$A$ vessel has $8 \ g$ of oxygen at pressure $P$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How many grams of oxygen leak out if the final pressure is $P/4$ and the temperature is $200 \ K$?

The kinetic theory of gases provides a base for:

What will be the volume occupied by $4.5 \, kg$ of water at $STP$ if the intermolecular forces are neglected?

$A$ long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the piston,it moves down. If the air in the enclosure is cooled from temperature $T$ to $T-\Delta T$,the piston moves back to its original position. Then $\Delta T / T$ is close to (Assuming air to be an ideal gas,$g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$)

If the volume of a given mass of a gas is increased four times,and the temperature is raised from $27^{\circ}C$ to $127^{\circ}C$,what happens to its elasticity?

$A$ given sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T.$ The mass of each molecule of the gas is $m.$ Which of the following gives the density of the gas $?$