insight hy stressing the microscopic content of the theory.

Atoms and meleaties are constructs na svencesfully cstablished in modern
science that a nineteenth-century distrust of them seers both obenieie and
inappropriats. For this reason I have deliberately chosen to boee the entire
scuasion: on the prnoive (hat all vmeroscopie syslens eouvint ullinabely of
toms obeying the laws of quantuio mechanics. A combination of these
icroscopir eoneepts with, sowe nlatiticad poalululen thea Beale realy Lo
tome very general eunclsions an a purely marruscapie level of description.
‘These canclusions are valid irrespective of any partielar morte that: aniybt bs
sssumed about Que nature or intorastions of the pacivles in the atuna under

cvideration; they poscess, therefore, the Full generality of the elnasieal laws
of thermodynamics. Indeed, they are more general, since they make clear
that the macroseie parmmctors of 9 aystern are siatistiesl in nature and
eshibit fuctustions which sre ealculshle and cbaervable under sppropriate
conditions, Despity the aivroacopie point of departure, the book thus cun-
tains much generat reasoning on @ purely mueroseopic Level—probably about
as much wi @ text on elassieal ehermodynuadcs—nut the microseonie vonvent
of the macroscopic arguravate reuusis cnar aball ages. Furthermore, face
is willing ta adont specific roierazeopic models soncerning the particles consti

wt
tuyting w uyster, then it is also apparent. haw one ean ealculate macroscopic
‘guantities on the basis of this uicroecopic information. ually, thestatiatieal
eomepts uscd ta discuss equilibriuu silaatious constitute an sppronriate
reputation for their extension to Une discussion of sysleus which are not
in equilibrium.

‘This appronch bse, in ny own teaching experience, proved (o be nu wore
ilifficutt then the customary one which begine with olassieal thermodynamics.
‘The tntter subject, developed along purely macroseapic lines, 4s conceptuslly
for from easy. He reasoning ie afton drlioate and af a type which eeems
unnatural to many Physies stodents, and the significance of the fundamental
concept of entropy is very bard to yrsep, A bave chosen la forego the subbtlo-
‘es uf Gaditional arguments bused on rleverly: chosen eyes and Lo mubstitule
insteud Uhe task of wsimnilating sume clenentary statiaical ideas ‘The fell
ing gsine are thereby urbieved: (a} lustead of speading much time discussing.
‘various atguments baved an heal engines, obe ean introduce the student at an
early stage to statistival cueltods whieh are of great and recurring importence
throughout all of physics. (©) The «ieroscovie sproach yields much betta
physieal insight into muny phenomena end leads to a ready appreciation of
the meaning of entropy. (©) Much of modera physies ig conecrned with the
‘explanation of macroutopic phenomena in terms of microscopic conrents. Tt
seers useful, therefore, to follow a presentation which stresses at al tines the
interrelation between ticrosoapic and macroscopic levels of description. The
treditional teaching of thermodynamics and statistieal mechanics ws divtinct
mmubjects has often Jet students with their knowledge conmportirentslized aud
Ihas also left thom ill-prepared lo accept newer iss, such as spia temperature
fo negative temperature, ax legitimate and natural. (4) Sines 6 unified presen
tation iy more economical, conceptaally az well as in terms of time, it permits
one to discuss sunre material and some more modern. topics.

“Toe havio plan of the book ia (ue following: The fret ehapter is designed La
introduce eame basic probability concepts. Statistical ideas are then spplied
to qyalems of particles in equilibrium so ax to develop the basic notions of
statistical muchenice and to derive therefrom une purely waerascopie
gaucral statements of thernodynguuies. The macroscopic aspects of the
‘theory are then discussed and illustrated at some keveth; the seme is then done
for the micresenpic aepects of Lhe theory. Son.e more complicated equilibrium
situetions, suck an vhuse transforcuations aux quantum: gaaee, are taken up
next. At this point the text auros to discussion of nonequilibrium situations
and treats transport theory in dilute gasce at varying levels of sophisti
Finally, the last chapter desls with some goncral questions involving inreversi-
ble processes and fuctuations. Several sypendices contain mostly various
‘useful mathematical results,

‘The book is intended chiefly as a text for an introductory couree in stu-
{istical and thermal phprics for eullege juniors or seniors, ‘The mimnagraphed

jntes oni which it ia baved have been used in this way for more than two Yeurd
by niysell and veveral of tay colleagues in teaching such a course.at the Uni-
verity of California in Berkeley. No prior imowledge of heat or thermo-
ynaries is presupposed; the
ef o course in iolroductery physics and of an clementary course in. atomic
physies, ‘The latter course is merely supposed to have given cho studeat
Salficient lsekground in evodern pkysies (a) to know that guanturn meets
describes rysieus in terms of quantum states and wave functions, (8) to have
earountered Lhe energy bevels of a siemple harrnonie oscillator aeul to Lave seen
The quantum description of a free particle in & box, and (c) lo have heard of the
Heismberg uncertainty aud Pauli exdusion principles, ‘These wry eaentially
all thi: quautum ideas thal ate needed.

“Pho material iochided here ie more thant can be eovered in» ruin semncalor
undergeviunte course. This was done purpeeely (a) to include # diswassion of
those hasie ileas Ekely to be most helpful in faciliteting the stuent’s baler
acces to more advanced works, (8) to allow stndenls with come curiosity: o
rend beyond the minimum on a given (opie, (6) la give the instructor aorac
‘possibility of wlecting between alteruats Lopies, snd (¢) lo nuticipate current
Jovirions Of the intreduetary physics wourse curriculuin which abould make
upper-divieion stadenls in the neat future much sore sophieticaled and beller
prepared (0 handle advaud rosterial than they are now. fn uelval practice
Thave nuocessfully covered the frat 12 chapters (omitting Chapter 10 and ost
slarred erctions) iu a ono-semester course, Chapter 1 containe @ discussion of
probability concepts more extensive than ie necied for Uke understanding of
Subsequent chapters. Ia addition, the chapters are arranged in such & Way
that it is ready putaible, after Uhe find eight chapters, to omit game chapters
in favor of othors withouL encountering diffualies with proroywisites,

“The book should also he suituble fe use in an intrnductory graduabe
course if ce includes the starred scctions und the last three chapters, which
Sontsin somewhat more advanced material, Indesd, seth students who have
studied euvsiesl thermodynamies but have had po sigaificant exposure to the
dene of statistics! urecharics iv their undergraduate: career, one cannot hope to
cover ing one-soester exaduate course uppreelably wore wihject roatter ther
ix treated here. One uf wy colleague bras thas used he cwterial in our
Berkeley staduate course on statiaical mechanies (@ course wbich is, ss yet,
mostly populated hy studeste with this kind of prepixeation)

‘Throughout the book I bave tried to keep the appoeach well-motivatedand
totrive for simplicity of presentaGon, Tt has not been my sis to-pursue rigor
in the forrm! mathematical vense. I have, bowever, attempted to keep
fhe basic physical ideas in the forefront snd to discs: thera with care, In the
process the book hex become longer than it might. have uthersese, for [ have
not besitated to increace the ratio of surds to formulas, la give illustrative
examples, or to prasont several ways of looking at # question mheuuver I felt
hal iL ould enhance understanding. My azn hex been to sires physical
insight aod icoportant methods af reasoning, wud V adviee most earnestly that
the student strass these aspects of the subject insted of trying to suercwrine
‘various formulls sncaniugless in themselves, To avoid losing the tender in
irrelevant details, Vhave eften refrained from presenting the zest general cane
fof problem an have sought instewa to (reat relatively sincple eases by power
a PREPACE

ful uod ewsily generalizable methods, ‘The hoak is not meant to be encyclo
poulie; i bs ware intended to provide 4 basic skeleton of same fundamental
idose most likely to bo useful to the student in bis future work. Nexlless to
fay, some choices had ta be yaade, Por exacmple, I dhought it inpurtant to
introdues the Holtzman equation, but resisted the templotion of dixcsing
applications of the Onsager relations to various itreversible phenomena such
aa thertaodlectri effects

Tis belpful if « reader can distinguish material of secondary importance
froun that which is essential to the main thread of ue argusient, ‘Two devices
have been used (0 indicate subjert matter of subsidiary importance: (a) Seo
tions marked by s star (ssterisk) contsin material which is enere nilyanced or
more detailed they con be omitted (and prohably should be ounitted iu a Bast
realing) without incurring a handicap in proceeding te wubsequent sections
(6) Many remarks, ecules and elabonutians wee interspersed throughout the
tex aud arm sel off on a gray backgeaund. Conversely, bincle marginal
pointers have been used (o exonhasize iuporiant resulle wnd to facilitate
referaney (o thom,

‘The beek contains cbout 230 probleme, which should bs regarded av aut
‘eeential part of the text. [tis indispensable that the student eolve an appreci-
able fraction of these problenus if be is to gain 2 meaningful understanding of
Ue eubject cuatter and uot merely « caaual hearsay nequaintanee wih it

T sso indebted 0 coverul of my colloagues fur way valuable criticisms
wud suggestions, In particular, I should like to thank Prof. Eyvind H.
‘Wichauann, who read an elder version of the entine mameript with eretioulous
cars, Prof. Owen Chamberlain, Prof. John J. Hopéeld, Dr. Allan N. Kaufman,
and Dr. dohn M. Warlock, Needless to aay, none of these peaple should be
‘blamed for the flaws of the €nal product.

Aclnuvwledgements are also due to Me. Roger F. Knncke for providing
the answers la the jrcblenie, Finally, I am pacticulaity grateful to «ay
ssoretary, Miss Beverly West, without. whoss devotion and uncanny ability
» tranaforar pages of utterly illegible herdwniting into « perfectly typed
techniest manuscript thia book could never have been wtten,

Ttdass been ea thal ua author never 6uistus a book, be merely handons
it” have come Lo appreciate vividly the truth of thiesulesnent sud dread
to see Cie day when, Jonking al the manuscript in print, I
‘oa. eo mmny thing could ave been dave bstéer end explained more clearly.
WL abandon the hook neverfbeles, itis in the modest hope that it may be
useful Lo othere despite its shortcomings.
Contents

Preface att

Introduction to statistica? methods

1 Elementary stitial conccta amd cxamica y
Th gta rondom walk grote sn ene tenon
General dixcusvion of rs eatuce

Protabilty distribution for tgs N17
Goesian grotubiity Qtirinutions — 8

1-7 Probabityy timibusions towoteing penral uariablon 8%
3-8 Comments on continuous probability diciibetions 87
1-9. General calzotion of rncam values for Borandon walk —
“110 Calculation ofthe probability distribution 85
“LAL Probability distribuion for large NST

Stotistical deneription of aystems of particler

SeavivewL, PORULLHIOY OF THE MMLASHCAL HURL
21 Speciation of Be alo elon 48

22 Staizalenentie 8

JOR Base pontiae 63

24 Probhiyclatont 00

2:5 Bahai te deni often 67

2
a
4 Calculation of wun sauce for De ronedos teak protien)
6

rr
ISTRRACTION BETWEEN MACKOSCUTIC SYSTEMS
2-6 Thermatinterostion 68

2-7 Mechanical intora:Non 88

28 General interaction 78

2-9 Quasialatic procemet 7
20 Quani-atese werk dome by Prenmute 78
BAL Brack and “ingract™ differentia 1

B Statistioal thermndynamnion e

IRREVDRSISILITY AND TUE ATEAINIORNT OF EQUIUHRUUSE

Q:1 Byuilibrium conditions und constraints 87
3-2 Prveraible ond irrenreible processet 91

3:3 DistrDtution of energy ehooon system in equiliriem — 2h

3-4 Theanproach fo Barmal emsitibrium — 100

8:8 Temperature 102

St Heal retereobe 108

3-7 Sharpness of the probability distibution 108

GENERAL LNCSHACTION BETWEEN MACROSCOPIC SYSTEMS

BR Dapendines of the density f statea on the external paramelers 118
8-9 Bguiltréam benccon tedcracting epatems 124
B10 Propertice ofthe entropy 117

B11 Thermodynamic laws and basic saticlical relaions 198
BAZ Alatisticalcatculatios uf erneynaonic quantities — 125

4 Macroscopic parumerers and their meusurement pz)

41 Work ond indernal energy 168

42 Hoot 181

4-3 Absolule temperature — 198

4-4 Heat eupueily and aparifie hoot 134

45 Butropy 148

46 Consequence of the absolute definition uf entropy — 145
4-7 Batonsise and intensive parameters 142

imple applications of macrovcupic thermudynamics as?

PADUERTIES OF WRAL GASES
BL Rquation of stave and internal energy 185
2 Specifeheaa 186