At what temperature does the volume of an ideal gas at $0^{\circ}C$ become triple? (in $^{\circ}C$)

The gas in a vessel is subjected to a pressure of $20 \ atm$ at a temperature of $27^{\circ}C$. If one-half of the gas is released from the vessel and the temperature of the remaining gas is raised by $50^{\circ}C$,the final pressure of the gas in the vessel is ....... $atm$.

In the figure,the volume of container $X$ is twice the volume of container $Y$. Both contain an ideal gas. The temperature of $X$ is $200 \, K$ and the temperature of $Y$ is $400 \, K$. If the mass of the gas in $X$ is $m$,what will be the mass of the gas in $Y$?

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.

$A$ 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 $\,atm$)?

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.