Two Particles in a Box: Similar Velocities, Momentum, or Kinetic Energy?

[nonequilibrium]

Hello,

Say you have a box with two (interacting) particles in them. If you had to venture a guess, what would be most reasonable: that they both have similar velocities, similar momenta or similar kinetic energies? (Or perhaps none of the above?)

NB: with "similar" I mean "of comparable magnitude"

 

[Vorde]

I'd say that this question can't probably be answered in a general way. If the interaction involved is physical (like the two particles bouncing into each other), my guess would be that over an arbitrarily large amount of interactions the two particles momenta would approach equality. I would say neither of the other two values would approach each other, and that this situation would change if the interaction changed.

 

[nonequilibrium]

And why would you think that the momenta would approach equality?

 

[Vorde]

More a guess than anything, it seems to be than in realistic collisions between two bodies the difference in momentum would be less after the collision.

 

[K^2]

Actually, there is a theorem in Thermodynamics that states that on average, available energy is distributed equally between available degrees of freedom. That means that if particles are identical, they will, on average, have equal kinetic energies.