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When you pump up a bike tire with a bicycle pump, the valve will heat up. Why is that? (If it because of the air passing through the valve, why doesn't the valve heat up when you fill your car tire at the gas station?)

When air is compressed it heas up, so when you use the hand pump, the air is compressed as you go and that heat is passed along to the valve. At the gas station, however, the air has been compressed for hours so the residual heat has already dissapated.