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I'm trying to explain this to my 8th grade brother. But I don't seem to understand this fully... I keep getting stuck because of my poor knowledge in thermodynamics. I'd like to ask a related question first :

1) I know that the energy decreases in an adiabatic expansion. This is because the gas molecues do the work on the piston and push it up, increasing the volume. But what happens if I push the piston up instead of the gas molecules ?(like, pulling a syringe) Would it still be called an adiabatic expansion ? I'm not adding any heat / matter to the system. So I think this should still be an adiabatic process. If so, the energy of the system shouldn't decrease as the gas didn't do any work. I did the work. Something wrong in my reasoning ?

2) Here is the actual question : Does the kinetic energy of an individual water molecule (vapor) decrease as it goes up in the atmosphere ? Or is it just the average kinetic energy that gets decreased due to low density at higher altitudes ? Also is this average, over space or is it over the number of molecules ? If the average is over space, then low density explains why the average kinetic energy decreases. If the average is over number of molecules, I don't get why the average kinetic energy decreases... Appreciate any help. Thank you !

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1) Yes, it is still an adiabatic process because no heat is transferred as you said. If you can manage to pull the syringe stop fast enough that the gas molecules can't keep up with it and put pressure on it, then yes all of the work is done by you and the internal energy of the system will not change. In any realistic scenario though, the gas will maintain more or less constant pressure on the syringe stop, so the work done by the gas will be the force it's exerting on the syringe stop times the distance the syringe stop moves. In other words, you're only doing part of the work.

2) The average is over the number of molecules. Density has nothing to do with it. Individual molecules do, on average, lose kinetic energy as they go up. Imagine just a single molecule moving upwards: it will obviously lose kinetic energy due to the gravitational pull. When we have a bunch of molecules, it's possible for this loss in kinetic energy due to gravity to be counterbalanced by getting hit at just the right angles by other molecules, but on average the kinetic energy of a single molecule will decrease.

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  • $\begingroup$ Thank you! This answers a lot of my questions. 1) So we just consider the work that is done by the gas molecules and subtract the work done by me from the total work. Awesome! 2) It seems gravity is the reason for cooling of gas at higher altitudes ? If we visualize a gas molecule as a projectile, it is under the influence of gravity, so its KE must decrease as its PE increases. Makes sense I guess... I'll give it more thought. Thank you so much (: $\endgroup$ – Hiiii Mar 10 '17 at 16:50

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