If the number of hydrogen molecules is twice the number of oxygen molecules at the same temperature,what is the ratio of their total kinetic energies? (Hydrogen : Oxygen)

An ideal gas in a container of volume $500 \text{ c.c.}$ is at a pressure of $2 \times 10^5 \text{ N/m}^2$. The average kinetic energy of each molecule is $6 \times 10^{-21} \text{ J}$. The number of gas molecules in the container is:

If the $rms$ speed of a gas is $v_{rms} = 1840 \ m/s$ and its density is $\rho = 8.99 \times 10^{-2} \ kg/m^3$,then the pressure of the gas will be .........

The total kinetic energy of translatory motion of all the molecules of $5 \, L$ of nitrogen exerting a pressure $P$ is $3000 \, J$. Which of the following statements is correct?

The pressure of a gas is proportional to

$Assertion$: The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and its volume.
$Reason$: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.