A rapid compression heats a gas, but a rapid expansion cools it - why?

Explanation

A rapid thermal process can be regarded as an adiabatic process, because the gas does not get sufficient time to exchange heat with the surroundings. So, Q = 0.
From the first law of thermodynamics , `U_()-U_(i) = Q -W = -W`.
`:. W = U_(i) - U_(f)`
(i) in an adiabatic compression. W is negative. So `U_(i)-U_(f) < 0, or, U_(i) < U_(f)`. This means that the internal energy of the gas increases. the internal energy of a gas depends only on its temperature. So the temperature increases and the gas is heated.
(ii) Conversely, in an adiabatic expansion. W is positive. So, `U_(f) < U_(i)`. i.e., the internal energy decreases. As a result, temperature decreases, so the gas is cooled.