1
PHYS 414: Homework 3
This homework due Friday Feb 10
1.
(7 points)
A particle of mass
m
moves in an anharmonic oscillator potential
V
(
x
) =
Ax
8
in one dimension. Estimate what the allowed quantummechanical energy levels of this
system might be by considering the area of phase space trajectories.
2. System A has entropy that varies with energy
E
A
as
S
A
=
k
B
(
E
A
/E
1
)
α
. System B has
entropy that varies with energy
E
B
as
S
B
=
k
B
(
E
B
/E
2
)
γ
. Here
k
B
is the Boltzmann
constant and
E
1
and
E
2
and
α
and
γ
are constants, and
E
1
,
E
2
,
α
,
γ
, and
T
are all
positive.
(a) (2 points) Now the two systems are placed in thermal contact and allowed to
reach equilibrium. Express the energy
E
A
of system A as a function of the energy
E
B
of system B.
(b) (2 points) What is the largest positive value that the constant
α
can have in a
real physical system?
(c) (2 points) What is the smallest value physically possible for the constant
α
?
(d) (2 points) The Helmholtz free energy
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 Spring '12
 SHUBEITA
 Physics, Thermodynamics, Energy, Mass, Work, Statistical Mechanics, Entropy, heat capacity CV

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