Slide 1Slide 2Slide 3Slide 4Slide 5Lecture 30 — The Planck Distribution Lecture 30 — 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 - 185)All of chapter 8 (pages 160 - 185)Homework 8 due Mon. Mar. 31stHomework 8 due Mon. Mar. 31stAssigned problems, Assigned problems, Ch. 8Ch. 8: 2, 6, 8, 10, : 2, 6, 8, 10, 1212Einstein and Debye models of vibrations in Einstein and Debye models of vibrations in solidssolidsAtom3N modes of vibration; N = number of atomsEinstein model of vibrations in solidsEinstein model of vibrations in solids•Assumes 3Assumes 3NN independent modes of vibration independent modes of vibration•All modes have same frequency, All modes have same frequency, EEE is 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 cut-off frequency There is a cut-off frequency DD..Debye model of vibrations in solidsDebye model of vibrations in solids( )1/ 326 /Ds N Vw p=s is sound speed;the only freeparameter in
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