1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation;

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Hi, Can you please solve the question and make explanation step by step? Both Option A and B. 

And If you are going to use handwriting please make sure that its readable and clear. 

1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of
identical atoms;
(a) in the Debye approximation;
(b) using the exact density of states (Eg. below).
With the same constants Kand M, which expression gives the greater heat capacity and why?
Show that at low temperatures both expressions give the same heat capacity, proportional to
T.
L (M\/2
2(K/M)2
(4K/M – w²)/²
N (M\1/2
g(») :
sec (įka):
%3D
naK
1/2
2N (4K
M
Transcribed Image Text:1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation; (b) using the exact density of states (Eg. below). With the same constants Kand M, which expression gives the greater heat capacity and why? Show that at low temperatures both expressions give the same heat capacity, proportional to T. L (M\/2 2(K/M)2 (4K/M – w²)/² N (M\1/2 g(») : sec (įka): %3D naK 1/2 2N (4K M
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