We can derive the Ideal Gas Law
from Kinetic Theory, and Einstein and others used Kinetic Theory successfully.
The expression for gas pressure developed
from kinetic theory relates pressure and volume to the average molecular kinetic energy.
For three different formal demonstrations (
from kinetic theory, stochastic, and from the Bolzmann distribution in phase - space) you can consult sections B, C and D of this paper:
Not exact matches
And researchers
from the University of Massachusetts at Amherst have now come up with an elegant way of describing grains that are shaken, drawing a direct analogy to the century - old
kinetic theory of gases.
Our research approach includes spacecraft observations (
from missions such as Cluster, THEMIS, MMS, Parker Solar Probe, Solar Orbiter), large scale
kinetic simulations, and fundamental plasma
theory to understand plasma phenomena throughout the universe.
He soaked up
kinetic theory from artists like Jean Tinguely and Lucio Fontana and evolved the concept of the immateriality of color pioneered by Yves Klein.
A paper that Joules Verne, of all people, sent to me that examines this extreme limit shows explicitly that if there is a thermal lapse across this gas it has a weak asymmetry in its conductivity that makes gas relax thermal gradients
from top to bottom slightly faster than it does gradients
from bottom to top, but the split smoothly vanishes as the gradient does, strongly suggesting that even in this limit if we (correctly) require that the length of a vertical parcel to be much greater than the MFP (and hence much much greater than) the bulk averages will still satisfy the usual
kinetic theory and I have a sneaking suspicion that overall they will still satisfy the MB distribution, even though the average itself will be extremely odd.
An averaging process is involved going up
from the atomic scale via
kinetic theory to the level of fluid motions, but chaos emerges at that scale (ie the averaged quantities exhibit chaotic behaviour).