Difficulty with Feynman's chapter on kinetic theory of gases

Question

I have been reading Chapter 39 of the Feynman Lectures in Physics. In this section he argues that collision between gas molecules will mix up their directions of motion such that ultimately any direction of motion will be equally likely. In particular he says:

Suppose, for a moment, that we watch all the collisions with the CM at rest. Suppose we imagine that they are all initially moving horizontally. Of course, after the first collision some of them are moving at an angle. In other words, if they were all going horizontally, then at least some would later be moving vertically. Now in some other collision, they would be coming in from another direction, and then they would be twisted at still another angle. So even if they were completely organized in the beginning, they would get sprayed around at all angles, and then the sprayed ones would get sprayed some more, and sprayed some more, and sprayed some more. Ultimately, what will be the distribution? Answer: It will be equally likely to find any pair moving in any direction in space.

My question is, if the gas molecules were point massess moving horizontally then shouldn't they continue to move horizontally after the collision? How then would we have the mixing?

In the figure above the quoted passage the molecules are depicted as spheres. If they really are spheres then they can hit each other at glancing angles and it is plausible that the directions of motion will get mixed up. Is this a correct reading of Feynman's logic? Or will his argument work even when the gas molecules are points?

Answer 1

I don't think of molecules as infinitely small points. If so, then as you are implying, there would be no reason for a head-on collision to go in another direction.

The reality is that there is a scattering cross-section. The nuclei don't actually collide when molecules collide. The collision is really an interaction of electric fields. As such, there is an interaction distance. In a sense, this scattering cross-section is a measure of the size of the molecule (or the size of its influence).

Now that we've added a diameter to the molecules, it is easy to imaging how two molecules traveling in the opposite direction, but slightly displaced, could result in a scatter in with a component in the orthogonal direction.

Now we have a motivation for your description of glancing angles.