The temperature of an ideal gas at atmospheric pressure is $300\,K$ and volume is $1\,m^3$. If the temperature and volume both become double,then the pressure will be:

An open and wide glass tube is immersed vertically in mercury in such a way that a length of $0.05 \, m$ extends above the mercury level. The open end of the tube is closed and the tube is raised further by $0.43 \, m$. The length of the air column above the mercury level in the tube will be ...... $m$. Take $P_{atm} = 76 \, cm$ of mercury.

The tyre of a motor car contains air at $15^{\circ} C$. If the temperature increases to $35^{\circ} C$, the approximate percentage increase in pressure is (ignore the expansion of the tyre).

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 $(g = 10 \ m \ s^{-2})$.

Equal masses of $N_2$ and $O_2$ gases are filled in containers $A$ and $B$ respectively. The volume of container $B$ is twice the volume of container $A$. What is the ratio of the pressure in container $A$ to that in container $B$?

Two different masses $m$ and $3m$ of an ideal gas are heated separately in a vessel of constant volume. The pressure $P$ versus absolute temperature $T$ graphs for these two cases are shown in the figure. The ratio of the slopes of curves $B$ to $A$ is