This is much longer than the normal post, so please bear with me. I was wondering if anyone here knows the complete derivation of Ideal Gas Law (or can recommend a book that describes it clearly and fully), who can tell me whether its conclusions are valid for any shape of gas particle, and if so, why. Please read on, however, to see where I'm coming from. Specifically, I'm interested in exploring the behavior of a dilute gas of uniquely shaped, infinitely hard particles that experience no forces other than impacts with other such particles, in which case they recoil instantly. They experience no friction, and by "dilute gas," I mean their occupation volume is much less than 1%, such that they normally travel many particle lengths between collisions. They are long rods with a "reverse toothpick" shape (i.e., the ends are fatter than the middle), and thus have a long and gradually sloping concave shape throughout their midsection (when viewed from the side). Their extreme tips, however, are tapering, like those of a regular toothpick, but also have a concave shape (also viewed from the side). Let's call these particles "batons" (similar to the kind band majorettes twirl), and we'll call their major axis the z-axis. Their thin midsection can be called a "waist", and the broadened ends can be called "hips" and "shoulders." (No jokes, please!) They also have an essentially infinite axial spin rate in relation to their linear velocities, such that in their collisions, their orientation in space does not change, and they do not precess appreciably. I'm wondering if a huge collection of randomly oriented such batons might not experience a "self-organizing" effect, such that like-oriented batons tend to aggregate to some extent, and the equilibrium state of such a gas would thus not be one of maximal entropy as normally conceived. The motivation for this mental exercise is the thought that convexly shaped objects naturally scatter at random angles during collisions, but that concave objects might not. And, spherical objects, even if concave on one side (i.e., if shaped like a bean-bag chair), would still be largely convex. But for extremely linear objects such as I've described, there could be a strong directional component to their mutual viscosity. To begin with, realize that for these thin batons, their preferred direction of motion is sideways, as they're much more likely to be hit on the side than on the very end, in the z-direction. But, those rare collisions with predominant z-axis approach angles would bring the particles' gentle concave curves into alignment, and this type of collision would consist of multiple, sliding-type contacts which would thrust the particles more into an x-y plane of relative motion, like a ski-chute. The same is true for almost all collisions that have any z-axis component, due to the batons' unique shape. (I should probably post a drawing to illustrate this, but don't have one at the moment.) For a spherical "flock" of such particles that happens to occur randomly, they might pack together more tightly, owing to their geometry (they can pack closer when lined up), and their mutual collisions would be such as to "lock" them together (i.e., waist of one baton locked with hips and shoulders of colliding, adjacent batons -- acting to prevent z-axis escape), while surrounding batons, having different orientations in space and hence much greater collisional cross-sections, would tend to keep them bunched together. I'm wondering whether space might not then become organized into regions of like-oriented batons, each region perhaps surrounded by orthogonally oriented flocks of batons. So, what I'd like from folks here is a general discussion of the collisional dynamics in relation to Ideal Gas Law and/or statistical mechanics. Does Ideal Gas Law really tell us that such a gas would not engage, to any degree whatsoever, in such spatial partitioning? Either way, I'd like to know what the thinking is. Thanks for reading!