## Fundamentals of statistical and thermal physics |

### From inside the book

Results 1-3 of 35

Page 224

Because the

significant domain of integration expand its logarithm in a power series about 0' =

0. Thus In [e»*Z(0)] = 0E + In Z(0) = (0 + i0')E + In Z{0) + Bid?) + iB2(i/3')J + □ • ...

Because the

**integrand**in (6-8 - 11) is only appreciable for 0' « 0, one can in thesignificant domain of integration expand its logarithm in a power series about 0' =

0. Thus In [e»*Z(0)] = 0E + In Z(0) = (0 + i0')E + In Z{0) + Bid?) + iB2(i/3')J + □ • ...

Page 395

-^/-^(^TTp1"'^ where x » 0(« - n) (9-17 -7) Since the

maximum for c = /», (i-e., for x = 0) and since /3m >?> 1, the lower limit can be

replaced by — w with negligible error. Thus one can write /„" (« - m)" d« = - (fcr)»/

m (9 -17 ...

-^/-^(^TTp1"'^ where x » 0(« - n) (9-17 -7) Since the

**integrand**has a sharpmaximum for c = /», (i-e., for x = 0) and since /3m >?> 1, the lower limit can be

replaced by — w with negligible error. Thus one can write /„" (« - m)" d« = - (fcr)»/

m (9 -17 ...

Page 613

/_"„ n" e~" e~H(t'n) d£ = n" e~n J"^ er-*«''"> d£ (A- 6 -9) In the last integral we have

replaced the lower limit — n by — °°, since for values £ < — n the

already negligibly small. By (A-4-6) this last integral equals \/ 2rn. Thus (A □ 6 ...

/_"„ n" e~" e~H(t'n) d£ = n" e~n J"^ er-*«''"> d£ (A- 6 -9) In the last integral we have

replaced the lower limit — n by — °°, since for values £ < — n the

**integrand**isalready negligibly small. By (A-4-6) this last integral equals \/ 2rn. Thus (A □ 6 ...

### What people are saying - Write a review

#### LibraryThing Review

User Review - JJMAlmeida - LibraryThingNever mind that this book was published in the mid '60s (before I was even born); if you must choose one book to learn from, choose this one. It is so concise, so well thought out that I have yet to ... Read full review

### Contents

Introduction to statistical methods | 1 |

GENERAL DISCUSSION OF THE RANDOM WALK | 24 |

Statistical description of systems of particles | 47 |

Copyright | |

26 other sections not shown

### Other editions - View all

### Common terms and phrases

absolute temperature approximation assume atoms becomes Boltzmann equation calculate canonical distribution chemical potential classical coefficient collision condition Consider constant container corresponding curve denote density depends derivatives discussion electrons ensemble entropy equal equation equilibrium situation equipartition theorem evaluated example expression external parameters fluctuations frequency gases given heat capacity heat reservoir Hence ideal gas independent infinitesimal integral integrand interaction internal energy isolated system kinetic liquid macrostate magnetic field mass maximum mean energy mean number mean pressure mean value measured metal molar mole molecular momentum number of molecules number of particles obtains partition function perature phase space photons physical piston position probability problem quantity quantum quantum mechanics quasi-static radiation range relation result satisfy simply solid specific heat spin statistical mechanics Suppose theorem thermal contact thermally insulated Thermodynamics tion total energy total number unit volume variables velocity