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Basis is the ideal gas law:

This law only states a mathematical relationship between many variables. It does not state what happens if one of the variables changes.

So we pin down the volume and increase moles of air by pumping in more gas. n obviously changes, so does P. But what happens to T? Does the temperature change at all?

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If the air is pumped in fast enough, you can assume that it happens adiabatically, so: $pV^{\gamma}=constant$ – fibonatic May 20 '13 at 22:30
up vote 3 down vote accepted

It really depends on how more gas is being "pumped in". For example, a typical pump will take air in at (roughly) one atmosphere, and pressurize it by doing work on it, which will increase the temperature. On the other hand, if the gas is coming from a cylinder of compressed air, it will cool on entering your volume, so the temperature would actually drop. You can even imagine a "Maxwell's Demon compressor", which just allows a molecule to enter whenever no other molecule would leave. This shouldn't change the temperature at all.

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