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If hot air rises, why is it cooler at th...

If hot air rises, why is it cooler at the top of a mountain than near sea level ?

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We know that the pressure decreases with height. When the hot air rises, it suffers adiabatic expansion. Now according to first law of thermodynamics `DeltaQ=DeltaU+DeltaWor0=DeltaU+DeltaW(thereforeDeltaQ=0)thereforeDeltaU=DeltaW` This causes a decrease in internal energy. So the temperature falls
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