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The decompression of air is an endothermic process. That means it absorbs heat. Air in a tire is under 35 to 40 psi of pressure. This pressure conpresses the gas inside the tire, so to speak. When you release the air, it rapidly expands and expanding gas cools the same as compressing gas warms up.

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Decompression is Exo-thermic! The pressure compresses the gas - err, well, yes. Compressing air means raising its pressure by reducing its volume; and if done rapidly also raises its temperature. The last bit is right: sudden expansion cools it.

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Q: If a tire is hot why does the air come out cold?
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