# When two individual gas molecules collide, do they transfer energy via work or heat?

Suppose we have a stationary billiards ball. Roll a cue ball so it hits the billiards ball, and the billiards ball starts moving. We would say that the cue ball does work on the billiards ball. That work can be calculated from the forces and displacements during the collision. If our collision is perfectly elastic, then presumably all the energy transferred it transferred via work.

Now suppose one gas molecule collides with another. This situation would seem to be the same; there's an elastic collision; energy should be transferred as work.

But now suppose there is a whole room full of heavy cold gas on bottom and light warm gas on top. Now we would say that heat flows through the gases via conduction, entropy is generated, etc. But at no point is there any physical process besides simply a collision between molecules. If the energy transfer is just a bunch of intermolecular collisions, each of which transfers energy via work, why is energy transferred via heat from the macroscopic perspective?

If all the above is correct, it would seem there is some sort of transition where as the number of molecules increases, energy transfer changes from work to heat, or else with some change of perspective from a microscopic to macroscopic description the energy transfer changes from work to heat. But in that case, why should things like the second law of thermodynamics depend on your choice of perspective, or the number of molecules in your system?