CM: GasLab Investigations

Investigation (A1): A typical molecule in an Ideal Gas/ Brownian Movement Models: Free Gas w/ Speedplot, Gas in a Box

This investigation will use StarLogoT models to explore the behavior of a single molecule in an ideal gas. This will be a starting point for thinking about the average behavior of a large number of similar molecules, which is what thermodynamics is all about.

If you could watch an individual molecule in a gas, what do you think its motion would look like?

Prediction:

Open the Free Gas w/ Speedplot model. Press SETUP. You will see a graphics window with a lot of green "molecules", which will move about when you run GO. With the sliders you can set the number of molecules, their initial speed (initspeed) and mass (initmass).

Briefly, the model works like this: molecules are modeled as perfectly elastic particles with no internal energy except that which is due to their motion. Collisions between molecules, which occur when two molecules find themselves on the same patch, are elastic. The molecules wrap the screen, that is, if they leave one edge they reappear on the other edge. Particles are colored according to speed blue for slow, green for medium, and red for high speeds.

Run the model for a while with the initial settings. [histogram off, trace on]. Watch the screen carefully, especially the one molecule whose path is traced in yellow. Note how it "wraps" the screen. Write a short description of what its behavior seems to be. Be specific. It may help to look at the Speed of One plot (plotwindow 4), which shows the traced moleculeąs changing speed (black) and the average speed of all the molecules (green).

Observations:

From looking at the model, what would you say is happening when the molecule changes direction or speed?

Double the number of molecules. How will the traced path be changed?

Prediction:

Run the model. Describe how the traced path is changed.

Observations:

Half the number of original molecules. . How will the traced path be changed?

Prediction:

Run the model again. Describe how the traced path is changed.

Observations:

Can you make any general predictions about how the motion an individual molecule changes as the density of the gas increases?

The motion you observe here looks much like Brownian Movement. This refers to a 19th-century experiment in which Š Brown directly observed the erratic path of pollen and other objects MUCH larger than molecules. If they were so large, why would they move like this? Is it still valid evidence for molecular theory? By the way, Brown needed to use materials besides pollen to show that the motion wasnąt caused by the pollen being "alive".

Now look at the colors of the molecules. The total numbers of fast (red), average (green), and slow (blue) molecules are shown in the Speed Counts plot (plotwindow 3). What ratio are they in, roughly? Does this seem to match up with the speed of the traced molecule?

How hard would it be to predict what the traced molecule is going to do? Would you say that this model is deterministic?

The molecules all start with the same speed, though with different headings. How could it be that they end up with a whole range of speeds? Use drawings to help explain your idea of how this could happen.

Now open the Gas in a Box model. The molecules follow the same rules, except that they "bounce" off the walls of the box, without losing energy. Run the model for a while and watch the path of the traced molecule. Do you think the walls will change the behavior of the gas?

How would you write a "bouncing" code for a molecule? Write it down (either as code or as a description of steps).

When a real molecule hits a wall, does it bounce like this? Under what conditions will it lose or not lose energy?

In what ways is this model a correct or incorrect idealization of the real world?

Authors: Edmund Hazzard and Uri Wilensky

Copyright 2000 by Uri Wilensky. All rights reserved. Permission to use, copy, or modify this software and its associated documentation, models and curricular materials for educational and research purposes only and without fee is hereby granted, provided that this copyright notice and the original authors' names app ear on all copies and supporting documentation. For any other uses of this software, in original or modifi ed form, including but not limited to distribution in whole or in part, specific prior permission must be obtained from Uri Wilensky. These programs shall not be used, rewritten, or adapted as the basis of a com mercial or hardware product without first obtaining appropriate licenses from Uri Wilensky. We make no rep resentations about the suitability of this software for any purpose. It is provided "as is" without expres s or implied warranty.

Investigation (A1): A typical molecule in an Ideal Gas/ Brownian Movement Models: Free Gas w/ Speedplot, Gas in a Box
This investigation will use StarLogoT models to explore the behavior of a single molecule in an ideal gas. This will be a starting point for thinking about the average behavior of a large number of similar molecules, which is what thermodynamics is all about.
If you could watch an individual molecule in a gas, what do you think its motion would look like?
Prediction:
Open the Free Gas w/ Speedplot model. Press SETUP. You will see a graphics window with a lot of green "molecules", which will move about when you run GO. With the sliders you can set the number of molecules, their initial speed (initspeed) and mass (initmass).
Briefly, the model works like this: molecules are modeled as perfectly elastic particles with no internal energy except that which is due to their motion. Collisions between molecules, which occur when two molecules find themselves on the same patch, are elastic. The molecules wrap the screen, that is, if they leave one edge they reappear on the other edge. Particles are colored according to speed blue for slow, green for medium, and red for high speeds.
Run the model for a while with the initial settings. [histogram off, trace on]. Watch the screen carefully, especially the one molecule whose path is traced in yellow. Note how it "wraps" the screen. Write a short description of what its behavior seems to be. Be specific. It may help to look at the Speed of One plot (plotwindow 4), which shows the traced moleculeąs changing speed (black) and the average speed of all the molecules (green).
Observations:
From looking at the model, what would you say is happening when the molecule changes direction or speed?
Double the number of molecules. How will the traced path be changed?
Prediction:
Run the model. Describe how the traced path is changed.
Observations:
Half the number of original molecules. . How will the traced path be changed?
Prediction:
Run the model again. Describe how the traced path is changed.
Observations:
Can you make any general predictions about how the motion an individual molecule changes as the density of the gas increases?
The motion you observe here looks much like Brownian Movement. This refers to a 19th-century experiment in which Š Brown directly observed the erratic path of pollen and other objects MUCH larger than molecules. If they were so large, why would they move like this? Is it still valid evidence for molecular theory? By the way, Brown needed to use materials besides pollen to show that the motion wasnąt caused by the pollen being "alive".
Now look at the colors of the molecules. The total numbers of fast (red), average (green), and slow (blue) molecules are shown in the Speed Counts plot (plotwindow 3). What ratio are they in, roughly? Does this seem to match up with the speed of the traced molecule?
How hard would it be to predict what the traced molecule is going to do? Would you say that this model is deterministic?
The molecules all start with the same speed, though with different headings. How could it be that they end up with a whole range of speeds? Use drawings to help explain your idea of how this could happen.
Now open the Gas in a Box model. The molecules follow the same rules, except that they "bounce" off the walls of the box, without losing energy. Run the model for a while and watch the path of the traced molecule. Do you think the walls will change the behavior of the gas?
How would you write a "bouncing" code for a molecule? Write it down (either as code or as a description of steps).
When a real molecule hits a wall, does it bounce like this? Under what conditions will it lose or not lose energy?
In what ways is this model a correct or incorrect idealization of the real world?

Authors: Edmund Hazzard and Uri Wilensky
Copyright 2000 by Uri Wilensky. All rights reserved. Permission to use, copy, or modify this software and its associated documentation, models and curricular materials for educational and research purposes only and without fee is hereby granted, provided that this copyright notice and the original authors' names app ear on all copies and supporting documentation. For any other uses of this software, in original or modifi ed form, including but not limited to distribution in whole or in part, specific prior permission must be obtained from Uri Wilensky. These programs shall not be used, rewritten, or adapted as the basis of a com mercial or hardware product without first obtaining appropriate licenses from Uri Wilensky. We make no rep resentations about the suitability of this software for any purpose. It is provided "as is" without expres s or implied warranty.