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1、Statistical Physics Dr. A. J. Macfarlane1 Lent 1998 1L ATEXed by Paul Metcalfe comments to soc-archim-noteslists.cam.ac.uk. Revision: 1.10 Date: 1998-06-03 20:13:39+01 The following people have maintained these notes. datePaul Metcalfe Contents Introductionv 1Quantum Statistical Mechanics1 1.1Introd
2、uction to Quantum Statistical Mechanics. . . . . . . . . . . .1 1.2Canonical ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . .2 1.3Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 1.4Towards thermodynamic variables . . . . . . . . . . . . . . . . . . .5 1.5Towa
3、rds applications . . . . . . . . . . . . . . . . . . . . . . . . . .7 1.5.1N particle partition function . . . . . . . . . . . . . . . . . .7 1.5.2Extensive and intensive variables. . . . . . . . . . . . . . .8 1.5.3Density of states. . . . . . . . . . . . . . . . . . . . . . . .8 1.5.4Gas of spinle
4、ss particles . . . . . . . . . . . . . . . . . . . .9 1.5.5Entropy and the Gibbs paradox . . . . . . . . . . . . . . . . .9 1.6Harmonic oscillator model . . . . . . . . . . . . . . . . . . . . . . .10 2Thermodynamics11 2.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 2
5、.2Applications of dE = TdS PdV. . . . . . . . . . . . . . . . . .12 2.2.1Integrability conditions . . . . . . . . . . . . . . . . . . . . .12 2.2.2 Specifi c heats . . . . . . . . . . . . . . . . . . . . . . . . . .13 2.2.3Adiabatic changes. . . . . . . . . . . . . . . . . . . . . . .14 2.2.4Entropy
6、 of n moles of ideal gas. . . . . . . . . . . . . . . .14 2.2.5van der Waals equation. . . . . . . . . . . . . . . . . . . .15 2.2.6The Joule effect . . . . . . . . . . . . . . . . . . . . . . . . .15 2.3Some thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . .16 2.3.1The second law . .
7、. . . . . . . . . . . . . . . . . . . . . . .16 2.4 Heat fl ow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 3Grand ensemble methods19 3.1The formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 3.2Systems of non-interacting identical particles. . . . . . . . .
8、. . . .21 3.2.1A little quantum mechanics. . . . . . . . . . . . . . . . . .21 3.2.2The partition functions . . . . . . . . . . . . . . . . . . . . .22 3.2.3Classical limit. . . . . . . . . . . . . . . . . . . . . . . . .24 3.3Black body radiation. . . . . . . . . . . . . . . . . . . . . . . . . .25
9、 3.4Degenerate Fermi gas . . . . . . . . . . . . . . . . . . . . . . . . . .26 3.4.1Heat capacity at low temperature . . . . . . . . . . . . . . . .27 3.5Bose-Einstein condensation . . . . . . . . . . . . . . . . . . . . . . .28 iii ivCONTENTS 3.6White dwarf stars . . . . . . . . . . . . . . . . . .
10、 . . . . . . . . . .29 4Classical statistical mechanics31 4.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 4.2Diatomic gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . .32 4.3Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32 4.4 Spec
11、ifi c heats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 4.5Weak interparticle forces . . . . . . . . . . . . . . . . . . . . . . . .34 4.6The Maxwell distribution . . . . . . . . . . . . . . . . . . . . . . . .35 Approximations37 Introduction These notes are based on the course “St
12、atistical Physics” given by Dr. A. J. Macfarlane in Cambridge in the Lent Term 1998. These typeset notes are totally unconnected with Dr. Macfarlane. The recommended books for this course are discussed in the bibliography. Other sets of notes are available for different courses. At the time of typin
13、g these courses were: ProbabilityDiscrete Mathematics AnalysisFurther Analysis MethodsQuantum Mechanics Fluid Dynamics 1Quadratic Mathematics GeometryDynamics of D.E.s Foundations of QMElectrodynamics Methods of Math. PhysFluid Dynamics 2 Waves (etc.)Statistical Physics General RelativityDynamical S
14、ystems They may be downloaded from http:/www.cam.ac.uk/CambUniv/Societies/archim/notes.htm or you can email soc-archim-noteslists.cam.ac.uk to get a copy of the sets you require. v Copyright (c) The Archimedeans, Cambridge University. All rights reserved. Redistribution and use of these notes in ele
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