We have a jar filled with gas characterized by parameters $P, V, T$ and another jar $B$ filled with gas having parameters $2P, V/4, 2T$,where symbols have their usual meaning. The ratio of the number of molecules in jar $A$ to those in jar $B$ is

The volume of a gas at $30^{\circ} C$ temperature and $760 \ mm$ of $Hg$ pressure is $100 \ cc$. Then its volume at the same temperature and $400 \ mm$ of $Hg$ is (in $cc$)

Two spheres are connected to each other as shown in the figure. The volume of sphere $I$ is twice the volume of sphere $II$. They contain an ideal gas at temperatures $100 K$ and $200 K$,respectively. If the mass of the gas in sphere $I$ is $m$,what is the mass of the gas in sphere $II$?

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: $1 \, atm = 1.01 \times 10^5 \, N \, m^{-2}$,$R = 8.31 \, J \, mol^{-1} K^{-1}$.

The volume of a given mass of a gas is increased by $7 \%$ at constant temperature. The pressure should be decreased by (in $\%$)

What is the mass of $2$ litres of nitrogen gas $(N_2)$ at $22.4$ atmospheric pressure and $273\,K$?