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673.8 958.8
187.5
4.40
23.65 · 10
13
0.571
0.141
M
d
2
U
n
dt
2
= −α
2U
n
− U
n−1
− U
n+1
ω =
ω
max
sin
ka
2
ϑ = aω
max
cos(ka/2)/2
V ω
2
dω
2π
2
1
ϑ
3
l
+
2
ϑ
3
t
θ =
~
k
B
"
18π
2
N
V
1/ϑ
3
l
+ 2/ϑ
3
t
#
1/3
9N
~
k
B
θ
3
ω
2
dω
exp
~ω/k
B
T
− 1
ε
p
= 1.6k
B
T ω
p
= 0.4k
B
θ
T = 0.625θ
n ∼ T n ∼ T
3
Sωd ω
ϑ
2
π
2~ϑ(πN/S)
1/2
k
B
270
U
0
+ 3Nk
B
T U
0
+
3π
4
5
Nk
B
T
T
θ
!
3
U
0
=
9
8
Nk
B
θ
3. Äèíàìèêà êðèñòàëëè÷åñêîé ðåøåòêè.
Òåïëîåìêîñòü êðèñòàëëîâ
1. 673.8 Äæ/K, 958.8 Äæ/K.
2. 187.5 Äæ/K.
3. 4.40 êÄæ.
4. 23.65 · 1013 ö.
5. 0.571 Äæ.
6. 0.141 Äæ/K.
d2 U n
7. M = −α 2Un − Un−1 − Un+1 .
dt2
ka
8. ω = ωmax sin .
2
9. ϑ = aωmax cos(ka/2)/2.
" #1/3
V ω 2dω 1 18π 2 N
2 ~
11. + 3 ,θ= .
2π 2 ϑ3l
ϑt kB 3 3
V 1/ϑl + 2/ϑt
3
ω 2dω
~
12. 9N , εp = 1.6kB T , ωp = 0.4kB θ ,
kB θ
exp ~ω/kB T − 1
T = 0.625θ.
13. 1837 ì/ñ.
14. 0.032 ýÂ.
15. n ∼ T , n ∼ T 3 .
Sωdω 2~ϑ(πN/S)1/2
16. , .
ϑ2 π kB
17. 270K.
18. 4820 ì/ñ.
!3
3π 4 T 9
19. U0 + 3N kB T , U0 + N kB T , U 0 = N kB θ .
5 θ 8
29
