The gas equation $\frac{PV}{T} = \text{constant}$ is true for a constant mass of an ideal gas undergoing:

$A$ vessel is filled with an ideal gas at a pressure of $10 \text{ atm}$ and temperature $27^{\circ} C$. Half of the mass is removed from the vessel and the temperature of the remaining gas is increased to $87^{\circ} C$. Then the pressure of the gas in the vessel will be (in $\text{ atm}$)

$A$ vessel has $6 \ g$ of oxygen at pressure $p$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How much oxygen has leaked out if the final pressure is $\frac{p}{2}$ and final temperature is $300 \ K$ (in $g$)?

Absolute zero $(0\, K)$ is that temperature at which

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 lowest pressure (the best vacuum) that can be created in the laboratory at $27^{\circ}C$ is $10^{-11} \; mm$ of $Hg$. At this pressure,the number of ideal gas molecules per $cm^{3}$ will be: