The pressure versus temperature graph of an ideal gas is as shown in the figure. The density of the gas at point $A$ is ${\rho _0}$. The density at point $B$ will be

$A$ 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 After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$.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 $27^{\circ}C$ 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 ...... $^{\circ}C$.

The molecular weights of $O_2$ and $N_2$ are $32$ and $28$ respectively. At $15^{\circ}C$,the pressure of $1 \, g$ of $O_2$ will be the same as that of $1 \, g$ of $N_2$ in the same bottle at the temperature of ...... $^{\circ}C$.

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston of cross-section $8.0 \times 10^{-3} \, m^2$. Initially,the gas is at $300 \, K$ and occupies a volume of $2.4 \times 10^{-3} \, m^3$,and the spring is in its relaxed state as shown in the figure. The gas is heated by a small heater until the piston moves out slowly by $0.1 \, m$. The force constant of the spring is $8000 \, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless,and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible.) (in $, K$)

$A$ cylinder contains $10\, kg$ of gas at a pressure of $10^7\, N/m^2$. The quantity of gas taken out of the cylinder,if the final pressure is $2.5 \times 10^6\, N/m^2$,will be ..... $kg$ (Temperature of the gas is constant).