Lecture 30 Lecture 30 ——The Planck Distribution The Planck Distribution Chapter 8, Friday March 28Chapter 8, Friday March 28thth• The Free energy of a photon gas• Radiation pressure• Quiz• Einstein and Debye models of vibrations in solidsReading: Reading: All of chapter 8 (pages 160 All of chapter 8 (pages 160 --185)185)Homework 8 due Mon. Mar. 31stHomework 8 due Mon. Mar. 31stAssigned problems, Assigned problems, Ch. 8Ch. 8: 2, 6, 8, 10, 12: 2, 6, 8, 10, 12Einstein and Debye models of vibrations in solidsEinstein and Debye models of vibrations in solidsAtom3N modes of vibration; N = number of atomsEinstein model of vibrations in solidsEinstein model of vibrations in solids••Assumes 3Assumes 3NNindependent modes of vibrationindependent modes of vibration••All modes have same frequency, All modes have same frequency, ωωEEωEis the only freeparameter in the modelDebye model of vibrations in solidsDebye model of vibrations in solidsWaves (phonons) travel at the speed of soundTreats lattice vibrations as elastic wavesTreats lattice vibrations as elastic waves••Distribution of frequencies (unlike Einstein), i.e. dispersion.Distribution of frequencies (unlike Einstein), i.e. dispersion.••There is a cutThere is a cut--off frequency off frequency ωωDD..Debye model of vibrations in solidsDebye model of vibrations in solids()1/326/DsNVωπ=s is sound speed;the only freeparameter in
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