Explain why the temperature of a gas drops in an adiabatic expansion, on basis of the kinetic theory of gases,

Explanation

In an adiabaticf expansion `Delta Q = 0`. But `Delta Q = Delta U = + Delta W` by the first law of thermodynamics. Therefore, in an adiabatic expanison,
`Delta W = - Delta U`
Thus, work down by a gas in an adiabatic expanison is associated with a decrease of internal energy. So its temperature decreasese.