3.8 The Einstein Model
3.8
45
The Einstein Model
For ω = ω0 we find for the inner energy
Z
U = 3 dωD(ω)
~ω
exp
~ω
kT
−1
and:
=
~ω0
exp
~ω0
kT
−1
3N
.
(3.43)
~ω
dU
3N ~ω e kT ~ω
CV =
=
2
~ω
dT
kT
e kT − 1
.
(3.44)
For high temperatures we again get:
CV = 3N k
.
(3.45)