Maxwell Boltzmann Summary Answer the following questions an

Maxwell Boltzmann: Summary
Answer the following questions and submit your responses as a
PDF.
1. Write down one major conclusion you can draw from this
week’s laboratory.
Please explain.
2. Describe the experimental evidence that supports your
conclusion. Please
explain.
3. Give one example of applications/situations for the
finding(s) you described
above in your everyday life outside of physics lab.
4.What
did
you
like
and
dislike
about
this
week;s
lab
Lab: The Maxwell-Boltzmann Distribution* Phys 242

*Some components of this lab are based on the activity
developed by Julia Chamberlain & Ingrid Ulbrich
(PhET, UC Boulder;
https://phet.colorado.edu/en/contributions/view/3687)
In this lab we will study several macroscopic quantities that can
be used to describe a gas and explore the
relationships among these quantities. using a simulation from
the PhET team:
https://phet.colorado.edu/si ms/html/gas-properties/latest/gas-
properties_en.html
This is a variant of the simulation you used for the Gas
Properties lab. The simulation can be run in a
browser. If you have issues with the simulation, try using
another browser. If you are unable to run the
simulation, your TA will provide you with remote assistance.
When you run the simulation, choose the
“Energy” option. At the very bottom of the screen you will see
the other options for the simulation,
including a home button, “Ideal,” “Explore,” “Energy,” and
“Diffusion.” If you accidentally navigate to
another area, you can return to the Energy option by clicking
the button.
The simulation shows a preset volume. In its initial
configuration the box is empty. On the right side of
the screen there is a menu labelled “Particles.” By expanding
this menu, you can choose to add so many
heavy or light particles. These particles will enter the volume
at a temperature of 300 K in the initial
setup.
Once there are particles in the box, the temperature and pressure

in the box can be read off the scales on
the right corner of the box. The units can be changed for these
values. To adjust the temperature of the
particles in the box, move and hold the slider bar below the box.
To the left of the box is a graph showing the speed of the
particles. This is a histogram. By clicking the
blue and red boxes below the graph, you can see the
distributions of the heavy and light particles,
respectively. The box above this shows the average speed of
the heavy and light particles.
Below the speed distribution graph is a menu that can be
expanded to show the kinetic energy distribution
of the particles. Again, by clicking the blue and red boxes
below the graph, you can see the distributions
of the heavy and light particles, respectively.
On the left there is a handle to change the size of the box.
There is also a lever at the top of the box that
can be lifted to open the box, allowing particles to escape.
Particles can also be removed from the box by
reducing the number of particles in the “Particles” menu.
Finally, to refresh the simulation to the initial point, click the
arrow in the bottom right.
https://phet.colorado.edu/en/contributions/view/3687
https://phet.colorado.edu/sims/html/gas-properties/latest/gas-
properties_en.html

2
I. Speed
Reset the simulation so that you begin with an empty box.
A. Imagine that you have 250 heavy particles and 250 light
particles in the box at a constant temperature.
Predict whether the light particles will move faster than, slower
than, or the same speed as the heavy
particles? Explain your reasoning.
B. Check your prediction from Part A by inserting 250 heavy
and 250 light particles into the box. Wait
a minute or so until the particles have mixed. In the upper left
panel, you can see the average speeds
of the heavy and light particles. Are the light particles moving
faster than, slower than, or the same
speed as the heavy particles?

C. The middle panel on the left shows the distribution of
particle speeds. By
checking the blue and red boxes (see the screenshot shown here)
you can see
the distributions for the heavy and light particles, separately.
Sketch the
resulting speed distributions for the two types of particles.
D. Predict what will happen if you remove the lid on the box for
a brief time (~5 sec). Consider what
will happen to:
• The number of particles in the box
• The average speed of the particles in the box
• The relative numbers of heavy vs. light particles in the box.
Explain your reasoning.

(PhET, UC Boulder;
E. Check your prediction by slightly pulling back the handle on
the top of the box for a few seconds.
Only make a small opening! Then pause the simulation.
1. How many particles are now in the box? (You can read this
number in the “Particles” panel on
the right.) Explain.
2. What are the average speeds of the particles after the lid had
been opened? Explain.
3. How many heavy particles were lost? How many light
particles? Explain.

F. Consider the following conversation between two students.
Student 1: "The distribution of particles within the box is
random, so only those
particles that happened to be near the opening will escape. This
means
that the particles that escaped will be randomly selected, so the
average
speed won’t change."
Student 2: “But the fast-moving particles will have a greater
chance of escaping the
box. This means that the average speed will decrease once the
box has
been opened. More light particles will also be lost, since they
are moving
faster.”
With which student, if any, do you agree? Explain your
reasoning.

4
II. Kinetic Energy
Reset the simulation so that you begin with an empty box.
A. Imagine that you will have 250 heavy particles and 250 light
particles in the box. Do you predict that
the average kinetic energy of the light particles will be higher
than, lower than, or the same as the
average kinetic energy of the heavy particles? Explain your
reasoning.
B. Check your prediction from Part A by inserting 250 heavy
and 250 light particles into the box. Wait
a minute or so until the particles have mixed. In the bottom left
panel, you can see the distribution of
kinetic energies. Check the blue and red boxes to see the
distributions for the heavy and light
particles. Is the average kinetic energy of the light particles
higher than, lower than, or the same as
the average kinetic energy of the heavy particles? (There are no
numbers in this plot, so you will
have to estimate from the graph.)

C. Consider the following statement made by a student.
"The kinetic energy of an object is ½mv2. Therefore, heavier
particles with
a higher mass will have a higher kinetic energy."
Explain what is incorrect about this student’s statement.
(PhET, UC Boulder;
III. Speed and temperature
Reset the simulation and add 250 heavy and 250 light particles
into the box.

A. Now imagine that you will heat the box. Predict whether the
average speeds of the heavy and light
particles will increase, decrease, or stay the same.
B. Predict whether the average kinetic energy of the heavy and
light particles will increase, decrease, or
stay the same if the box is heated.
C. Check your predictions from Parts A and B by heating the
box.
1. Did the average speeds of the heavy and light particles
increase, decrease, or stay the same?
2. Did the average kinetic energy of the heavy and light
particles increase, decrease, or stay the
same? (There are no numbers in this plot, so you will have to
watch the graph change.)

6
D. Now, for a variety of temperatures, record the average speed
of the heavy and light particles in the
table below. Calculate v2avg.
T (K) Heavy vavg (m/s) Heavy v2avg
(m2/s2)
Light vavg (m/s) Light v2avg (m2/s2)
E. Make a plot of v2avg vs. T.

(PhET, UC Boulder;
F. Find the slopes of the lines in your above plot for the heavy
and the light particles.
G. Recall that the average velocity squared is proportional to
T/m, where m is the mass of a particle.
This means that if we plot v2 vs. T, the slope will be
proportional to 1/m.
Assuming the mass of the light particles is 1, use your plot from
Part D to find the mass of the heavy
particles.

H. Is it possible for the heavy and light particles to have the
same average speed? Explain.
https://phet.colorado.edu/en/contributions/view/3687A. Imagine
that you have 250 heavy particles and 250 light particles in the
box at a constant temperature. Predict whether the light
particles will move faster than, slower than, or the same speed
as the heavy particles? Explain your reasoning.B. Check your
prediction from Part A by inserting 250 heavy and 250 light
particles into the box. Wait a minute or so until the particles
have mixed. In the upper left panel, you can see the average
speeds of the heavy and light particles. Are the ...C. The
middle panel on the left shows the distribution of particle
speeds. By checking the blue and red boxes (see the screenshot
shown here) you can see the distributions for the heavy and
light particles, separately. Sketch the resulting speed dis...D.
Predict what will happen if you remove the lid on the box for a

brief time (~5 sec). Consider what will happen to:E. Check
your prediction by slightly pulling back the handle on the top of
the box for a few seconds. Only make a small opening! Then
pause the simulation.1. How many particles are now in the box?
(You can read this number in the “Particles” panel on the right.)
Explain.2. What are the average speeds of the particles after the
lid had been opened? Explain.3. How many heavy particles
were lost? How many light particles? Explain.F. Consider the
following conversation between two students.With which
student, if any, do you agree? Explain your reasoning. II.
Kinetic EnergyWith which student, if any, do you agree?
Explain your reasoning. II. Kinetic Energy
Maxwell-Boltzmann
Distributions
• How
do
we
describe
the
energy
of
a
whole
bunch
of
par6cles?
• More

useful
to
describe
the
energy
of
a
system
of
par6cles
Energy Equipartition
Each
degree
of
freedom
contributes
to
the
energy
of
a
system,
where
possible
degrees
of
freedom

are
those
associated
with
transla6on,
rota6on,
and
vibra6on
of
molecules.
Energy Equipartition: Monatomic
gas
(made
of
single
atoms)
3
Dimensions,
so
3
transla6onal
degrees
of
freedom

�= 3/2  �↓�  �
Kinetic Energy
�= 1/2  ��↑2 
Par6cles
of
different
masses
and
veloci6es
will
have
different
energies
Relate velocity and
temperature
• For
an
ideal
monatomic
gas

�=�
3/2  �↓�  �= 1/2  ��↑2 
�↓��  =√⁠ 3�↓�  �/�   
So let’s take a look at a system
of particles with different
masses
hEps://phet.colorado.edu/sims/html/gas--‐ proper6es/latest/gas-
-‐ proper6es_en.html
2
0 B
3/2
/220
B

4
2
m v k T
v
m
N N v e
k T
π
π
−⎛ ⎞ ⎜ ⎟
⎝ ⎠
Figure
20.10
Equa6on
20.42
Maxwell Boltzmann
Distribution
�↓��  =
most
probable
velocity

�↓��  =
average
velocity
�↓��  =
root--‐ mean--‐ square
velocity
How would the MB distribution
change with T?
Figure
20.11
2
0 B
3/2
/220
B
4
2
m v k T
v

m
N N v e
k T
π
π
−⎛ ⎞ ⎜ ⎟
⎝ ⎠
Figure
20.11

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