Kinetic Theory of Gases: Why do gas molecules have translational motion? The title pretty much asks the question.  I was reminded of the Kinetic Theory of Gases recently and I am puzzled as to why gas molecules would have any translational motion.  Is it because collisions are presumed to be perfectly elastic, like billiard balls bouncing around on a billiard table forever after a break?  If so, where does the initial momentum come from?
 A: Translational motion just means linear 'velocity'. That is, motion 'across-ways' (ie: in x-, y- and z- directions). So the question can be rephrased as 'why do molecules have velocities'? Well, if they didn't, everything would be realtively motionless, there would be nothing happening in the universe and you wouldn't be able to ask the question and we wouldn't be able to hear, see, think or for that matter, do anything!
It aught to come as no surprise that molecules like to move in 'straight lines', until they 'bump' into another molecule and change momentum. This change in momentum is 'mediated' by 'quantum of electromagnetic radiation' called a 'photon', which has momentum $p=h/\lambda$. To put it in simplistic terms, when the molecule absorbs the energy if the photon, it gets 'excited' to a higher energy state. This higher energy state is less 'stable' than the lower energy states, so in some brief time later, it is likely to drop to a lower energy state and emit a photon with energy equal to the difference between the two energy states. This photon will (most likely) have a momentum different to the original photon absorbed (in direction and/or magnitude). The molecule will subsequently 'recoil' in a different direction. Repeat this billions of times per second for a large number of molecules and voila => Kinetic theory of gases.
Actually, molecules can generally absorb energy into a various 'modes', including:


*

*translational (move from one place to another => linear momentum)

*rotational (turn around => angular momentum)

*vibrational (oscillate)


This last one (vibrational modes) is probably the most complex, especially for large molecules with lots of bonds which can 'stretch, bend and twist'... but thats a topic for another question.
The 'ideal' gas which forms the basis of the kinetic gas theory ignores rotational and vibrational modes, which is usually valid for monatomic gases such as helium.
A: Molecular motion is a manifestation of heat. Even at absolute zero, molecules in their ground state, have a zero-point energy ($\ne 0$), in the form of molecular vibrations. As temperature rises, rotational and other vibrational modes get excited. Translational motion arises as the solids melt into liquids or sublime into gases. (For materials, like Helium, that remain in liquid state even very close to absolute zero, the translational motion never ceases.)
