Virtual Laboratory: Kinetic Theory of Gases



Overview

In this experimental module you will be working with particles inside a balloon that is at constant volume (unless you pop it). This simulation has opened in a separate window from the text you are reading now.

You can control the temperature of the gas in the balloon by using the thermometer. Gauges read out the pressure inside the balloon as well as the mean particle speed (MPS). A graph shows the distribution of particle speeds. The peak of that graph is approximately the same as the mean particle speed.

This applet is designed to demonstrate what the concept of temperatures is, how pressure is related to temperature under conditions of fixed volume and how the distribution of particle speeds depends on the temperature.

The user controls only one thing in this applet - the temperature of the gas inside the balloon.

Note that this experiment has a failure mode: if the pressure inside the balloon exceeds 150 units the balloon will pop (you will hear that). To recover from the popped condition, simply lower the thermometer temperature

The experimental procedure is fully outlined below. Please follow the instructions closely.

Technical Details

Experimental Instructions

In this applet the following quantities are readout in gauges:

  • The thermometer records the temperature of the gas in units of degrees kelvin
  • The mean particle speed (MPS) is given in meters per second
  • The pressure guage records the pressure in units of Pascals

There are 100 particles in the balloon at an initial temperature of 300K. Disregard the graph for the present set of exercises. Email your results to the instructor:

Temperature vs. Pressure at Fixed Volume

  1. Record the initial pressure
  2. Raise the temperature to 600K and record the pressure.
  3. Raise the temperature to 900K and record the pressure.
  4. Raise the temperature to 1200K and record the pressure.
  5. Raise the temperature to 1500K and record the pressure.
  6. Predict at what temperture the pressure will pop the balloon (i.e. be 150).
Reset the temperature to 300K and hit the clear graph button.

Temperature vs mean particle speed at Fixed Volume

  1. Record the initial MPS
  2. Raise the temperature to 600K and record the MPS and note the behavior of the graph.
  3. Raise the temperature to 900K and record the MPS and note the behavior of the graph.
  4. Raise the temperature to 1200K and record the MPS and note the behavior of the graph.
  5. Raise the temperature to 1500K and record the MPS and note the behavior of the graph.
  6. Raise the temperature to 1800K and record the MPS and note the behavior of the graph.
  7. If you double the temperature does the MPS double? If not, by what factor does it increase (i.e. 10%, 20%, etc ...).
  8. Determine a functional relation between MPS and temperature. This relation will be non-linear and of the form

    T a  MPSn

    Determine from the experimental data you that just took what the value of n is likely to be.

  9. Now qualitatively describe how the graph, which is showing the distribution of particle speeds, behaves as the temperature increases. (ignore the red vertical line on the graph).

  10. Now hit the clear graph button and reset the temperature to 400K.
  11. Raise the temperature to 1200K

  12. Count the approximate number of boxes that are under the purple curve and under the white/yellow curve. In doing this you are measuring the amount of area under these curves (in calculus this is called an integral).

  13. Compare the two counts. Note that the Y-axis is the number of particles per cubic centimeter that are at some velocity. What might this comparison be telling you about the distribution of particle energies in this enclosed volume. Yes, this is an advanced question which I don't expect anyone to answer correctly but I expect you to try.

Lastly do this one