Simulate the mixture of gas molecules. Solve Exercise 8.39 when the wall dividing the box is not completely removed, but instead we make a small hole in the wall initially. Name of program file:...

Simulate the mixture of gas molecules. Solve Exercise 8.39 when the wall dividing the box is not completely removed, but instead we make a small hole in the wall initially. Name of program file: disorder2.py.

Exercise 8.39

Simulate the mixture of gas molecules. Suppose we have a box with a wall dividing the box into two equally sized parts. In one part we have a gas where the molecules are uniformly distributed in a random fashion. At t = 0 we remove the wall. The gas molecules will now move around and eventually fill the whole box. This physical process can be simulated by a 2D random walk inside a fixed area A as introduced in Exercises 8.37 and 8.38 (in reality the motion is three-dimensional, but we only simulate the two-dimensional part of it since we already have programs for doing this). Use the program from either Exercises 8.37 or 8.38 to simulate the process for A = [0, 1] × [0, 1]. Initially, place 10000 particles at uniformly distributed random positions in [0, 1/2] × [0, 1]. Then start the random walk and visualize what happens. Simulate for a long time and make a hardcopy of the animation (an animated GIF file, for instance). Is the end result what you would expect? Name of program file: disorder1.py. Molecules tend to move randomly because of collisions and forces between molecules. We do not model collisions between particles in the random walk, but the nature of this walk, with random movements, simulates the effect of collisions. Therefore, the random walk can be used to model molecular motion in many simple cases. In particular, the random walk can be used to investigate how a quite ordered system, where one gas fills one half of a box, evolves through time to a more disordered system.