This model illustrates various kinematical properties of multi-particle collisions. There are three setups. The first is a random ball setup that involves two types of balls separated by a barrier when the barrier is removed the balls interact and their speed and velocities change as a result of the interactions. This illustrates that at equilibrium the average kinetic of different types of interacting particles is approximately equal. The second setup involves just two balls colliding. This illustrates the symmetry of two particle collisions under time reversal. The third setup involves one ball colliding with six other balls which are arranged in an ordered arrangement. After the collision a disordered arrangement results, but when time is reversed the ordered arrangement reappears. This illustrates that the apparent time asymmetry in natural phenomena is actually the result of finally tuned (or far from equilibrium) initial conditions.
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Balls move in a straight line with a particular speed until there is a contact collision. A ball may collide with others balls, the walls and the barrier as appropriate. Kinetic energy is conserved in all collisions. Momentum is conserved in collisions between balls. In the simulation each ball checks when it will collide with another ball, wall or barrier. The simulation then steps forward in time until the first collision occurs. The velocities of the colliding balls is updated according to the standard conservation of energy and momentum rules
Choose a setup option, then click setup and go.
Random Balls Option: Here there are red balls on the right and blue balls on the left. Their number, speed and mass can be set with sliders. When the simulation first runs the barrier is in place and the two types of balls bounce in their own chambers, much like two different ideal gases with different temperatures and pressures. When the barrier is removed the two sets of balls interact.
Two Balls Option: Here their are only two balls which are arranged so that they collide. After the collision occurs press the reverse time button. You should see that they collide again. The reverse process does not seem unusual or unexpected. This is because Newton's Laws or symmetric under time reversal.
Order Balls Option: Here one ball (the cue ball) collides with an ordered arrangement of essentially stationary red balls (they actually have very small initial velocities to avoid what is usually the vanishingly unlikely chance of three balls colliding at exactly the same time). After the collision, balls move in a random fashion around the screen. Press the reverse time button and you should see the balls return to their original position
Random Balls Option: When the red and blue balls interact you should see that the average kinetic energy of the balls ends up being approximately equal, regardless of the mass, number or initial speeds of the balls. The temperature of an ideal gas is a measure of the average kinetic energy of the gas molecules, so what happens is that as the gases mix they also reach the same temperature. The average speeds are not equal unless the masses of the balls are the same. You should see that lighter balls end up moving much faster. This effect is also true in gases. The speed of sound is much faster in Helium than Air because Helium atoms are much lighter (and hence move much faster) than the molecules of Oxygen and Nitrogen that make up most of Air.
Two Balls and Ordered Balls Option: You should notice that when time is reversed in the two balls option, the balls collide in much the same way as they did originally. Nothing seems to be unusual. However in the Ordered Balls option, when time is reversed a bunch of randomly moving balls suddenly converge into an ordered arrangement. If we observed this in a movie we would assume that time is going backwards. Infact, all that we have done is reversed the velocities of all the balls. In effect we have finely tuned the initial conditions so that an ordered arrangement occurs in the future. Such finally tuned initial conditions are extremely unlikely to occur by chance, which reflects the increase in entropy as a result of the collision
In this model the barrier does not move. It would be interesting to allow the barrier to move when hit by a particle. This could be done by assigning it a position, mass and velocity. The velocity would be modified after a collision according to conservation of momentum, and the position would be updated during each time step. The detect-barrier-collision procedure would need to be modified slightly to account for the moving barrier. With a moving barrier it would be possible to illustrate pressure related gas laws of thermodynamics.
See the other Entropy Models in this series
Copyright 2006 David McAvity
This model was created at the Evergreen State College, in Olympia Washington
as part of a series of applets to illustrate principles in physics and biology.
Funding was provided by the Plato Royalty Grant.
The model may be freely used, modified and redistributed provided this copyright is included and it not used for profit.
Contact David McAvity at mcavityd@evergreen.edu if you have questions about its use.