c) At low temperatures pUst kB the heat caposity. You may use an integral table values for %3D 15 d) Show that at high temperatures C = 8N kB recovering the classicall limit

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Only want the solution od c and d parts.
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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