$A$ gas has a volume of $251 \,cm^3$ at $20^{\circ} C$ and a pressure of $78 \,cm$ of $Hg$. Find its volume at $NTP$. (in $\,cm^3$)

The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours,the extra oxygen needed by them corresponds to $30,000 \, cc$ at sea level (pressure $1 \, atm$,temperature $27^{\circ}C$). Assuming that the temperature around Mount Everest is $-73^{\circ}C$ and that the oxygen cylinder has a capacity of $5.2 \, L$,the pressure at which $O_2$ must be filled (at site) in the cylinder is .... $atm$.

When the temperature of a gas at constant volume is increased by $5^{\circ}C$,its pressure increases by $0.5\%$ of its initial value. The initial temperature of the gas is..... $K$.

State Gay-Lussac's Law of Gaseous Volumes.

$28\, g$ of $N_2$ gas is contained in a flask at a pressure of $10\, atm$ and at a temperature of $57^\circ C$. It is found that due to leakage in the flask,the pressure is reduced to half and the temperature is reduced to $27^\circ C$. The quantity of $N_2$ gas that leaked out is

$A$ container $A$ contains a gas at pressure $P$,volume $V$,and temperature $T$. Another container $B$ contains a gas at pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in container $A$ to that in container $B$ is: