PHYS-4420 THERMODYNAMICS & STATISTICAL MECHANICS
SPRING 2006
Class Activity - Class 20 April 4, 2006
Name_____________SOLUTION_____________
Two different solids consist of the same number of atoms, and the speed of sound is the same in
both. However, the spacing between atoms in solid A is twice as great as the spacing between
atoms in solid B. According to the Debye model:
a) For which solid will the Debye temperature be greater? (Circle the correct answer.)
SOLID A
SOLID B
THEY ARE EQUAL
By what factor will it be greater?
1/3
D c  2  N 
D 
 6   . If the distance between atoms in A is twice as big as in B, and
k
k 
 V 
each has the same number of atoms, the volume of the solid A will be larger than the volume
1 N 
N
of solid B by a factor of 2³ = 8. Then,      .
 V  A 8  V B
 D, A
c  2  N  

6   
k 
 V A
1/ 3
c  2 1  N  

6   
k 
8  V B 
1/ 3
1 c  2  N  

6   
2 k 
 V B 
1/ 3

1
 D ,B
2
D,B is larger. D,B = 2D,A
Factor = _____2___________
b) At low temperatures, which solid will have the greater heat capacity? (Circle the correct
answer.)
SOLID A
SOLID B
THEY ARE EQUAL
By what factor will it be greater?
12 Nk 4  T 
In class you saw that the heat capacity at low temperatures equaled, CV 
  .
5

3
12 Nk 4  T 
 
5
 D, A 
3
3
 
C
  D , B   23  8
Then, V , A 
3
CV , B 12 Nk 4  T 
  D, A 


 
5
 D, B 
Factor = _____8___________