lab Assignment

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/sims/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.

Lab: The Maxwell-Boltzmann Distribution* Phys 242

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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.

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)

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.

Lab: The Maxwell-Boltzmann Distribution* Phys 242

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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.

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)

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.)

Lab: The Maxwell-Boltzmann Distribution* Phys 242

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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.

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)

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.