How will accelerating a container with an ideal gas in it affect the conditions? My initial thoughts are that the ideal gas will collect at the opposite end of acceleration, which means that the volume drops. According to the formula $PV = nRT$, either the pressure or the temperature would have to raise as well. Firstly, which quantity would rise if I just squeezed a gas in normal conditions? I don't see how I can differentiate between squeezing isothermally and squeezing isobarically, so would they both rise? Upon further thought however, we are already experiencing 9.8 metres per second squared acceleration, and that has minimal effect at low heights. So does this mean at low accelerations the afore-mentioned effect can be ignored?
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In the case of the atmosphere, we usually assume that the stationary atmosphere is adiabatic, that is, there is very little transferral of heat between regions of different height . Combining hydrostatic equilibrium with the adiabatic law of an ideal gas gives you a variation of temperature (and pressure) in the direction of acceleration.
Check out Richard Fitzpatrick's notes for a good discussion.
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