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Physics Qualifying Examination
Problems 1–6
Thursday, August 28, 2008
1–5 pm
Problems 712
Friday, August 29, 2008
15 pm
1. Solve each problem.
2. Start each problem solution on a fresh page. You may use multiple pages per
problem.
3. At the top of each solution page put the problem number (1–12) and your
Social Security number, but not your name or any other information.
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View Full Document Problem 1
Consider an ideal monatomic gas consisting of
N
particles each with mass
m
. The gas
is first expanded from volume
V
1
to volume
V
2
at constant pressure so that
P
1
=
P
2
.
The gas is then further expanded isothermally to a final volume
V
3
with pressure
P
3
.
The corresponding temperatures are
T
1
,
T
2
and
T
3
, with
T
2
=
T
3
.
(a)
Using classical thermodynamics compute the total entropy change and express
it in terms of
V
1
,
V
3
,
T
1
,
T
3.
(Recall that the heat capacity of an ideal
monatomic gas at constant pressure is
5
2
P
B
CN
k
=
, where
k
B
is Boltzmann’s
constant).
B
L
(b)
Using the partition function of the ideal classical monatomic gas, calculate the
Helmholtz free energy of the system as a function of particles
N
, the volume
V
, and the temperature
T
.
(c)
Using the Helmholtz free energy obtained in part (b), obtain an expression for
the entropy of the system. Use this expression to compute the total entropy
change of the gas and compare your result to that obtained in part (a).
Problem 2
A particle is in the ground state of a onedimensional infinite square well of width
L
.
The box undergoes a sudden expansion
L
α
→
, with
1
>
.
(a)
What is the probability that the particle will be in the ground state of the
expanded well?
(b)
Find the behavior of the probability obtained in part (a) in the limit
1
±
and
1
→
.
Problem 3
A vessel holds 2
μ
g of tritium. The halflife of tritium is
, and its
mass is
.
3
1/2
1
(
)
12.3 y
tH
=
32
1
(
)
3.02 u
5.01 10
kg
mH
−
==
×
7
(a)
What is the initial decay rate of tritium?
(b)
How much time will elapse before the amount of tritium falls to 1% of its
initial value?
Problem 4
Consider an electron in a hydrogen atom that has the following wave function at a
particular time,
t
= 0:
(0)
( 100
2 210
2 322 ).
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This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.
 Fall '1
 staff
 Physics

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