NetLogo Models Library:
This model simulates the behavior of gas particles as the volume changes. In this model, the volume is slowly changing over time by a piston that is rising and falling. As the piston lowers, the volume of the box decreases and as the piston rises, the volume of the box increases. This systematic motion of the piston does no work on the particles inside the box. The piston only serves a mechanism to change the volume of the box.
The particles start with the same mass and speed upon the start of the simulation. The mass of the particles stays constant throughout the simulation, whereas, the speeds will change once particles start to collide. Particles are in constant motion colliding with other particles and the walls. All collisions are modeled as elastic collisions, in that the total kinetic energy before and after the collision is conserved. For example, when a fast moving particle collides with a slow moving particle, the fast moving particle will give some of its speed to the slow moving particle. Therefore, the fast moving particle will leave the collision moving slower then when it entered the collision. And the slow moving particle will speed up a bit. The speed in a particle to particle collision is still conserved. The collisions between a particle and a wall is modeled the same way. When the particles hit the wall they transfer momentum to the wall. After this transfer occurs, the particles then bounce off the wall with a different direction and speed. The system's pressure is calculated by averaging the number of collisions the particles have with the walls at each time step.
The Moving Piston model is one of a collection of GasLab models that use the same basic rules for expressing what happens when gas particles collide. Each model in this collection has different features to show the different aspects of the Gas Laws.
Multiple adaptations of this model can be found in the Chemistry folder of the Curricular Models section under the names Chem Volume 1 and 2. It is part of a suite of models used to teach students about the chemistry of the Gas Laws.
The particles are modeled as single particles, all with the same mass and initial velocity. Molecules are modeled as perfectly elastic particles with no internal energy except that which is due to their motion. Collisions with the box and between molecules are elastic. Particles are colored according to speed -- blue for slow, green for medium, and red for high speeds.
The exact way two particles collide is as follows: 1. Two turtles "collide" if they find themselves on the same patch. 2. A random axis is chosen, as if they were two billiard balls that hit and this axis was the line connecting their centers. 3. They exchange momentum and energy along that axis, according to the conservation of momentum and energy. This calculation is done in the center mass system. 4. Each turtle is assigned its new speed, energy and heading. 5. If a turtle finds itself on or very close to a wall of the container, it "bounces" -- that is, reflects its direction and keeps its same speed.
SETUP - puts in the initial conditions you have set with the sliders. Be sure to wait till the SETUP button stops before pushing GO. GO - runs the code again and again. This is a "forever" button.
BOX-HEIGHT - height of the container BOX-WIDTH - width of the container NUMBER - number of particles PISTON-SPEED - rate of the piston SCALE - number of clock cycles over which to average the pressure
HISTOGRAM? - turns histograms on or off
VOLUME - plots the volume over time PRESSURE - plots the pressure over time PRESSURE VS. VOLUME - plots pressure over volume PRESSURE * VOLUME - plots the value of pressure * volume over time TEMPERATURE - plots the average temperature SPEED HISTOGRAM - illustrates the number of particles at their various speeds ENERGY HISTOGRAM - illustrates the number of particles at their various energy levels
Adjust the BOX-HEIGHT, BOX-WIDTH, NUMBER, and PISTON-SPEED variable before pressing SETUP. The SETUP button will set the initial conditions. The GO button will run the simulation.
In this model, though, the collisions of the piston with the particles are ignored. Note that there's a physical impossibility in the model here: in real life if you moved the piston down you would do work on the gas by compressing it, and its temperature would increase. In this model, the energy and temperature are constant no matter how you manipulate the piston. Nonetheless, the basic relationship between volume and pressure is correctly demonstrated here.
How does the pressure change as the volume of the box changes? Compare the two plots of volume and pressure.
How does the pressure change as the shape of the box changes?
Measure changes in pressure and volume. Is there a clear quantitative relationship?
How can the relationship between pressure and volume be explained in terms of the collisions of molecules?
How does more particles change the relationship between pressure and volume?
What shapes do the energy and speed histograms reach after a while? Why aren't they the same? Do the pressure and volume affect these shapes?
How would you calculate pressure? How does this code do it?
Change the number, mass, and initial velocity of the particles. Does this affect the pressure? Why? Do the results make intuitive sense? Look at the extremes: very few or very many molecules, high or low volumes.
Figure out how many molecules there really are in a box this size --- say a 10-cm cube. Look up or calculate the real mass and speed of a typical molecule. When you compare those numbers to the ones in the model, are you surprised this model works as well as it does?
Are there other ways one might calculate pressure?
Create an isothermal piston example where the user can manually move the piston to any level in the box.
Add in a temperature variable that allows for the particles to move the piston to the appropriate volume.
Notice how collisions are detected by the turtles and how the code guarantees that the same two particles do not collide twice. What happens if we let the patches detect them?
This model was developed as part of the GasLab curriculum (http://ccl.northwestern.edu/curriculum/gaslab/) and has also been incorporated into the Connected Chemistry curriculum (http://ccl.northwestern.edu/curriculum/ConnectedChemistry/)
If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.
For the model itself:
Please cite the NetLogo software as:
Copyright 2002 Uri Wilensky.
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at firstname.lastname@example.org.
This model and associated activities and materials were created as part of the project: MODELING ACROSS THE CURRICULUM. The project gratefully acknowledges the support of the National Science Foundation, the National Institute of Health, and the Department of Education (IERI program) -- grant number REC #0115699. Additional support was provided through the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT -- NSF (REPP & ROLE programs) grant numbers REC #9814682 and REC-0126227.