$12\,g$ of gas occupies a volume of $4\times 10^{-3}\,m^3$ at a temperature of $7\,^oC$. After the gas is heated at constant pressure,its density becomes $6\times 10^{-4}\,g/cc$. Find the temperature $T$ (in $K$) to which the gas was heated.

State and explain Dalton's law of partial pressure.

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

At a room temperature of $23^{\circ}C$,a person inhales $1500 \, ml$ of air at a body temperature of $37^{\circ}C$. If the pressure and mass remain constant,what will be the volume of the air in the person's lungs in $ml$?

Oxygen gas is filled in a container of volume $20 \, L$ at a pressure of $2.5 \times 10^5 \, N \, m^{-2}$. Find the mass of the oxygen gas in the container. The temperature of the oxygen in the container is $27 \, ^\circ C$,the molar mass of oxygen is $32 \, g \, mol^{-1}$,and $R = 8.31 \, J \, mol^{-1} K^{-1}$.

The volume of a gas at pressure $21 \times 10^4 \ N/m^2$ and temperature $27^\circ C$ is $83 \ L$. If $R = 8.3 \ J/mol/K$,then the quantity of gas in $gm-mole$ will be: