Would compressed air generate the same heat in 1000 years as 1 day?

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Offline jammie001

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Lets say we have a volume of air and compress it a certain amount in 1 day and it generates heat.  Would this same
volume of air generate the same amount of heat if compressed by the same amount but over the course of 1000 years?


Offline chris

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Yes; the work done in compressing the molecules would be identical and hence, assuming no losses, the resulting temperature change would be the same, albeit over a much longer time scale.
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Offline Soul Surfer

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Both compressions suggested are relatively slow and the heat would escape but the rate of generation of heat would be slower the slower the compression.  It gets more interesting if the compression is done quickly say in a tenth of a second or less.

If the gas was totally isolated and no heat was allowed to escape it would be true but to compress any gas it is necessary to have it in a containing vessel and with a slow compression the heat generated would be lost to the walls of the vessel.  Let us assume that this has a large thermal capacity and stays at the same temperature as the gas is slowly compressed.  You would find that the effort expended to reduce the gas to say half its original volume was less than the effort needed to do it quickly. 

This is also easy to understand  if you think about what would happen with the quick compression reducing the volume to half.  the gas would heat up and the pressure would obviously be higher than if I held the volume the same and allowed it to cool back down to the starting temperature.

Note the quick change is called an adiabatic change (meaning that thermal equilibrium is not maintained) the slow change is called an isothermal change (i.e. thermal equilibrium is maintained)
« Last Edit: 21/09/2011 20:29:01 by Soul Surfer »
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