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
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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Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0965fd5a-8199-4fde-9833-605a0a8edd4f%2F3044c708-65c3-4b34-8a5f-4a0aced5e479%2Fw9zeoz9_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0965fd5a-8199-4fde-9833-605a0a8edd4f%2F3044c708-65c3-4b34-8a5f-4a0aced5e479%2Fb7dxzvl_processed.jpeg&w=3840&q=75)
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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