State Gay-Lussac's Law of Gaseous Volumes.

$S.I.$ unit of universal gas constant is

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

Molar volume is the volume occupied by $1 \; mol$ of any (ideal) gas at standard temperature and pressure ($STP$: $1 \; atm$ pressure,$0^{\circ} C$). Show that it is $22.4 \; L$.

An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

The floor area of a room is $20 \, m^2$ and its walls are $3 \, m$ high. If the pressure of air in the room is $1 \, atm$ and the temperature is $27 \, ^\circ C$,find the mass of the air in the room. (Take the molar mass of air as $29 \, g/mol$). Given: $1 \, atm = 1.01 \times 10^5 \, N \, m^{-2}$,$R = 8.31 \, J \, mol^{-1} K^{-1}$.