The pressure of a given mass of gas at $20^{\circ}C$ is $P$. At constant volume,at what temperature in $^{\circ}C$ will the pressure of the gas become $2P$?

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 $cc$)

$A$ 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 $\,K$)

Estimate the total number of air molecules (inclusive of oxygen,nitrogen,water vapour,and other constituents) in a room of capacity $25.0 \; m^{3}$ at a temperature of $27^{\circ} C$ and $1 \; atm$ pressure.

Column-$I$ represents gas laws and Column-$II$ represents the physical quantity which is constant for the given law. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Boyle's law	$(i)$ Pressure
$(b)$ Charles's law	$(ii)$ Volume
	$(iii)$ Temperature

$A$ vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_1,$ and that below the piston is $l_2,$ such that $l_1 > l_2.$ Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T.$ If the piston is stationary,its mass $m$ will be given by: ($R$ is the universal gas constant and $g$ is the acceleration due to gravity)