$A$ cylinder of capacity $200 \ L$ is filled with $H_2$ gas. The total average translational kinetic energy of the molecules is $1.52 \times 10^5 \ J$. Calculate the pressure of $H_2$ in the cylinder in $N \ m^{-2}$.

The average force applied on the walls of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

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 $m = 5 \times 10^{-27} \, kg$).

The total momentum of the molecules of $1 \,gm$ $mol$ of a gas in a container at rest at $300 \,K$ is

At what temperature in $^\circ C$ will the kinetic energy of gas molecules be double the kinetic energy at $27^\circ C$?

$A$ container of volume $10^{-3} \ m^3$ contains $3.0 \times 10^{22}$ gas molecules,each having a mass of $5.3 \times 10^{-26} \ kg$. If the $rms$ speed of the molecules is $400 \ m/s$,calculate the pressure exerted by the gas.