In the kinetic theory of Gases , we rely purely on classical mechanics. We derive the equations using classical mechanics, and they turn out to be fairly accurate at ideal gas approximation condition of low pressure and high temperature. Now my question is, since in the kinetic theory , we are considering the collisions of atoms or molecules, why does classical theory give accurate results? In view of the uncertainity principle ,Ideally, Quantum theory should be applied?
I think quantum effects become appreciable when we go beyond the conditions for which the ideal gas equation gives approximately correct answers,for example when we go to very high temperatures and the collisions become exciting or ionising.
So much of the kinetic theory is nearly true regardess of the differences between classical and quantum mechanics. For example, the assumption that the spaces between molecules are so much larger than the sizes of the molecules that it's nearly the case that molecules exert no forces on each other except very briefly during collisions, and collisions are elastic, so you can use a statistical description of independent particles traveling in straight lines most of the time, and having a normal distribution of speeds, random amounts of x,y and z components of velocity, their collisions with walls being the underlying cause of pressure on the walls, etc. Most of these assumptions and line of reasoning in the kinetic theory are not dependent on whether you have classical particles or quantum mechanics. One exception would be the calculation of a mean free path (mean distance between collisions among molecules) with a formula that has been derived with the assumption that molecules are spheres. I don't know the amount of error introduced by treating molecules as classical spheres. It is often assumed for much of the kinetic theory that molecules are geometric points, having zero probability of colliding with one another, and colliding only with the walls, but then this point mass assumption has to be dropped to permit an estimation of the mean free path.