$A$ gas at absolute temperature $300\,K$ has pressure $P = 4 \times 10^{-10}\,N/m^2$. Given the Boltzmann constant $k = 1.38 \times 10^{-23}\,J/K$,the number of molecules per $cm^3$ is of the order of:

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 \,cm$, the total length of the hollow cylinder is: (in $\,cm$)

$A$ perfect gas of a given mass is heated first in a small vessel and then in a large vessel,such that their volumes remain unchanged. The $P-T$ curves are

Two vessels $A$ and $B$ contain oxygen. The volume of $B$ is twice that of $A$,the pressure of $B$ is thrice that of $A$ and the temperature of $B$ is half of that of $A$. Then,find the ratio of number of molecules of oxygen in vessels $A$ and $B$.

At $0^{\circ}C$,the density of a fixed mass of a gas divided by pressure is $x$. At $100^{\circ}C$,the ratio will be

To double the volume of a given mass of an ideal gas at $27^{\circ}C$ keeping the pressure constant,one must raise the temperature in degrees Celsius to ....... $^{\circ}C$.