The $rms$ speed of an ideal hydrogen gas molecule in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. What is the pressure of the hydrogen gas in atmospheres? (Given: Density of hydrogen gas $\rho = 8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$)

The temperature at which the kinetic energy of oxygen molecules becomes double its value at $27^{\circ}\,C$ is $............^{\circ}\,C$.

Internal energy of an ideal gas depends on which factors and does not depend on which factors?

The number of molecules in one litre of an ideal gas at $300 \, K$ and $2$ atmospheric pressure with mean kinetic energy $2 \times 10^{-9} \, J$ per molecule is $.... \times 10^{11}$.

The molecules of air in the room where you are sitting are all experiencing the force of gravity tending to bring them down. The molecules are also frequently and randomly undergoing collisions,which tend to oppose the effect of the fall under gravity. The density of air is nearly uniform throughout the room because:

The graph which represents the variation of mean kinetic energy of molecules with temperature $t^{\circ} \text{C}$ is