For container $A$,the pressure is $P$,volume is $V$,and temperature is $T$. For container $B$,the pressure is $2P$,volume is $V/4$,and temperature is $2T$. Find the ratio of the number of molecules in container $A$ to that in container $B$.

$A$ 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?

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 $1 \ atm = 10^5 \ Pa$)

You have two containers of equal volume. One is full of helium gas. The other holds an equal mass of nitrogen gas. Both gases have the same pressure. How does the temperature of the helium compare to the temperature of the nitrogen?

At a given temperature,the pressure of an ideal gas of density $\rho$ is proportional to

$A$ gas is collected over water at $25^{\circ}C$. The total pressure of the moist gas was $735 \, mm$ of mercury. If the aqueous vapour pressure at $25^{\circ}C$ is $23.8 \, mm$,then the pressure of the dry gas is..... $mm$.