The average translational kinetic energy of a molecule in a gas becomes equal to $0.69 \ eV$ at a temperature of about,[Boltzmann's constant $= 1.38 \times 10^{-23} \ J \ K^{-1}$] (in $^{\circ} C$)

The average kinetic energy of $H_2$ molecules at $300 \ K$ is $E$. At the same temperature,the average kinetic energy of an $O_2$ molecule is:

The average translational kinetic energy of nitrogen (molar mass $28$) molecules at a particular temperature is $0.042 \ eV$. The translational kinetic energy of oxygen molecules (molar mass $32$) in $eV$ at double the temperature is:

$A$ cylinder of capacity $20 \text{ litres}$ is filled with $H_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5 \times 10^5 \text{ J}$. The pressure of hydrogen in the cylinder is

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 ratio of the mean kinetic energy of hydrogen and oxygen at a given temperature is