Why do randomly flying gas molecules have a distribution of energies? This is a question from my chemistry textbook (not homework, just questions to help us think about and understand the concepts). The professor is very unclear. To make matters worse he uses a textbook that he wrote himself. I can't understand what exactly the professor is asking in the review question.
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$\begingroup$ Does your professor's book at least have a definition about "a distribution of energies"? Taking the term generally, just about everything has. $\endgroup$– Gyro GearlooseCommented Jan 13, 2016 at 20:01
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3$\begingroup$ @juicebox as the question is supposed to help you think, it would be nice for you to post your thoughts on in. Why do you think the molecules don't have the the same energy? Might them all be moving with the exact (or almost exact?) same speed? Or is it reasonable for them to have randomly distributed velocities/energies? $\endgroup$– AccidentalFourierTransformCommented Jan 13, 2016 at 20:14
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$\begingroup$ From the other side. Why would expect randomly flying gas molecules to all have the same energy? en.wikipedia.org/wiki/Root-mean-square_speed $\endgroup$– paparazzoCommented Jan 13, 2016 at 23:11
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When two balls hit each other elastically, energy and momentum are conserved - but they don't usually leave the collision with the same velocity.
Each air molecule is like a ball, and at every collision there is a possible distribution of velocities. There is a very small probability that a molecule will be either much faster than all the others, or much slower; but there is even less chance that they would all be the same.
If you feel brave, you could read these notes which describe one possible approach to the derivation of the Boltzmann distribution. The argument there is that if you have many particles with a certain total energy, and you divide that energy randomly between the particles, the Boltzmann distribution "appears". It may be more detail than you need...
