Wednesday, 19 August 2020

thermodynamics - How do you explain the fact that when air expands freely into an evacuated chamber from a constant pressure atmosphere, its temperature increases?


I came across this paper:



Baker, B. (1999). An easy to perform but often counterintuitive demonstration of gas expansion. American Journal of Physics, 67(8), 712-713. http://scitation.aip.org/content/aapt/journal/ajp/67/8/10.1119/1.19357



And I didn't fully understand the explanation. I can't see how this is any different from the Joule free expansion experiment with no temperature change.


Essentially the author of the article says that the atmosphere does work on the gas and increases its internal energy. This is the reason for the temperature increase. However wouldn't that logic also lead to a temperature increase in the joule free expansion?


Any insight would be much appreciated.



Answer




There is a huge difference with the usual Joules experiment. Here the system is not isolated during the gas expansion into the evacuated chamber. Two things enter in competition in principle when a setup as the one considered in the article you mention is considered:



  • Whether the gas has to work to expand itself in the larger chamber

  • Is there anything from outside that helps the gas expanding?


Having an evacuated chamber deals with point 1 and tells us that the gas does not have to work (and hence loose energy) to expand in the chamber to gain extra room. The fact that the whole system is connected to a piston in contact with atmospheric pressure tells us that the system is a) not isolated and b) that the atmospheric pressure will "help" the gas expanding in the chamber.


Now, assuming an expansion that is quasi-static, the pressure on the piston has to be balanced at every time during the expansion process. Basically, the piston will work a little bit each time there is a pressure drop on the gas side (due to leaking into the chamber) so as to balance pressures again. If the process is adiabatic, the work provided by the atmosphere has nowhere to go and stays in the gas as an increase in temperature/kinetic energy.


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