Why will be air from a punctured tyre cool?
The law that applies here is gas laws. When a gas travels from a high pressure area to low pressure area through a small hole, the gas gets cooled. It is called Joule-Thomson effect in physics. The air inside the cycle tube will be at a higher pressure than the out side air. When the tube gets punctured, the air moves from the region of high pressure to the region of low pressure through the hole. The air inside the tyre has to do some work in order to come out of the tube through the hole. The energy required to do this work will be got from the heat energy of the air. Hence, the temperature of air is lowered.