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.

On $0^{\circ}C$,the pressure measured by a barometer is $760 \, mm$. What will be the pressure at $100^{\circ}C$?

An open-mouthed container is filled with air at $60^{\circ}C$. The container is heated to a temperature $T$ such that $1/4$ of the air escapes. The value of $T$ is ........ $^{\circ}C$.

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

The pressure-temperature graph for an ideal gas is shown in the figure. At point $A$,the density of the gas is $\rho_0$. What will be the density at point $B$?

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $B$ in the $V-T$ graph. Then the expansion of the same ideal gas of mass $2m$ at a pressure $2P$ is given by the straight line: