We use finite number of particles to simulate the real system. In the simulation we did not take into account collisions between particles. The collision between particles and wall are treated as elastic collision. Due to the limited number of particle (200 as default), the simulation will show deviation from equilibrium state. In the real world, there are 10[sup]19[/sup] particles cm[sup]3[/sup]. The statistatic error is inverse proportional to squar root of the number of particles. So we can measure fix number of pressure or volume in real world when the system is in equilibrium. But we can not reach that goal for a real simulation with only several hundred of particles.

[1] When we change the width of the chamber we get different volumes even though we are keeping the same values for the variables. Do you why this would happen?

R: User can drag the boundary to change the boundary for the chamber. The simulation will move back to new equilibrium condition. As long as "Pressure" and "number of particles" and "average velocity" are not changed, the volume should return back to the original value. The deviation is due to statistatic error as explained above.

[2] When the piston is near the top or bottom of the chamber the instantaneous volumes shows greater deviations than when the piston is more centered vertically. Is there a reason for this?

R: The velocity in the simulation is much smaller than that in the real world. If we put the velocity in the simulation close to the real case, you would not be able to see any of the particles. Because it will be too fast. In real world, the velocity of the particle in room temperature is several hundred meter per second. And the size of the chamber usually are less than meter. The deviation is due to the velocity is too small.

[3] Sometimes the bottom line of the piston disappears above the top of the chamber and the volume output is essentially constant. Are the instantaneous volumes collected valid when the piston moves out of sight or have we exceeded the limits of the algorithm?

R: The volume output should change when the piston move above the top of the simulated region. It is not a constant. I do not why you said it is essentially a constant.

[4] Can you tell us the units for the parameters used to calculate the volumes? Also, are the particles considered to have volumes or are they treated as point particles?

R: The particles did not considered to have volumes in the simulation. The volume in the simulation is calculated from width* height in unit of pixel divided by 1000.

[5] If the students generate three proportionality constants by varying each parameter individually, would you expect that they could derive a combined proportionality constant that would correctly predict the volume of gas when all three parameters vary? This would be a constant for the simulation analogous to the ideal gas law constant, R.

R: you will find the volume of the gas is propotional to number of particle, square of velocity and inverse propertional to pressure.

So Pressure*Volume= N * k * velocity

You can ask students to find out the constant k.