The ratio of the mean kinetic energy of hydrogen and nitrogen at temperatures $300 \, K$ and $450 \, K$ respectively is:

What is the pressure of hydrogen in a cylinder of volume $10 \text{ litre}$ if its total energy of translation is $7.5 \times 10^3 \text{ J}$?

$Assertion$: 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.

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?

At $300 \ K$,the number of $H_2$ molecules is twice the number of $O_2$ molecules. What is the ratio of the total kinetic energy of $H_2$ to that of $O_2$?

In a vessel,an ideal gas is at a pressure $P$. If the mass of all the molecules is halved and their speed is doubled,then the resultant pressure of the gas will be