If $300 \ ml$ of a gas at $27^{\circ}C$ is cooled to $7^{\circ}C$ at constant pressure,then its final volume will be ...... $ml$.

An air bubble of volume $2.9 \ cm^3$ rises from the bottom of a swimming pool $5 \ m$ deep. At the bottom of the pool, the water temperature is $17^{\circ} C$. The volume of the bubble when it reaches the surface, where the water temperature is $27^{\circ} C$, is . . . . . . $cm^3$. ($g = 10 \ m/s^2$, density of water $\rho = 10^3 \ kg/m^3$, and $1 \ atm = 10^5 \ Pa$)

Column-$I$ represents a graph and Column-$II$ represents a physical quantity or condition that is constant for that graph. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Top graph	$(i)$ Constant pressure
$(b)$ Bottom graph	$(ii)$ Constant volume
	$(iii)$ For ideal gas

An ideal gas has volume ${V_0}$ at ${27^{\circ}C}$. It is heated at constant pressure so that its volume becomes $2{V_0}$. The final temperature is

Inside a cylinder having insulating walls and closed at ends is a movable piston,which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2m$ of the same gas. What fraction of the total volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? Consider that the movable piston is conducting so that the temperature is the same throughout.

$A$ vessel is filled with an ideal gas at a pressure of $10 \text{ atm}$ and temperature $27^{\circ} C$. Half of the mass is removed from the vessel and the temperature of the remaining gas is increased to $87^{\circ} C$. Then the pressure of the gas in the vessel will be (in $\text{ atm}$)