# Two particles, take a guess: same velocity or same momentum or same kinetic energy?

1. Mar 26, 2012

### 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"

2. Mar 26, 2012

### Vorde

Re: two particles, take a guess: same velocity or same momentum or same kinetic energ

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.

3. Mar 26, 2012

### nonequilibrium

Re: two particles, take a guess: same velocity or same momentum or same kinetic energ

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

4. Mar 26, 2012

### Vorde

Re: two particles, take a guess: same velocity or same momentum or same kinetic energ

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.

5. Mar 26, 2012

### K^2

Re: two particles, take a guess: same velocity or same momentum or same kinetic energ

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.