www.TheSolutionManual.com www.TheSolutionManual.com Mathematical Symbols = == ~ is equal to — oc is of the order of is (by definition) identically equal to is approximately equal to is proportional to is not equal to is not close to > > is greater than is much greater than is very very much greater than > is greater than or equal to > is greater than or approximately equal to < is smaller than < 9 X i to alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu nu xi omicron Pi rho sigma tau upsilon phi chi psi omega www.TheSolutionManual.com The book covers The movie strips on the covers illustrate the fundam ental ideas o f irre versibility and fluctuations by showing the motion o f 40 particles inside a two-dimensional box The m ovie strips were produced by an electronic computer programmed to calculate particle trajectories (For details, see pp 7, 24, and 25 inside the book.) The fron t cover illustrates the irre versible approach to equilibrium starting from the highly nonrandom initial situation where all the particles are located in the left h a lf o f the box The back cover (read in the upward direction from bottom to top) illustrates the irreversible approach to equilibrium if, starting from the initial situation a t the top o f the fron t cover, all the particle velocities are reversed (or equivalently, i f the direction o f time is im agined to be re versed) The back-cover and front-cover movie strips together, read con secutively in the downward direction, illustrate a very large fluctuation occurring extremely rarely in equilibrium www.TheSolutionManual.com statistical physics www.TheSolutionManual.com _ m cgraw -hill book com pany New Y o r k St Louis S an F n c is c o T o ro n to London Sydney www.TheSolutionManual.com sta tistica l p h y s ic s b e r k e l e y p h y s i c s c o u r s e —v o l u m e T he preparation o f this course was supported by a grant from the National Science Foundation to Educational Services Incorporated F Reif Professor of Physics University o f C alifornia, B erkeley www.TheSolutionManual.com STATISTICAL PHYSICS C opyright © 1964, 1965, 1967 by Education D evelopm en t Center, Inc (successor b y merger to E du cation al Services Incorporated) All R ights R eserved Printed in th e U nited States o f A m erica This book, or parts th ereof, may n ot b e reprodu ced in an y fo r m w ithou t the w ritten perm ission o f E d u cation D evelopm en t Center, Inc., Newton, M assachusetts Portions o f s t a t i s t i c a l p h y s i c s are also subject to the copyright provisions o f F U N D A M EN T A L S O F S T A T IS T IC A L AND T H E R M A L P H Y S IC S Copyright © 1965 by McGraw-Hill, Inc Rights Reserved Library o f Congress C atalog Card Num ber 64-66016 ISBN - 0 - HDBP 75 All www.TheSolutionManual.com Preface to the Berkeley Physics Course This is a two-year elementary college physics course for students majoring in science and engineering The intention of the writers has been to pre sent elementary physics as far as possible in the way in which it is used by physicists working on the forefront of their field We have sought to make a course which would vigorously emphasize the foundations of physics Our specific objectives were to introduce coherently into an ele mentary curriculum the ideas of special relativity, of quantum physics, and of statistical physics This course is intended for any student who has had a physics course in high school A mathematics course including the calculus should be taken at the same time as this course There are several new college physics courses under development in the United States at this time The idea of making a new course has come to many physicists, affected by the needs both of the advancement of science and engineering and of the increasing emphasis on science in elementary schools and in high schools Our own course was conceived in a conver sation between Philip Morrison of Cornell University and C Kittel late in 1961 We were encouraged by John Mays and his colleagues of the National Science Foundation and by Walter C Michels, then the Chair man of the Commission on College Physics An informal committee was formed to guide the course through the initial stages The committee con sisted originally of Luis Alvarez, William B Fretter, Charles Kittel, Walter D Knight, Philip Morrison, Edward M Purcell, Malvin A Ruderman, and Jerrold R Zacharias The committee met first in May 1962, in Berkeley; at that time it drew up a provisional outline of an entirely new physics course Because of heavy obligations of several of the original members, the committee was partially reconstituted in January 1964, and now con sists of the undersigned Contributions of others are acknowledged in the prefaces to the individual volumes The provisional outline and its associated spirit were a powerful influence on the course material finally produced The outline covered in detail the topics and attitudes which we believed should and could be taught to beginning college students of science and engineering It was never our intention to develop a course limited to honors students or to students with advanced standing We have sought to present the principles of physics from fresh and unified viewpoints, and parts of the course may therefore seem almost as new to the instructor as to the students www.TheSolutionManual.com The five volumes of the course as planned will include: I II III IV V Mechanics (Kittel, Knight, Ruderman) Electricity and Magnetism (Purcell) Waves (Crawford) Quantum Physics (Wichmann) Statistical Physics (Reif) The authors of each volume have been free to choose that style and method of presentation which seemed to them appropriate to their subject The initial course activity led Alan M Portis to devise a new elementary physics laboratory, now known as the Berkeley Physics Laboratory Because the course emphasizes the principles of physics, some teachers may feel that it does not deal sufficiently with experimental physics The laboratory is rich in important experiments, and is designed to balance the course The financial support of the course development was provided by the National Science Foundation, with considerable indirect support by the University of California The funds were administered by Educational Services Incorporated, a nonprofit organization established to administer curriculum improvement programs We are particularly indebted to Gilbert Oakley, James Aldrich, and William Jones, all of ESI, for their sympathetic and vigorous support ESI established in Berkeley an office under the very competent direction of Mrs Mary R Maloney to assist the development of the course and the laboratory The University of Califor nia has no official connection with our program, but it has aided us in important ways For this help we thank in particular two successive Chairman of the Department of Physics, August C Helmholz and Burton J Moyer; the faculty and nonacademic staff of the Department; Donald Coney, and many others in the University Abraham Olshen gave much help with the early organizational problems Your corrections and suggestions will always be welcome January, 1965 Berkeley, California Eugene D Commins Frank S Crawford, Jr Walter D Knight Philip Morrison Alan M Portis Edward M Purcell Frederick Reif Malvin A Ruderman Eyvind H Wichmann Charles Kittel, Chairman www.TheSolutionManual.com Chapter 3.1 (a) P( —3juo) (c) = P(lM>) = f , P(M) = otherwise; (b) same as in (a) and (fo) i 3.3 (a) N\[n\(N- 3.4 (n'/n)2 n )!]" 1; (c) n'/n (b) (Er - E 0)/2noB; (d) (n'/n)**; /3 = In (n/n')/2fi0B 3.6 (a) (TT2h 2/2m)(nx2 / L x2 )(2/Lx); (b) F = f(E / L ) 3.7 (a) 1.9 X 1029; (b) 4.5 X 1018 3.9 (a) N\[n\(N - n)\]-i(8E/2iioB) 3.5 (a) AM[n!(]V — n)!]_1; (e) www.TheSolutionManual.com Chapter 4.1 (a) No; 4.2 0.025 electron volt (b ) no 4.3 (a) percent; 4.4 1.1 X -2 (b ) X 1043 4.5 1.5 X IO -5 4.6 Power oc T~1 4.7 (b) N3/ 2/N 1/2 ~ E Ntn for T —> 0 , E —> iN (ei + c2); change when kT ~ (e2 — «i) (b) N[( + e2e_^(,2_tl)] [l + IVa ( W a/kT) ^Nea (eat/2kT ) (a) Separation betw een levels increases; (b) increases; (c) positive; (d) increases; (e) increases (a) Separation betw een levels increases; (b ) decreases; (c) negative; (id) increases; (e) increases (Nt + N2)kT/V (a) (b ) —[ioB (/8/i,0B) (a) e- 0*“/2[ l — (b) — I ) -1 ]; (d) (e ) kT (a) 2A//3ft2; (fc) kT 4.8 4.9 4.10 4.12 4.13 4.14 4.21 4.22 4.23 (a) N3 / 2/N 1/2 ~ 0.5; (a) F o r T —>0, 4.25 (a) e“ ^ne; 4.26 (a) C(M/27Tj8)3/2(V/ft3); (fo) AM[n!(]V — n)!]_1 in each case (fo) C[(M/27rJ8)3/2(V/*3)][(m/277y8)3/2(V/ft3)]e-/!'‘; (c) (rnkT/Zrtrh2)3 '2 Ve~u/kT; (e) undissociated; (d) (mkT/2irh 2)3/*(V/N) / 2e - u/2kT; (/ ) dissociated 4.27 (a) (n/N )2 = (m/2,rr)3 / 2f r (kT )5/2 p~ie~u/kT; 4.28 (a) |McT 4.29 (a) —NhqB tunh (noB/kT); (b) 0.4 percent (b) Nfio (poB/kT) www.TheSolutionManual.com Chapter (b) x 10“ °K (b ) x 10-8 °K 5.1 (a) °K ; 5.2 (a) 0.62 gauss; rR T ki (V 2/ V i) 5.4 3.6 X 1010 ergs 5 a —» c —>b\ a —» d —» b: a —> b: W — x 10s ergs, Q = —2.9 x 1010 ergs; W = 2.1 X 1011 ergs, Q = 1.8 X 1011 ergs; W = 1.4 X 1011 ergs, Q = 1.1 x 1011 ergs (b) T = |T0 + (2MgV0/5vRA), V ~ f Vo + (3vRAT0/5Mg) 5.8 (a) Mg/A; 5.9 (b) 14.8 joules/cm (b) 1.35 X 103 joules 5.10 (a) 9.92 X 103 joules; 5.11 (b ) E = N [t ! + t 2e - ^ - ^ /kT][l + g-(«2-'i)/fcr]-i, C = (N /kT )(t2 - e )2e - ^ - ^ /kT[l + e-(«2-«i)/*r]-2 (c) —AfyioB (noB/kT); (d) Nk(noB/kT)2[cosh B/kT)]~2 5.13 (a) 2Nt(ee/kT + ) " 1; (b) (2 Ne2/ k T 2)e‘/kT(e; 6.9 Greater (c) kT ^ > e n1/3 (fo) g-(i/ W) v02(kT/m c2) (d) 0; (b ) k T /a ; (c) (ctkT)1 '2 / g (c) ffcT; (d) 1R 6.18 (a) Mg/a; 6.19 (a) £fcT; 6.20 B (a) E = 3Nhu[i + (e*“/fcr - I)-1]; (fe) 3R (ha/kT ) 2eK“/i‘T(e*“/l‘T - I ) " 2; (e) (kT/m)( + b 2) (fo) \kT- (/) R (@ /T ) 2e~s/T ; (h) hu /k www.TheSolutionManual.com Chapter 7.3 (a) 6.21 atmospheres; (b) 832°K (a) (cv/R) ( T ^ ) ™ ; (c) _ r 2i/2)2 (a) vRT In (Vc/V*); (fo) j»RT In (Va/Vd); (c) Va/Vh = Vd/Vc; (d) q'/q = T '/T 7.18 - (V i/V 2)v- i www.TheSolutionManual.com Chapter 8.1 (a) 2; 8.2 (a) t ; (b) 2; (b) r; (c) unaffected (c) unaffected 8.3 (a) %tc; (b) %tc; (c) atc, %atc = cit; (d) iatc2, \atc = ar 8.4 Decreases, 8.5 (a) 2Trr]R3L u /S ; unchanged 1.4 x 10- (b) Approximately dyne cm 8.7 gm cm -1 sec-1 (a) a ac V-4/(s-i); (fo) r, oc TL2)- 8.13 (c) r 8.14 ^ 8.15 AT = (PR/2nbK ) In (b/a) 8.16 (a) (7r/8)(pa4/r)L)(pi - p2); = pc (c) (W ^ iK i^ i/ M ; 10-8 cm dz (b) (ir/16)(im4/t)RTL)(p 12 - p2 www.TheSolutionManual.com Supplementary Problems P l 0.013 P.2 (2|Uo)- (27r]Vp