$A$ sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T,$ the mass of each molecule is $m.$ The expression for the density of gas is ($k =$ Boltzmann's constant)

The adjoining figure shows the graph of pressure $(P)$ and volume $(V)$ of a gas at two temperatures $T_1$ and $T_2$. Which of the following inferences is correct?

$A$ 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.

$A$ graph between volume $V$ and absolute temperature $T$ is obtained when a given mass of a gas is heated. During the heating process from state-$1$ to state-$2$,the pressure

$A$ gas at $27^oC$ 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 ...... $^oC$.

Dry air at sea level contains $75.5\%\, N_2$ by mass. If the total atmospheric pressure is $1 \,atm$,the partial pressure of nitrogen is approximately $... \,atm$.