Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
**Assertion (A):** In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
**Reason (R):** Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below:
Answer: (B) (A) is false but (R) is true
**(A)** In an adiabatic compression, work is done on the gas and no heat leaves, so its internal energy and temperature **increase** ($TV^{\gamma-1}$ = constant). False.
**(R)** Free expansion happens suddenly into vacuum, with no heat exchange ($Q = 0$) and no way to reverse it by an infinitesimal change: it is irreversible and adiabatic. True.
Solution by Sreeraj P, M.Sc Physics