Here is a quote from the link Bill posted; it brushes over the general physics of the debate.
“N2 and air being gases, in the conditions we’re concerned with, will both act ideally (pv=nrt) and so will expand and contract to exactly the same volume at the same temperature. Even using Van Der Waal’* equation to correct for the ever-so-slight deviations from idealness you’d encounter at high tire temp, the difference is so small you probably couldn’t measure it.
Now you may get a difference based on the fact that nitrogen has a slightly higher heat capacity than oxygen (it will reach a slightly lower temperature than oxygen if exposed to the same amount of heat), but the difference is very small, about 3 per cent, and since air is ~78% n2 to begin with, the final difference will be vanishingly small.
Also, someone mentioned that n2 is three times larger than normal air, well, since normal air is, again, 78% n2, that doesnt’ really make sense. It is larger than o2 (which takes up the remaining 22% minus some change), but again, only by a few per cent.”
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