$A$ vessel containing $5 \, L$ of a gas at $0.8 \, Pa$ pressure is connected to an evacuated vessel of volume $3 \, L$. The resultant pressure inside will be ...... $Pa$ (assuming the whole system to be isolated).

For $H_2, O_2$,and $He$ gases at the same temperature and pressure,the volumes are equal. Which of the following has the highest number of atoms?

$A$ gas has a volume $V$ at a temperature of $27^{\circ}C$. If the temperature is increased to $327^{\circ}C$ while keeping the pressure constant,what will be the new volume of the gas?

The temperature of a gas at pressure $P$ and volume $V$ is $27^{\circ}C$. Keeping its volume constant,if its temperature is raised to $927^{\circ}C$,then its pressure will be (in $P$)

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 After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$.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

Find the ratio of the density of air at the top of a mountain to the density of air at the bottom of the mountain,given the conditions shown in the image.