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a) Storting from the general form of of States dosity g(k) dk= 272 Show that g(w) dw = 3 x Vw? dw for phonons 272 Q3 under the assumption that the phonons are acoustic, meaining U = W doesn't depend on wor

a) Storting from the general form of of States dosity g(k) dk= 272 Show that g(w) dw = 3 x Vw? dw for phonons 272 Q3 under the assumption that the phonons are acoustic, meaining U = W doesn't depend on wor

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a) Storting of desity of Steltes from the general formula 272 Show that g(w) dw = 3 x Vw?dw for phonons 272 83 under the assumption that the phonons are ac custic, meaning U = 3. doesn't depend on w or b)n a solid of N atoms, there are 3N vibrati- onal modes (phonons) with the highelt frequ- eicy wp Wp Using 9(w) dw =3N find wD, and find characteistie temperature Kwo kB
Transcribed Image Text:a) Storting of desity of Steltes from the general formula 272 Show that g(w) dw = 3 x Vw?dw for phonons 272 83 under the assumption that the phonons are ac custic, meaning U = 3. doesn't depend on w or b)n a solid of N atoms, there are 3N vibrati- onal modes (phonons) with the highelt frequ- eicy wp Wp Using 9(w) dw =3N find wD, and find characteistie temperature Kwo kB
c) At low temperatures T<< Kwe frnd kB the heat capasity. You may use an integral table values for 15 d) Show tha t at high temperatures C = 3Nkg recovering the classicall limit
Transcribed Image Text:c) At low temperatures T<< Kwe frnd kB the heat capasity. You may use an integral table values for 15 d) Show tha t at high temperatures C = 3Nkg recovering the classicall limit
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