The $P-V$ diagram for two gases during an adiabatic process is shown in the figure. Curves $A$ and $B$ correspond to:

$A$ gas at initial temperature $T$ undergoes sudden expansion from volume $V$ to $2 \, V$. Then,

$A$ polyatomic gas follows a law $T^2 V^\alpha = \text{constant}$. Find $\alpha$ for which the heat exchange of gas in the process becomes zero.

The initial pressure and volume of a given mass of an ideal gas (with $\frac{C_{p}}{C_{V}}=\gamma$), taken in a cylinder fitted with a piston, are $p_{0}$ and $V_{0}$ respectively. At this stage, the gas has the same temperature as that of the surrounding medium, which is $T_{0}$. It is adiabatically compressed to a volume equal to $\frac{V_{0}}{2}$. Subsequently, the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?

$A$ gas is being compressed adiabatically. The specific heat of the gas during compression is

$Assertion :$ Air quickly leaking out of a balloon becomes cooler.
$Reason :$ The leaking air undergoes adiabatic expansion.