Take an ordinary underinflated bicycle tire, connect it to an ordinary hand pump

Question

Take an ordinary underinflated bicycle tire, connect it to an ordinary hand pump, and pump up the tire to be fully inflated. Feel it. The tire is now hotter than it was before. Two questions: (1) Did the thermal energy of the gas inside increase? (2) Did you add heat to the gas in the tire. Incidentally, there is a subtlety here which you should not worry about. The gas we're interested in here is only those molecules of air which were initially in the tire. When you pumped the tire up, there are more molecules inside, but the question instead means to ask about the thermal energy of those molecules which were originally present. (The thermal energy of ALL of the final molecules is of course greater that of those originally present simply because there are more of them, but that's not what the question is.)

Explanation / Answer

for the initial molecules only if you consider, NO you are not giving it thermal energy. You are doing work to fill the tire. hence the work is being utilized to increase the thermal energy of the gas that are filled new. old ones are staying same. no work was done on them hence no increase in thermal energy for those initial molecules.

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