Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B$. Under these conditions,the density of $A$ is found to be $1.5$ times the density of $B$. The ratio of the molecular weights of $A$ and $B$ is:

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)

An open glass tube is immersed in mercury such that a length of $8 \ cm$ extends above the mercury level. The open end of the tube is then closed and sealed,and the tube is raised vertically by an additional $46 \ cm$. What will be the length of the air column above the mercury in the tube now? (Atmospheric pressure = $76 \ cm$ of $Hg$)

State Boyle's law and Charles's law.

If $300 \ ml$ of a gas at $27^{\circ}C$ is cooled to $7^{\circ}C$ at constant pressure,then its final volume will be ...... $ml$.

The volume of a gas will be double of what it is at $0^{\circ}C$ (pressure remaining constant) at: