Statistical Physics, Second Revised and Enlarged Edition
68 Maxwell–Boltzmanngases 6 .3 The connection to thermodynamics This is an important section. We can now calculate the propertie ...
The connection to thermodynamics 69 asfollows: S/kkkB=ln definition =lnt∗ usual approximation =ln (∏ gnii/ni! ) usingtttMB,( 5. ...
70 Maxwell–Boltzmanngases 6 .3.3 Free energy and pressure Now let us turn to the free energyF,and Method 3 of section 2.^5 , the ...
Summary 71 2.Extensivity.Next,afew wordsabout that extraN!in ( 6 .1 6 b). For our treatments of gases or of localized particles ...
72 Maxwell–Boltzmanngases However,itisevidentfrom expressionsforSandCthat classical ideasmust fail at low enough temperatures. ...
7 Diatomic gases This chapter is a slight diversion, and could well be omitted at a first reading. However, the studyofdiatomic ...
74 Diatomicgases in a state of highrotationalenergyofadiatomicmoleculethebondwillstretchalittle from the inertia of the atoms, a ...
Heat capacity ofa diatomic gas 75 eachinternaldegree offreedomis particularlysimple. Itgives merely a−NkkkBTlnZ additiontoF;and ...
76 Diatomicgases 7 .2.3 Vibrational contribution Similarly, the contribution from vibrational motion has been calculated earlier ...
Heat capacity ofa diatomic gas 77 states tolevell,correspondingintuitivelytodifferent possibledirectionsfor the angular momentum ...
78 Diatomicgases 7.3 The heat capacityof hydrogen As an example of the above results, we consider in greater detail the heat cap ...
The heat capacity ofhydrogen 79 fivedegrees offreedom a totalof^52 kkkBTtoU,andthereforeCV=^52 NkkkB,inagreement with(7.10). At ...
80 Diatomicgases However, the truthis moreinterestingthan that, andthe resultisdifferentfor H 2 and forD 2 .Let us concentrate u ...
Summary 81 Hence the ratioofortho- to para-hydrogen molecules when thegas equilibrates at high temperature is 3:1. When the hydr ...
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8 Fermi–Dirac gases We return now to the main stream of the book, and to the basic statistical properties of idealgases as intro ...
84 Fermi–Diracgases 8.1 Properties ofanidealFermi–Dirac gas As we have seen, FD statistics is needed, (i) when we are dealing wi ...
Properties ofan ideal Fermi–Dirac gas 85 1 2 3 1 0 ff() Fig. 8. 1 The Fermi–Dirac distribution function at three different ...
86 Fermi–Diracgases Attheabsolute zero,the Fermifunctionf(ε)takes thesimpleform notedearlier, that f=1forε<μ( 0 )butf=0 forε& ...
Properties ofan ideal Fermi–Dirac gas 87 Three remarksabout the Fermienergy follow. We can now quantify the need for FD statist ...
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