$A$ large flask contains air at $27 \, ^{\circ}C$. In order to expel half the mass of air from the flask, the flask should be heated up to what temperature in $^{\circ}C$?

$A$ metre-long narrow bore held horizontally (and closed at one end) contains a $76 \; cm$ long mercury thread,which traps a $15 \; cm$ column of air. What happens if the tube is held vertically with the open end at the bottom?

$A$ vessel containing $5 \, L$ of a gas at $0.8 \, Pa$ pressure is connected to an evacuated vessel of volume $3 \, L$. The resultant pressure inside will be ...... $Pa$ (assuming the whole system to be isolated).

$A$ vessel has $6 \text{ g}$ of hydrogen at pressure $P$ and temperature $500 \text{ K}$. $A$ small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\frac{P}{2}$ and the temperature falls to $300 \text{ K}$ (in $\text{ g}$)?

The figure shows two flasks connected to each other. The volume of flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperatures $100\,K$ and $200\,K$ respectively. If the mass of the gas in flask $1$ is $m$,what is the mass of the gas in flask $2$?

An ideal gas undergoes a process maintaining the relation between pressure $(P)$ and volume $(V)$ as $P = P_o(1 + (\frac{V_o}{V})^2)^{-1}$, where $P_o$ and $V_o$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_o$ and $3V_o$ respectively undergo the above-mentioned process, calculate the difference in the temperatures of these samples, $T_B - T_A$, assuming the process is evaluated at their initial states. ($R$ = gas constant)