# Why the temperature of a gas drops in adiabatic expansion ?

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 .