CM: GasLab Investigations

Investigation (C1): Free Expansion of a Gas Model: Free Expansion

What happens to a gas as it expands into an empty space? What does this simple situation teach us about thermodynamics?

Open the model Free Expansion. When you push SETUP you will see a box with two chambers. The upper one is filled with molecules and lower one is empty. With the buttons you can open and close a window between the two chambers. When the model is run, the molecules collide as in Gas in a Box. It allows you to simulate free expansion of a gas into a vacuum and keep track of things that are very difficult to measure in nature.

Before you run the model, make some predictions about what will happen when you open the window. It seems likely that molecules will make their way into the empty chamber. How fast will they do it? Will there ever be an equal number of molecules in the upper and lower chambers? How long will it take for the system to reach a steady state, if indeed it does? Do a sketch of the plot of numbers of molecules above and below the window.

[add labeled plot here to draw on]

But what will happen to the energy of the gas? What about the average speed of the molecules?

How will these values compare for the molecules in the upper and lower chambers? Will they eventually be the same?

Now run the model. Let the gas come to an equilibrium distribution of speeds in the upper chamber. Then open the window and watch the plot of numbers of molecules above and below the window. Does its match your prediction as time goes by?

Observation:

Try changing the size of the window opening. This is done with the slider WINDOW. "100" means 100% of the width of the box. Does the size of the opening affect the behavior of the model?

Observation:

If you open the window and then close it again, you can "trap" the model in a new state. Can you make two chambers with the same number of molecules, but with different average energies, hence with different temperatures? If you can, is this a violation of the Second Law of Thermodynamics, since youšve created two heat reservoirs at different temperatures out of a single heat reservoir, without doing any work?

If you left the window open long enough, would the gas ever return to its original state namely, all the molecules above the window? If not, then this would appear to be an "irreversible" situation. Why would any mechanical system be irreversible?

We are told that a gas cools as it expands a fire extinguisher, for example. Does it appear to be true in this model? If not, what do you make of that statement?

Authors: Edmund Hazzard and Uri Wilensky

Copyright 2000 by Uri Wilensky. All rights reserved. Permission to use, copy, o r modify this software and its associated documentation, models and curricular m aterials for educational and research purposes only and without fee is hereby gr anted, provided that this copyright notice and the original authors' names appea r on all copies and supporting documentation. For any other uses of this softwar e, in original or modified form, including but not limited to distribution in wh ole or in part, specific prior permission must be obtained from Uri Wilensky. Th ese programs shall not be used, rewritten, or adapted as the basis of a commerc ial or hardware product without first obtaining appropriate licenses from Uri Wi lensky. We make no representations about the suitability of this software for an y purpose. It is provided "as is" without express or implied warranty.

Investigation (C1): Free Expansion of a Gas Model: Free Expansion
What happens to a gas as it expands into an empty space? What does this simple situation teach us about thermodynamics?
Open the model Free Expansion. When you push SETUP you will see a box with two chambers. The upper one is filled with molecules and lower one is empty. With the buttons you can open and close a window between the two chambers. When the model is run, the molecules collide as in Gas in a Box. It allows you to simulate free expansion of a gas into a vacuum and keep track of things that are very difficult to measure in nature.
Before you run the model, make some predictions about what will happen when you open the window. It seems likely that molecules will make their way into the empty chamber. How fast will they do it? Will there ever be an equal number of molecules in the upper and lower chambers? How long will it take for the system to reach a steady state, if indeed it does? Do a sketch of the plot of numbers of molecules above and below the window.
[add labeled plot here to draw on]
But what will happen to the energy of the gas? What about the average speed of the molecules?
How will these values compare for the molecules in the upper and lower chambers? Will they eventually be the same?
Now run the model. Let the gas come to an equilibrium distribution of speeds in the upper chamber. Then open the window and watch the plot of numbers of molecules above and below the window. Does its match your prediction as time goes by?
Observation:
Try changing the size of the window opening. This is done with the slider WINDOW. "100" means 100% of the width of the box. Does the size of the opening affect the behavior of the model?
Observation:
If you open the window and then close it again, you can "trap" the model in a new state. Can you make two chambers with the same number of molecules, but with different average energies, hence with different temperatures? If you can, is this a violation of the Second Law of Thermodynamics, since youšve created two heat reservoirs at different temperatures out of a single heat reservoir, without doing any work?
If you left the window open long enough, would the gas ever return to its original state namely, all the molecules above the window? If not, then this would appear to be an "irreversible" situation. Why would any mechanical system be irreversible?
We are told that a gas cools as it expands a fire extinguisher, for example. Does it appear to be true in this model? If not, what do you make of that statement?

Authors: Edmund Hazzard and Uri Wilensky
Copyright 2000 by Uri Wilensky. All rights reserved. Permission to use, copy, o r modify this software and its associated documentation, models and curricular m aterials for educational and research purposes only and without fee is hereby gr anted, provided that this copyright notice and the original authors' names appea r on all copies and supporting documentation. For any other uses of this softwar e, in original or modified form, including but not limited to distribution in wh ole or in part, specific prior permission must be obtained from Uri Wilensky. Th ese programs shall not be used, rewritten, or adapted as the basis of a commerc ial or hardware product without first obtaining appropriate licenses from Uri Wi lensky. We make no representations about the suitability of this software for an y purpose. It is provided "as is" without express or implied warranty.