Q: Why the temperature of a gas drops in adiabatic expansion ?
Sol: In adiabatic expansion , there is no exchange of heat between system and surroundings i.e. ΔQ = 0 .
By the first law of thermodynamics $\large \Delta Q = \Delta U + \Delta W $
Therefore in Adiabatic expansion ; $\large \Delta W = – \Delta U$
Thus , work done by a gas in adiabatic expansion is associated with a decrease of internal energy , so its temperature decreases .