An inverted bell lying at the bottom of a lake $47.6 \ m$ deep has $50 \ cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ...... $cm^3$ (atmospheric pressure $= 70 \ cm$ of $Hg$ and density of $Hg = 13.6 \ g/cm^3$)

$A$ container holds $13 \, g$ of gas at a temperature of $27^{\circ}C$. If the temperature of the container is raised to $52^{\circ}C$ while keeping the pressure constant,the amount of gas that must be released is ..... $g$.

$A$ vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_1,$ and that below the piston is $l_2,$ such that $l_1 > l_2.$ Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T.$ If the piston is stationary,its mass $m$ will be given by: ($R$ is the universal gas constant and $g$ is the acceleration due to gravity)

The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. Another gas in jar $B$ has pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in jar $A$ to jar $B$ is:

What is the equation of state for $8 \, g$ of $O_2$?

$A$ container $A$ contains a gas at thermodynamic coordinates $P, V,$ and $T$. Another container $B$ contains a different gas at $2P, V/4,$ and $2T$. The ratio of the number of molecules in container $A$ to the number of molecules in container $B$ is: