$A$ sample of oxygen gas and a sample of hydrogen gas both have the same mass,same volume,and the same pressure. The ratio of their absolute temperatures is (Molecular weights of $O_2$ and $H_2$ are $32$ and $2$ respectively).

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

When the temperature of a gas in a closed vessel is increased by $1 \ ^\circ C$,its pressure increases by $0.4 \ \%$. The initial temperature of the gas is:

$A$ vessel that can withstand a pressure of $100 \,atm$ is filled with hydrogen at $27^{\circ} C$ up to a pressure of $20 \,atm$. If the vessel is heated, then the temperature at which it explodes is (in $\,K$)

The equation of state for $5\,g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be where $R$ is the gas constant.

At constant pressure,the ratio of the increase in volume of an ideal gas per degree rise in Kelvin temperature to its original volume is $(T =$ absolute temperature of the gas$)$