An ideal gas at temperature T₁ is expanded adiabatically. Its final temperature T₂ is:

1. In adiabatic expansion, gas does positive work on surroundings (W > 0). 2. Since Q = 0, ΔU = −W < 0. 3. For an ideal gas U ∝ T, so ΔU < 0 ⇒ ΔT < 0. 4. Hence the gas cools on adiabatic expansion — the principle behind cloud formation in rising air. _Source: syllabus Physics Ch 11, §11.7 Adiabatic Process_