Worksheet Boltzmann Distribution Applications
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Date
Dec 6, 2023
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7
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5/7/2021
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Review Test Submission: Worksheet: Boltzmann Distribution Applications
PHYS 260 Intro Thermal Physics (41588) 2021 Spring
Weekly Content
Week 9 begins Monday, March 8
Review Test Submission: Worksheet: Boltzmann Distribution Applications
User
Yacoub Awimrin
Course
PHYS 260 Intro Thermal Physics (41588) 2021 Spring
Test
Worksheet: Boltzmann Distribution Applications
Started
3/8/21 8:42 PM
Submitted
3/14/21 6:11 PM
Status
Completed
Attempt
Score
43 out of 55 points
Time
Elapsed
140 hours, 28 minutes
Instructions
Results
Displayed
All Answers, Submitted Answers, Correct Answers, Feedback, Incorrectly Answered Questions
Units
: Include units in your answer when instructed. Use SI units only in your
answers. For example, use Pascals not atmospheres.
Numbers
: Use either the normal form, such as 132 or 132.5, or the exponential
form, which represents 132 as 1.32E+2, represents 5 x 10
4
as 5E+4 or 5E4, or
represents 52 x 10
-3
as 5.2E-2, unless instructed otherwise. Do not use the form 5 x
10
4
.
If your answer is positive, do
not
place a "+" sign before your answer.
Repeat Once
: You can do worksheets twice before the due date. After submitting
the ±rst time, click the OK on the bottom right of the page and you will be informed
of your total score and which questions were answered incorrectly (during a one-
time view, so you might want to take a screen-shot for future reference). Accept the
score or redo the entire worksheet. Your highest score will be recorded. Answers and
feedback to all problems will be available after the due date and can be accessed
within My Grades.
Question 1
Selected
Answers:
d.
e.
A harmonic oscillator with energy levels
ε
is in equilibrium with a reservoir at
temperature
T
.
Choose the correct statements below.
The ground state has the highest probability of being occupied,
independent of the temperature.
If
kT
<<
ε
, only the ground state is occupied.
5 out of 5 points
5/7/2021
Review Test Submission: Worksheet: Boltzmann Distribution ...
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Answers:
a.
b.
c.
d.
e.
Response
Feedback:
If
kT
>>
ε
, higher energy states are preferentially occupied over lower
energy states.
If
kT
>>
ε
, all states will be equally occupied.
If
kT
= 2
ε
, only the second excited state is occupied.
The ground state has the highest probability of being occupied,
independent of the temperature.
If
kT
<<
ε
, only the ground state is occupied.
The ground state has the highest probability of being occupied. As the
temperature is increased above
kT
=
ε
, the probability of occupying higher
energy states increases.
Question 2
Selected Answer:
0.932
Correct Answer:
0.932 ± 1%
A molecule has states with the following energies: 0, 1
ε
, 2
ε
, 3
ε
, and 4
ε
, where
ε
= 0.9 x
10
-20
J.
Calculate the probability of molecules in the ground state (with zero energy) for a
collection of molecules in thermal equilibrium at
T
= 242 K.
Provide your answer as a number in normal form to 3 decimal places (in the form
X.XXX).
Hint: note that this molecule has a ±nite number of states so you must take a ±nite
sum, not the expressions discussed in the video for in±nite sums.
Question 3
Selected Answer:
0.149
Correct Answer:
149 ± 5%
Response
Feedback:
A molecule has states with the following energies: 0, 1
ε
, 2
ε
, 3
ε
, and 4
ε
, where
ε
= 0.5 x 10
-20
J.
Calculate the average number of molecules in the ±rst excited state (1
ε
) for a collection of 1000
molecules in thermal equilibrium at
T
= 213 K.
Note that the average number of molecules in a state is just the probability of the state times
the number of molecules.
Provide your answer as a number in normal form.
An example calculation for
T
= 300 K and
ε
= 1 x 10
-20
J:
6 out of 6 points
0 out of 6 points
5/7/2021
Review Test Submission: Worksheet: Boltzmann Distribution ...
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3/7
If there are a 1000 molecules, then the average number in the ±rst excited state is
0.081 * 1000 = 81.
Question 4
Selected Answer:
0.424
Correct Answer:
0.297 ± 2%
Response
Feedback:
A molecule has states with the following energies: 0, 1
ε
, 2
ε
, where
ε
= 0.4 x 10
-20
J.
Calculate the average energy of this molecule in thermal equilibrium at
T
= 215 K.
Provide your answer in units of
ε
. In other words, your solution should have the form
of
(number)
ε
, such as 2.137
ε
,
but
the answer that you enter is just
2.137, a number in normal form with 3 decimal
places (X.XXX).
An example calculation for
T
= 300 K and
ε
= 1 x 10
-20
J:
0 out of 6 points
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