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Lecture12

# Xi1 2 2 i 1 2 m n solufon of mofon can be decomposed

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Unformatted text preview: Fons RotaFonal 70 K = 6 meV = 200 um acFvaFon So at low temperatures, collisions do not exchange energy through rotaFonal or vibraFonal excitaFon. These are quanBzed. 10 How about solids? m m m x1 x1 x3 Can imagine a solid much like being masses joined by springs. (actually this a bejer approximaFon than it appears) " pi2 1 % E = (\$ + k ( xi ! xi+1 )2 ' 2 i =1 # 2 m & N SoluFon of moFon can be decomposed into N normal modes (i.e. N independent oscillators) Actually are SOME collisions or crystal would never reach equilibrium. Total energy should be: U CV = 3Nk "2 % "2 % = N ! \$ kT ' in 1D and 3 ! N ! \$ kT ' = 3NkT in 3D #2 & #2 & Dulong ­PeBt Law 11 CV of real solids CV [J/mole K] 2...
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