Find the average kinetic energy for $1$ gram-mole of a monatomic gas.

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 $.... \times 10^{11}$.

Consider a rectangular block of wood moving with a velocity $v_{0}$ in a gas at temperature $T$ and mass density $\rho$. Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to $v_{0}$ is $A$. Show that the drag force on the block is $4\rho A v_{0} \sqrt{\frac{kT}{m}}$,where $m$ is the mass of the gas molecule.

The average translational kinetic energy of ${O_2}$ (molar mass $32$) molecules at a particular temperature is $0.048 \; eV$. The translational kinetic energy of ${N_2}$ (molar mass $28$) molecules in $eV$ at the same temperature is:

$A$ container has $N$ molecules at absolute temperature $T$. If the number of molecules is doubled but the total kinetic energy in the box remains the same as before,the absolute temperature of the gas is ...........

The internal energy of air in a $4 \ m \times 4 \ m \times 3 \ m$ sized room at $1$ atmospheric pressure will be . . . . . . $\times 10^6 \ J$. (Consider air as a diatomic molecule)