The equation of state for $5\,g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be where $R$ is the gas constant.

$A$ gas at $27^{\circ}C$ has a volume $V$ and pressure $P$. On heating,its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be ...... $^{\circ}C$.

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 ...... $ml$.

At the top of a mountain,a thermometer reads $7^{\circ}C$ and a barometer reads $70 \, cm$ of $Hg$. At the bottom of the mountain,these read $27^{\circ}C$ and $76 \, cm$ of $Hg$ respectively. The ratio of the density of air at the top to that at the bottom is

$A$ vessel of volume $8 \, L$ contains an ideal gas at $300 \, K$ and $2 \, atm$ pressure. The gas is allowed to leak until the pressure becomes $125 \, kPa$. Calculate the number of moles that leaked out if the temperature remains constant.

$A$ flask containing air at $27\,^{\circ}C$ at atmospheric pressure is corked up. $A$ pressure of $2.5\,atm$ would force the cork out. The temperature at which it happens is