If the kinetic energy of a helium atom at temperature $T$ is $E$,then the Avogadro constant $N_A$ is given by:

$A$ gas has volume $V$ and pressure $P$. The total translational kinetic energy of all the molecules of the gas is :-

$10^{23}$ molecules of a gas, each having a mass of $3 \times 10^{-27} \,kg$, strike per second per $cm^2$ of a rigid wall at an angle of $60^{\circ}$ with the normal and rebound with a velocity of $500 \,m/s$. The pressure exerted by the gas molecules on the wall is: (in $\,N/m^2$)

The kinetic energy,due to translational motion,of most of the molecules of an ideal gas at absolute temperature $T$ is proportional to:

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

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).