This preview shows page 1. Sign up to view the full content.
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
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '12
 SHUBEITA
 Physics, Energy, Mass, Work

Click to edit the document details