The number of gas molecules striking per second per square metre of the top surface of a table placed in a room at $20^{\circ} C$ and $1$ atmospheric pressure is of the order of (given $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$ and the average mass of an air molecule is $m = 5 \times 10^{-27} \, kg$).

Two gases $A$ and $B$ are contained in the same vessel which is at temperature $T$. The number of molecules of gas $A$ is $N$ and the mass of each molecule is $m$. The number of molecules of gas $B$ is $2N$ and the mass of each molecule is $2m$. If the mean square velocity of the $x$-component of velocity of gas $B$ is $v^2$ and the mean square velocity of the $x$-component of velocity of molecules of gas $A$ is $u_x^2$,then $\frac{u_x^2}{v^2}$ is:

Pressure of an ideal gas is increased by keeping temperature constant. The kinetic energy of molecules

$A$ vessel of volume $10 \text{ liters}$ is filled with $H_2$ gas. The total average translational kinetic energy of its molecules is $4.5 \times 10^5 \text{ J}$. The pressure of hydrogen in the vessel is

The average kinetic energy of a monatomic molecule is $0.414 eV$ at temperature : (Use $K_{B} = 1.38 \times 10^{-23} J/K$) (in $K$)

The kinetic energy of one mole of a gas at $300 \, K$ is $E$. If the kinetic energy at $400 \, K$ is $E'$,then what is the ratio $E'/E$?