Heat is not being exchanged in a body. If its internal energy is increased,then

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

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d}=32$, then $\frac{P^{\prime}}{P}$ is:

$A$ cylinder with a movable piston contains $3 \ moles$ of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator,and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

The following figure shows an adiabatic cylindrical container of volume $V_0$ divided by an adiabatic smooth piston (area of cross-section = $A$) into two equal parts. An ideal gas $(C_P/C_V = \gamma)$ is at pressure $P_1$ and temperature $T_1$ in the left part,and a gas at pressure $P_2$ and temperature $T_2$ is in the right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose $x$ = displacement of the piston):

$A$ rigid diatomic gas undergoes adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^x$ where $x$ is (in $.5$)