Why does the temperature of a tyre rise when it is pumped up rapidly?
Once the pressure in the tire has risen a little, the volume of the tire doesn't change much any more.  But, you are increasing the number of moles of air inside the tire when you pump air into it.  The new air pumped into the tire compresses the gas that was already in there previously and raises its pressure.  So the new gas is doing work on the previous gas to compress it  adiabatically and approximately reversibly.  This causes the internal energy of the gas and its temperature to increase.