Final answer:
A bicycle pump feels warm during tire inflation primarily because of the compression of air, which increases both the air pressure and temperature.
Step-by-step explanation:
The warmth felt from a bicycle pump while inflating a tire is chiefly due to the compression of air. When you use a pump, you are doing work on the air by compressing it into a smaller volume. This process increases the pressure and the temperature of the air, which in turn heats up the pump itself.
The initial stage of adding air to a deflated tire increases its volume without significantly increasing pressure. As the tire becomes filled and the walls resist further expansion, the pressure within the tire will increase, causing more air to necessitate higher pressure for the additional volume.
At this stage, if you continue to pump air into the tire (which has nearly a constant volume), the temperature goes up as well due to the compression of the gas.