Statistical Physics, Second Revised and Enlarged Edition
8 Basic ideas Step I. The mechanicalproblemistobesolvedtogive the possible states ofone particle. We take the solution to be sta ...
Amodel example 9 Step IV. The averagevalue ofeverydistribution number can nowbeobtainedbyan equal averaging over every microstat ...
10 Basic ideas another wayofcalculatingit)is to appreciate that microstates withUUAB= 3 ε,2ε,ε, 0 are now accessible in addition ...
Summary 11 betweenSandissuggested,andmoreover a monotonically increasingone,in agreement with (1. 5 ). For a composite assembl ...
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2 Distinguishable particles The next stepistoapplythe statisticalmethodoutlinedinChapter 1 to realistic thermodynamic systems. T ...
14 Distinguishable particles 2.1 TheThermalEquilibrium Distribution We follow the method outlined in section 1. 5. For the macro ...
The thermal equilibrium distribution 15 (equation (2.3)) as statisticalweights. This taskcanbe performed,butfortunatelywe are sa ...
16 Distinguishable particles by differentiatinglntandsettingthe result equalto zero. Usingthefact thatNis constant, and noting t ...
What areαandβ? 17 aredefinedwiththe opposite signin some other works. Lookingat afamiliar result (e.g. the Boltzmann distributio ...
18 Distinguishable particles or U/N= ∑ j εεjexp(βεεj) /∑ j exp(βεεj) (2.15) The appropriate value ofβis then that one which, whe ...
Astatistical definition oftemperature 19 and ∑ j nnjεεj+ ∑ k n′kε′k=U (2.18) whereUis the total energy(i.e.UUUP+UUUQ)of the two ...
20 Distinguishable particles 2 .3.2 Temperature and entropy We now come to the form of this relationβandT. The simplest approach ...
The Boltzmann distribution and the partitionfunction 21 Theargumentin outlineisasfollows. Startbyconsideringhowachangeinln can ...
22 Distinguishable particles withthepartitionfunctionZdefined as Z= ∑ j exp(−εεj/kkkBT) (2.24) (From now on we shall for simplic ...
Summary 23 fromU= ∑ nnjεεj,but this sum can be neatlyperformed bylookingback at (2.15), which can be re-expressed as (U/N)=( 1 / ...
24 Distinguishable particles 6 .βis a ‘potentialfor energyU’andthus relates to temperature. Note theincon- sistency in the sign ...
3 Two examples We now applythe generalresults ofthe previous chapter to two specific examples, chosenbecause theyare easilysolub ...
26 Two examples Thethermalequilibriumdistribution numbers (or occupation numbers)n 0 andn 1 may now be evaluated from (2.23) to ...
Aspin-^12 solid 27 frozen outinto thelowest energy(ground) state, andno particleis excitedinto the higher state. On theotherhan ...
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