One mole of an ideal diatomic gas expands from volume $V$ to $2 V$ isothermally at a temperature $27^{\circ} \mathrm{C}$ and does $W$ joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^{\circ} \mathrm{C}$ doing the same amount of work $W$, then its final temperature will be (close to) $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$.

$$ \left(\log _e 2=0.693\right) $$

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of $17 \mathrm{~cm}^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^{\circ} \mathrm{C}$, then the piston will move $\_\_\_\_$ cm.

(atmospheric pressure $=10^5 \mathrm{~Pa}$ )

An air bubble of volume $2.9 \mathrm{~cm}^3$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^{\circ} \mathrm{C}$. The volume of the bubble when it reaches the surface, where the water temperature is $27^{\circ} \mathrm{C}$, is $\_\_\_\_$ $\mathrm{cm}^3$.

( $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$, density of water $=10^3 \mathrm{~kg} / \mathrm{m}^3$, and 1 atm pressure is $10^5 \mathrm{~Pa}$ )

Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The molecular size of $A$ is half of that of $B$ and mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18} / \mathrm{s}$ then collision frequency in gas $A$ is $\_\_\_\_$ /s.