The average kinetic energy of a helium atom at $30^oC$ is

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:

The translational kinetic energy of the molecules of a gas at absolute temperature $T$ can be doubled by

Discuss the main points to be considered while deriving the equation of pressure on the basis of the kinetic theory of gases.

The temperature at which the kinetic energy of oxygen molecules becomes double its value at $27^{\circ}\,C$ is $............^{\circ}\,C$.

Estimate the average thermal energy of a helium atom at:
$(i)$ room temperature $(27^{\circ} C)$,
$(ii)$ the temperature on the surface of the Sun $(6000\; K)$,
$(iii)$ the temperature of $10$ million kelvin (the typical core temperature in the case of a star).