Air is filled at $60^{\circ} C$ in a vessel of open mouth. The vessel is heated to a temperature $t^{\circ} C$ so that $\frac{1}{4}$th of the air escapes from the vessel. Assuming air as an ideal gas and the volume of the vessel remains constant,the value of '$t$' is: (in $^{\circ} C$)

$A$ container $X$ has a volume double that of container $Y$,and both are connected by a thin tube. Both contain the same ideal gas. The temperature of $X$ is $200\,K$ and that of $Y$ is $400\,K$. If the mass of the gas in $X$ is $m$,then the mass of the gas in $Y$ will be:

The tyre of a bicycle has a volume of $2 \times 10^{-3} \ m^3$. Initially,the tube is filled to $75 \%$ of its volume with air at an atmospheric pressure of $10^5 \ N \ m^{-2}$. When a rider is on the bicycle,the area of contact of the tyre with the road is $24 \times 10^{-4} \ m^2$. The mass of the rider with the bicycle is $120 \ kg$. If a pump delivers a volume of $500 \ cm^3$ of air in each stroke,then the number of strokes required to inflate the tyre is $(g = 10 \ m \ s^{-2})$.

$A$ jar $P$ is filled with a gas having pressure,volume,and temperature $P, V, T$ respectively. Another gas jar $Q$ is filled with a gas having pressure $2P$,volume $\frac{V}{4}$,and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is:

Find the value of the universal gas constant $R$ in $J \ mol^{-1} K^{-1}$.

What is molar volume? Write its $SI$ unit.