An ideal gas at pressure $P$ and temperature $T$ is enclosed in a vessel of volume $V$. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P^{\prime}$. Assuming that the temperature of the gas remains constant during the leakage,the number of moles of the gas that have leaked is

Pressure versus temperature graphs of an ideal gas are as shown in the figure. Choose the wrong statement.

$A$ container $X$ has a volume double that of container $Y$,and both are connected by a thin tube. Both contain the same ideal gas. The temperature of $X$ is $200\,K$ and that of $Y$ is $400\,K$. If the mass of the gas in $X$ is $m$,then the mass of the gas in $Y$ will be:

Two containers $C_{1}$ and $C_{2}$ of volumes $V$ and $4V$ respectively,hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in $C_{1}$ and $C_{2}$ are $p$ and $5p$,respectively. Heat baths are employed to maintain the temperatures in the containers at $300 \, K$ and $400 \, K$,respectively. The valve is now opened. Select the correct statement.

The pressure and temperature of an ideal gas in a closed vessel are $720 \, kPa$ and $40^\circ C$ respectively. If $\frac{1}{4}^{th}$ of the gas is released from the vessel and the temperature of the remaining gas is raised to $353^\circ C$,the final pressure of the gas is ....... $kPa$.

$A$ cylinder contains hydrogen gas at a pressure of $249\; kPa$ and temperature $27^{\circ} C$. Its density is $............. kg/m^{3}$ $(R = 8.3\; J\; mol^{-1} K^{-1})$.