The next two problems use the program THERMO *. This program simulates the motion of gas molecules in a two-dimensional box. The molecules have a size equal to 1 pixel (point) on the screen. You can do many things with this program. To control it: Note the menu bar at the top of the screen. You can select any of the items from the menu bar by pressing the highlighted letter. A menu will pop down. Continue selecting using the highlighted letter. When you have selected the item you want, press <ENTER>. Then press <ESCAPE> until all the menus disappear except the main menubar. You will know you have pressed it enough times if it says "Spacebar to toggle run/stop" in the upper left. Then use the spacebar to start and stop the program. Note the status bar at the bottom of the screen. This tells you which forces and view options are turned on. (The ones turned on are displayed in white.)

1. Reset the parameters in THERMO by selecting Data/Read settings/Settings from the menu bar. A box should appear that says "Settings.dat". Press <ENTER> to accept this and then press <ESCAPE> until you are back in the simulation. This should reset the parameters as follows: number of particles = 500 reset type = mono square box size = 100x100 histogram = on histogram type = velocity forces = none You can reset these values yourself one at a time using the menubar or you can do them all by selecting <KeyIn> and following the instructions there.

(a) Start the program using the spacebar and observe both the histogram and the distribution of the particles in the box as the particles move.
(b) Let the program run for a few minutes until the particles are reasonably uniformly distributed in the box.
(c) Turn on collisions and let the system continue to evolve.

Describe your observations at each step in a few sentences.
Were the particles in equilibrium at the end of step (b)? At the end of step (c)? Explain.

2. Start with the conditions you finished the last problem with.

(a) Turn on Trace by selecting Screen/Trace and pressing <ENTER>. This will display one of the particles' paths and hide the rest.
(b) Watch the motion of the particle until it travels at least 5 times the size of the box. How often does it collide in this time?
(c) Turn on gravity.

Watch the path of the particle for at least four or five bounces. Describe the paths. Use your observations to discuss the question: If the particles fall in a gravitational field, and if they lose energy by colliding with other particles, why doesn't the whole gas "run down"? That is, why don't all the particles eventually lie at the bottom of the box at rest with all their energy dissipated?

a. Suppose that the molecules of water are close-packed. From the density of water and Avogadro's number, estimate the approximate linear dimensions of a water molecule (i.e., how big is it measured from one end to another).
b. The program THERMO simulates a gas of molecules in a two-dimensional box. In H&R the derivation of the equation of state of an ideal gas was given, but in three dimensions. Reconstruct this derivation in two dimensions and indicate whether or not PV = NkT is true in 2D as well as in three.