### SimuLab 2: Velocity Distribution

 Your objective is to: Investigate the distribution of particle velocities and its dependence on temperature and mass. You will be able to: Explain why, in a system at fixed temperature, particles have a wide range of velocities. Contrast the velocity distribution of a gas at low temperature with a velocity distribution of a gas at high temperature. Contrast the velocity distribution of heavy particles with the velocity distribution of light particles.

 1. Open SMDPlayer, select Temperature from the StatesofMatter folder. Press Play. Read the captions and follow the instructions. Select File - Quit
 In the introductory movie we see that the average kinetic energy of particles increases with temperature. We also see that velocities of the majority of particles increases with temperature.

 2. Open SMD, select the file Temperature1 in the States of Matter folder. Press Start
 Your system represents a high density gas of 200 green particles at high temperature.

 Q1.27: What is the temperature of your system?

 Observe the temperature graph. Go to graph panel and switch the graph to Kinetic Energies.
 The green line represents the average kinetic energy of the green particles.

 Q1.28: What is the average kinetic energy of the green particles?

 Q1.29: Does the kinetic energy graph coincide with temperature graph? Explain.

 3. Switch Display Particles by: to Absolute Kinetic Energies.
 The colors of the particles indicate their kinetic energies in the rainbow order: red particles have small kinetic energies, violet particles have large kinetic energies. Observe how the velocities of the particles (and their color) change as they collide.

 4. Press Pause. Set Iterations Between Displays to 50. Select Edit - Select Particles. Choose Select Particle(s) and click on any particle in the display window. Press Start.
 A white rim will appear around the selected particle. You will observe changes in the kinetic energy of this particle over time.

 Q1.30: Does the kinetic energy and the velocity of the selected particle remain constant? Explain.

 Q1.31: Why are the velocities of the particles not equal? Why do the colors of the particles change? Explain.

 5. Set Iterations between Displays to 100. Switch the graph to Velocity Distribution.
 The x-axis of the graph represents the velocity and the y-axis represents the percentage of particles with that velocity. At each update of the screen, the computer program measures the velocities of all 200 particles and adds these values to the histogram.

 Q1.32: Describe what happens to the histrogram of velocities as more and more velocity updates are taken into account.

 6. Wait until the velocity distribution becomes a smooth curve with a well-defined maximum which usually happens when the number of velocity updates (# of obs) reaches approximately 10000. Press Pause and select Take a Snapshot - Graph and Take a Snapshot - Screen. Type the name of the picture T=4,m=1''.
 You will need these snapshots to compare the velocity distributions at different temperatures. This snapshot represents the particles of mass m=1 and temperature T=4.

 Q1.33: Which velocity value corresponds to the maximum of the histogram? Predict what will happen to the velocity value for the maximum of the histogram as the temperature is lowered to T = 0.25 and T = 1

 7. Hit Pause. Using the temperature scroll change the Temperature to T=0.25, and repeat Step 6, naming the snapshots T=.25,m=1''.

 8. Change the Temperature to T=1, and repeat Step 6, naming the snapshot T=1,m=1''.

 Q1.34: Do the actual positions of the maxima of the velocity distributions coincide with your predictions in Q.1.33?

 9. Enlarge snapshot gallery window (by dragging bottom right hand corner). Arrange screen shots on top, velocity distributions below screen shot.

 Q1.35: Compare the velocity distributions at different temperatures from the Snapshot Gallery. Explain how they are similar how they are different.

 Q1.36: Compare the snapshots of the screen at different temperatures. Relate the range of colors of the particles in the screen snapshots and the width of the velocity distributions.

 10. Select menu item Edit - Particles. Choose Change all particle(s) to B and click on the particle screen. You will not see a change in the particles because they are displayed in Absolute Kinetic energy mode but now you can vary the particle's mass. Using scroll bar for mass change B particle mass to 4. Set Temperature T=1. Press Start.
 We will investigate how the velocity distribution depends on the mass of the particle. In our program, only the blue particles have variable mass. Green particles always have mass m=1. So in order to change a particle's mass, we have to change the particle type to B.

 Q1.37: Predict what will happen to the histogram of particle velocities when the particles have mass: (a) m=4 and (b) m=0.1. Predict the positions of the maxima of the velocity distributions for each case.

 11. Repeat Step 6, naming the snapshot T=1,m=4''

 12. Change B particle mass to 0.1. Repeat Step 6, naming the snapshot T=1,m=0.1''

 Q1.38: Compare the velocity distributions for different particle masses: m=1, m=4, and m=0.1. Explain how they are similar and how they differ.

 Q1.39: Does the actual position of the maximum of the distribution coincide with your predictions in Q.1.37? Explain any difference.

 Q1.40: Compare the snapshots of the screen (colors representing kinetic energies) with the corresponding snapshots of the velocity distributions. Explain why the colors are the same while the velocity distributions are different.