$200 \ cc$ of an ideal gas $(\gamma = 1.5)$ expands adiabatically. If the rms speed of the gas molecules becomes half of the initial value,the final volume of the gas is (in $cc$)

Consider a cycle tyre being filled with air by a pump. Let $V$ be the volume of the tyre (fixed) and at each stroke of the pump $\Delta V$ ( < < V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from $P_1$ to $P_2$?

$A$ certain mass of gas at $273 \ K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^\circ C$

The mean kinetic energy of monoatomic gas molecules under standard conditions is $\langle E_1 \rangle$. If the gas is compressed adiabatically $8$ times to its initial volume, the mean kinetic energy of gas molecules changes to $\langle E_2 \rangle$. The ratio $\frac{\langle E_2 \rangle}{\langle E_1 \rangle}$ is

An ideal monoatomic gas of volume $V$ is adiabatically expanded to a volume $3V$ at $27^{\circ}C$. The final temperature in Kelvins is (use $\frac{C_P}{C_V} = \frac{5}{3}$)

$A$ monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one-eighth of its original volume. The final pressure at constant entropy will be $.....P$.