Q12.1.a
You put an ice cube into a styrofoam
cup containing hot coffee. You would
probably be surprised if the ice cube
got colder and the coffee got hotter.
Would this be a violation of the energy
principle?
1) Yes
2) No
3) The energy principle does not
apply in this situation
Q12.2.a
Consider 3 quantized oscillators (a model for 1 atom).
They share 4 "quanta" of energy. One way to arrange
the energy among these oscillators can be written as
"400" (4 in the first oscillator, none in the others).
Another is "103" (1 in the first oscillator, none in the
second, 3 in the third). List all the ways you can
arrange these 4 quanta of energy among the 3
oscillators; how many arrangements are there?
1) 3 ways
2) 9 ways
3) 12 ways
4) 15 ways
5) 18 ways
6) 21 ways
Q12.2.b
Consider 4 quantized oscillators (a model for 1 and
1/3 atoms!). They share 2 "quanta" of energy. List all
the ways you can arrange these 2 quanta of energy
among the 4 oscillators (such as "2000"); how many
arrangements are there?
1) 4
2) 7
3) 10
4) 15
5) 20
Q12.2.b1
If q = 300 and N = 100 what is the value of  = (q + N – 1)! / (q!(N-1)!) ?
1) 4.158 e 81
2) 5.605 e 95
3) 1.681 e 96
4) 2.241 e 96
5) 0
Q12.2.c
Two objects share a total energy E = E1+E2. There
are 10 ways to arrange an amount of energy E1 in
the first object and 15 ways to arrange an amount
of energy E2 in the second object. How many
different ways are there to arrange the total
energy E = E1+E2 so that there is E1 in the first
object and E2 in the other?
1) 10
2) 15
3) 25
4) 150
5) 1E15
Q12.2.d
A system of 300 oscillators contains 100 quanta of energy. What is the
physical meaning of this model?
1) one atom oscillating in 300 dimensions
2) 300 atoms, each in the 100th energy level
3) 300 atoms with 100 joules of energy distributed among them
4) 100 atoms with 300 joules of energy distributed among them
5) 100 atoms with 100 ks m joules of energy among them
6) something else
Q12.2.e: Which arrangement is most
probable?
1) A
2) B
3) C
4) D
5) They’re equally probable
Q12.5.a
Inside an insulated container two
aluminum blocks, 1 kg and 2 kg,
have been in contact for a long
time. What physical property is
the same for the two blocks?
1) the mass
2) the temperature
3) the volume
4) the thermal energy
5) the weight
Q12.5.b
The slope of a graph of entropy vs. energy (dS/dE) in a metal block is related
to the temperature of the block. From the graph of entropy for two blocks in
contact, we see that the block with the larger slope tends to gain energy
from the block with the smaller slope. Therefore, which of these statements
is true?
1) Big dS/dE means high temperature
2) Small dS/dE means high temperature
Q12.5.c
There is thermal transfer of energy of 5000 J into
a system. The entropy of the system increases
by 50 J/K.
What is the approximate temperature of the
system?
1) 5000 K
2) 100 K
3) 50 K
4) 0.01 K
5) 0.0002 K
Q12.5.d
Initially the entropy of object A is 100 J/K, and the entropy of object B is
also 100 J/K. Then both objects are immersed in large vats of hot water.
When the thermal energy of A has increased by 1000 joules, its entropy is 200 J/K.
When the thermal energy of B has increased by 2000 joules, its entropy is 300 J/K.
Which object is at a higher temperature?
1) A is at a higher temperature than B
2) B is at a higher temperature than A
3) Their temperatures are the same.
Q12.5.e
Consider a 3 kg block of aluminum. One mole of
aluminum has a mass of 27 grams (0.027 kg).
From Young's modulus we determined that the
stiffness of the interatomic bond is 16 N/m, but in
the Einstein model the x, y, and z oscillations
each involve 2 half-length springs, so the
effective stiffness is 64 N/m.
  1.05  10 34 J  s ; 1 mol = 6  10 23 atoms
What is the energy in
joules of one quantum
of energy?
1) 1.62e-34 J
2) 4.85e-34 J
3) 5.11e-33 J
4) 1.25e-22 J
5) 3.96e-21 J
Q12.5.f Here is a table of the number of ways to arrange energy in a certain
microscopic object, as a function of the energy in the object:
E, J
4E-21
6E-21
8E-21
10E-21
12E-21
14E-21
16E-21
#ways
6
20
37
60
90
122
148
When the energy is 12E-21 J, what is the temperature? k = 1.38E-23 J/K.
1) 193.2 K
2) 357.4 K
4) 476.4 K
5) 2114.0 K
3) 408.4 K
Q12.5.g
When the energy is 12E-21 J, what is the temperature? k = 1.38E-23 J/K.
1) 193.2 K
2) 357.4 K
4) 476.4 K
5) 2114.0 K
3) 408.4 K
Q12.5.h
When the energy is 12E-21 J, what
is the heat capacity (per object)?
k = 1.38E-23 J/K.
1) 4.25E-24 J/K per object
2) 8.5E-24 J/K per object
3) 1.0E-24 J/K per object
4) 1.7E-23 J/K per object
5) 4.2E-23 J/K per object
Q12.6.a: We have two blocks, one aluminum (Al) and one lead (Pb), each containing
6e23 atoms (one mole). The aluminum block has a mass of 27 grams, and the lead
block has a mass of 207 grams. Which of the following pictures shows the blocks in
the correct relative sizes?
1)
2)
3)
Initially the two blocks are at a temperature very near absolute zero (0 K). We will
add 1 J of energy to the aluminum block, and 1 J of energy to the lead block, and see
which block has the larger increase in temperature. We will step through a chain of
reasoning using statistical mechanics to answer this question, which will let us
determine whether aluminum or lead has the higher heat capacity at low
temperatures.
Q12.6.b: From Young’s modulus we found that the effective stiffness of the
interatomic bond for Al is about 16 N/m and for Pb is about 5 N/m. A mole of Al is 27
grams, and a mole of Pb is 207 grams. Here are energy level diagrams for the
quantized harmonic oscillators used in the Einstein solid. Which diagram represents
Al and which represents Pb?
1) (A) is Al and (B) is Pb
2) (A) is Pb and (B) is Al
3) (B) is both Al and Pb (they are the same)
A
B
Q12.6.c: We add 1 J of energy to each block. Given the fact that Al has the greater
energy-level spacing, which block now has the larger number of quanta
of energy, q?
1) The number of quanta q is greater in the Al
2) The number of quanta q is greater in the Pb
3) The number of quanta q is the same for Al and Pb
Q12.6.d: What about the number N of quantized oscillators in the two blocks?
1) N is greater in the Al
2) N is greater in the Pb
3) N is the same for Pb and Al
Q12.6.e: The Pb block has more quanta corresponding to the 1J of thermal energy.
Therefore, in which block is there a larger number of ways  of arranging the
thermal energy?
1) The number of ways  is greater in the Al
2) The number of ways  is greater in the Pb
3) The number of ways  is the same in the Pb and the Al
Q12.6.f: The Pb block has the larger number of ways  to arrange the energy. So
which block now has the larger entropy S?
1) The entropy S is now greater in the Al
2) The entropy S is now greater in the Pb
3) The entropy S is the same in the Al and the Pb
Q12.6.g: Originally the temperature of the blocks was near absolute zero, with
almost no thermal energy in the blocks. How many ways are there to arrange zero
energy in a block? Just 1. So what was the original entropy in a block?
1) 0 J/K
2) 1 J/K
3) infinite
Q12.6.h: We found that after adding 1 J to each block, the entropy S is now greater in
the Pb block. Both blocks started with zero entropy. Therefore which block
experienced a larger change in entropy S?
1) The entropy change S was greater in the Al
2) The entropy change S was greater in the Pb
3) The entropy change S was the same in the Pb and the Al
Q12.6.i: We added the same amount of energy E = 1 J to each block, and the
entropy change S was greater in the Pb block. Which block now has the higher
temperature?
1) The temperature of the Al is now higher
2) The temperature of the Pb is now higher
3) The temperature of the Al and Pb are the same
Q12.6.j: The original temperature was 0 K, and the final temperature of the Al block is
higher than that of the Pb block, so the Al block has the larger change in temperature,
T. At low temperatures, which block has the greater heat capacity per atom, C =
(E/T)/6e23?
1) The low-temperature heat capacity per atom of Al is greater
2) The low-temperature heat capacity per atom of Pb is greater
3) The low-temperature heat capacity per atom is the same for Pb and Al
Here are actual heat capacity data for Al and Pb (see textbook):
Q12.7.a
The Sun’s surface temperature is about 6000 K.
Approximately what is the probability of finding
a hydrogen atom in its first excited state (10.2
eV above the ground state)?
k = 1.38e-23 J/K
1)
2)
3)
4)
5)
1e-10
3e-10
1e-9
3e-9
1e-8
Q12.7.b
At approximately what temperature would the
probability of finding a hydrogen atom in its first
excited state (10.2 eV above the ground state)
be about 1%?
k = 1.38e-23 J/K
1)
2)
3)
4)
5)
10000 K
15000 K
20000 K
25000 K
30000 K
Q12.7.c
The energy spacing for quantized oscillations in
aluminum is 
4k s
 4e-21 J or 0.025 eV. At
m
approximately what temperature is there a 10%
probability of finding one quantum of energy in
one of these oscillators?
k = 1.38e-23 J/K
1)
2)
3)
4)
5)
60 K
120 K
240 K
360 K
420 K
Q12.7.d
Approximately what fraction of the sea-level air
density is found at the top of Mount Everest, a
height of 8848 meters above sea level?
k = 1.38e-23 J/K
1)
2)
3)
4)
5)
0.05
0.1
0.3
0.5
0.7
Q12.7.e
Calculate the rms speed of a nitrogen molecule
in this room.
1)
2)
3)
4)
5)
50 m/s
100 m/s
300 m/s
500 m/s
700 m/s
Q12.7.f
In a vacuum, how high would an object go if
thrown upward with initial speed 500 m/s?
1)
2)
3)
4)
5)
100 m
1200 m
2600 m
13000 m
25000 m