$A$ container of $10 \,L$ is filled with an ideal gas at a temperature of $27^{\circ} C$ at a pressure of $12 \,atm$. The volume of the container is reduced to $6 \,L$ and the temperature of the gas is increased by $30^{\circ} C$. What is the final pressure of the gas (in $\,atm$)?

The $PV$ versus $T$ graph for equal masses of $H_2, He$,and $O_2$ is shown in the figure. Choose the correct alternative:

The equation of state for $5 \, g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be (where $R$ is the gas constant).

At the top of a mountain,a thermometer reads $7^{\circ}C$ and a barometer reads $70 \, cm$ of $Hg$. At the bottom of the mountain,these read $27^{\circ}C$ and $76 \, cm$ of $Hg$ respectively. The ratio of the density of air at the top to that at the bottom is

Inside a cylinder having insulating walls and closed at ends is a movable piston,which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2m$ of the same gas. What fraction of the total volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? Consider that the movable piston is conducting so that the temperature is the same throughout.

If the density of the Sun is $1.4 \, g \, cm^{-3}$, the pressure is $1.4 \times 10^9 \, \text{atm}$, and the molar mass of the gas in the Sun is $2 \, g \, mol^{-1}$, then the temperature of the Sun will be: [Take $R = 8.4 \, J \, mol^{-1} \, K^{-1}$]