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Chapter 7
CT-1
A system S is in thermal contact with a heat bath at temperature T.
The system can exchange energy only with the bath. Consider two
quantum states of the system:
state 1 with low energy E1
state 2 with high energy E2
P(state 1)
The ratio of the probabilities
is ...
P(state 2)
A) always greater than 1
B) always less than 1
C) greater, less than, or equal to one, depending on the
temperature.
Bath
T
system
CT-2
If the temperature T is increased, the probability P(i) that the
system is in a particular quantum state i (say, i = 6) will
A) decrease
B) increase
C) remain constant
D) not enough info to answer question
CT-3
An ideal gas is in a container divided into two halves. Initially, the
two samples of gas are identical. Some more particles are added to
the sample on the left, keeping the temperature constant. The
chemical potential on the left is
A) increases
B)decreases
C) stays the same as
the chemical potential on the right
CT-4
An atom (say an H-atom) is sitting in a gas of electrons with
temperature T and chemical potential The atom can either be in
its ground state (occupied) or be ionized (empty). [We pretend that
excited states can be ignored.]
If the chemical potential is kept constant, and the temperature is
raised, the probability that the atom is found in its ionized state
A) increases
B) decreases
c) remains constant
CT-5An atom (say an H-atom) is sitting in a gas of electrons with
temperature T and chemical potential The atom can either be in
its ground state or be ionized (occupied or empty). [We pretend
that excited states can be ignored.]
If the chemical potential is lowered (made more negative), while
the temperature is maintained at a very low value (kT<<I), the
probability that the atom is found in its ionized state
A) increases
B) decreases
c) remains constant
CT-6 For a single particle in a box, the partition function is
Z1 =
å
- e (n2x + n2y + n2z ) / kT
e
n x ,n y ,n z
This is the same as
A)
B)
æ
ö
æ
ö
æ
ö
2
2
2
e
(n
)
/
kT
ç
÷
÷
e
(n
)
/
kT
e
(n
)
/
kT
çç e x ÷ç e y ÷
ç
z
÷
÷
e
ç
÷
å
å
÷
÷
ç
ççå
ç
÷
÷
÷
ç
ç
÷
è nx
øè n y
ø
øè n z
æ
ö
æ
ö
æ
ö
2
2
2
e
(n
)
/
kT
ç
÷
÷
e
(n
)
/
kT
çç e- e(n x ) / kT ÷+ ç e y ÷
ç
z
÷
÷
+
e
ç
÷
å
å
÷
÷
ç
ççå
ç
÷
÷
÷
ç
ç
÷
è nx
ø è ny
ø
ø è nz
C) Neither of these
CT-7
Suppose you have a “box” in which each particle can occupy any one of 4
single particle states, and each state has energy zero.
E
0
I. If the box contains one particle, what is the value of the partition function?
A) 1
B) 4
C)42
D)Not enough info to answer question
II. What is the partition function, if the box contains two distinguishable
particles?
A) 4
B) 42 = 16
C) 16 – 4 = 12
D) none of these
III. What is the partition function, if the box contains two identical
fermions?
A) 4x3=12
B) 42 = 16
C) (4X3)/2 = 6
D) none of these
IV. What is the partition function, if the box contains two identical bosons?
A) 4x4=16
B) 16 – 4=12
C) 16/2 = 8
D) 4+ (4x3)/2=10
V. If the box contains N=2 particles, what is the partition function,
Z1N
according to the formula Z =
N!
A) 4x4=16
B) 16 – 4=12
C) 16/2 = 8
D) 4+ (4x3)/2=10
CT-8 About how long has the sun been shining?
A)50 millions years
D) 50 billion yrs
B) 500 million years C) 5 billion yrs
E)500 billion years
CT-9 If more mass is added to the surface of a white dwarf, the
diameter of the star gets...
A) larger
B) smaller
C) stays the same
[White dwarf stars are frequenty members of a binary star system
and stellar matter from the other star falls into the white dwarf.]
M
Hint:
R
F M2 / R 2 M2
p gravity =
:
:
2
A
R
R4
2/3
ö
U NeF N æ
N
çç ÷
p deg eneracy :
:
:
÷ :
ø
V
V
V çè V ÷
5/3
5/3
5/3
æN ÷
ö
æM ö
M
÷
çç ÷ : çç ÷ :
÷
èç V ÷
ø
èç R 3 ø
R5
CT7-10
What is the relation between frequency, wavelength and speed c of
a sinusoidal wave?
c
f
=
A)
l
B) f = l c
l
f
=
C)
c
D) None of these
CT7-11
A standing wave (not necessarily the one shown) has wavelength
.
What is the frequency f of the standing wave?
c
A)
l
2l
B)
c
lc
C)
2
D) depends on how many nodes are in the standing wave
E) none of these
CT7-12
What does the Planck distribution function n =
1
e hf / kT - 1
look like, as a function of temperature?
n
n
A
B
kT/hf
kT/hf
n
n
C
kT/hf
D
kT/hf
CT7-13 Consider a thin shell of constant radius in “m-space”.
Each point in m-space corresponds to a normal mode of the
radiation within an oven.
mz
True(A) or False(B):
All the modes in this shell (m  m+dm)
have the same average energy E.
True(A) or False(B): the average energy E of
the states in the shell depends on
temperature.
my
mx
True(A) or False(B): All the modes in this
shell have the same frequency f.
True(A) or False(B): for all the states in this shell, E = hf, where E
is the average energy of the mode and f is the frequency of the
mode.
y
x
y
x