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. 

Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that the pressure is 

The temperature of a gas at pressure $P$ and volume $V$ is $27^{\circ} \mathrm{C}$. Keeping its volume constant, if its temperature is raised to $927^{\circ} \mathrm{C}$, then its pressure will be 

If the R.M.S velocity of a gas at a given temperature (Kelvin scale) is $300 {\mathrm{ms}}^{-1}$. What will be the R.M.S velocity of the gas having twice the molecular weight and half the temperature on Kelvin scale?

Two vessels $A$ and $B$ are identical. A has $1 \mathrm{g}$ hydrogen at $0^{\circ} \mathrm{C}$ and $\mathrm{B}$ has $1 \mathrm{g}$ oxygen at $0^{\circ} \mathrm{C} .$ Vessel $\mathrm{A}$ contains $x$ molecules and $\mathrm{B}$ contains $y$ molecules. The average kinetic energy per molecules in $A$ is $n$ times the average kinetic energy per molecule in $\mathrm{B}$. The value of $n$ is

The average kinetic energy of molecules are 

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