$A$ volume $V$ and pressure $P$ diagram was obtained from state $1$ to state $2$ when a given mass of a gas is subjected to temperature changes. During this process the gas is

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?

$A$ container $A$ contains an ideal gas at pressure $P$,volume $V$,and temperature $T$. $A$ second container $B$ contains the same gas at pressure $2P$,volume $2V$,and temperature $\frac{T}{2}$. The ratio of the mass of gas in $A$ to that in $B$ is:

The correct graph between pressure $(P)$ and density $(\rho)$ of a gas at constant temperature is

$A$ 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 After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$.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 $32 \times 10^{-3} \, kg/mol$)

The number of molecules in a gas at pressure $1.64 \times 10^{-3} \text{ atm}$ and temperature $200 \text{ K}$ having the volume $1 \text{ cc}$ is: