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Probability in Thermo & Stat Mech

  • I6-25: DIFFUSION - DISTRIBUTION OF PING PONG BALLS

    I6-25
    Demonstrate on a macroscopic scale using ping pong balls how random molecular motion causes substances to diffuse.

    This model consists of a wooden frame with clear plastic covers, about one ping pong ball in width, ten bins at the top and bottom for setting up initial and analyzing final distributions, with several rows of pegs in between. When the horizontal plastic baffle holding the balls at the top is pulled away, balls will drop through the peg array, become randomly scattered, and drop into bins at the bottom.
    Engagement Suggestions
    • Put four orange balls into bin 5 and four white balls into each of bins 3, 4, 6, and 7. Challenge students to predict whether they will keep this same arrangement as they fall. (When the balls reach the bottom, the four orange balls will have become distributed into the white balls.)
    Background
    This shows on a larger scale how random molecular motion causes substances to diffuse. The array of fallen balls will approximate a probability curve; this is an opportunity to introduce statistical concepts in a physical, measurable manner.

    i6-25a

  • I6-51 ENTROPY - SORTING MARBLES

    I6-51
    Demonstrates that increasing entropy requires less energy than decreasing entropy
    Shaking the system with the larger holes on the top causes the marbles to separate by size (yellow, green, pink, and blue). Simply inverting allows them to fall under the influence of gravity to their lowest level and mix. It apparently takes more energy to unmix the marbles than to mix them.
    I6

  • I6-52: ENTROPY - FOUR BALLS IN GAS DIFFUSION MODEL

    I6-52
    Demonstrate that an ordered state is statistically possible.

    Place two balls of each of two different colors in the diffusion apparatus. To start, either place all four one the same side of the apparatus; or place two of one color on one side of the apparatus, and two balls of another color on the other side. Start the machine going with the hole between sides open.
    Engagement Suggestions
    • Encourage students to notice that although statistically it is less probable, the arrangement of both orange balls on one side and both green balls on the other side will happen occasionally.
    • Ask: Is this as likely to happen using three balls of each color? With four?
    Background
    This is essentially showing the exception to the general principle of demonstration I6-21. With a small enough number of balls in the model, it is statistically possible to “reverse entropy” to a limited extent – that is, occasionally, the balls will randomly organize themselves so that they are once again sorted by color.
    FS1

  • I6-61: MAXWELL'S DEMON

    I6-61
    Example of a "Maxwell Demon."
    A Maxwell demon is some gizmo which presumably allows you to do something which otherwise might be statistically unlikely. For example, the system photographed contains ten balls which are apparently identical except that five are white and five are black. If you rotate the device with the big end up you can separate the black and the white balls, and allow only one color of balls to fall into the neck, as shown in the photograph above. You act as the "Maxwell Demon."

    i6-61a