The $P-T$ diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct?

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)

$A$ gas at a temperature of $27^{\circ}C$ has a volume $V$ and pressure $P$. If the pressure is doubled and the volume is tripled,what will be the new temperature in $^{\circ}C$?

The graph of pressure $P$ and volume $V$ of $1 \text{ mole}$ of an ideal gas at constant temperature is:

The equation of state for $5 \ g$ of oxygen gas at pressure $P$,volume $V$,and temperature $T$ is given by:

$A$ gas at the temperature $250\,K$ is contained in a closed vessel. If the gas is heated through $1\,K,$ then the percentage increase in its pressure will be ...... $\%$