Equilibrium and Elastic Collsions

Hi,

In working out the perfectly elastic collision of two spherical
particles of equal mass, I noticed that the solution was very simple:
they just excahanged velocities! (It is easy to see this if you
transform the problem to the rest frame of one of the particles).

This made me wonder about the implications of this result, and I came
up with the following thought experiment which I have not yet been able
to resolve to my satisfcation.

Consider a monatomic ideal gases kept in a perfectly insulated
container with temperature T1. Now consider the same type of gas in a
second perfectly insulated container at a lower temperature T2. Now
suppose we open a valve between the two gases and let them mix. What is
the final velocity distribution of the mixture? It seems that the
standard thermal physics/stat mech result is that the they come to
equilibrium and assume a Maxwell-Boltzmann distribution for some
temperature T, T2<T<T1. Intuitively, I think of this as the hotter gas
"warming up" the other, so that the hotter gas loses energy at the
expense of the colder gas gaining energy. But, based on the result that
ideal spherical particles of the same mass undergoing perfectly elastic
collisions simply exchange energy, this would suggest that the final
speed distribution would be the weighted average of the two
distributions from the mixed species. Moreover, the cold gas never
"warms up"; instead, the colder particles persist, and they simply get
swapped between particles during each collision like a game of "It".

What feature of real gases prevents the persistence of two distinct
populations like this even when they are mixed? Is it the
non-idealities in the gases (esp their collisions), and how can we see
that this feature leads to what we expect to see (i.e. a
"homogenization" of the two populations as they come to equlibrium).

Thanks for your thoughts,

Matt

.

Relevant Pages

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