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

If the average translational kinetic energy of a molecule in a gas is equal to the kinetic energy of an electron accelerating from rest through $10 \,V$, then the temperature of the gas molecule is (Boltzmann constant $= 1.38 \times 10^{-23} \,JK^{-1}$)

Obtain an expression for the momentum of a gas transferred to the walls of a container in time $\Delta t$.

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).

Increase in temperature of a gas filled in a container would lead to

$A$ container of volume $10^{-3} \ m^3$ contains $3.0 \times 10^{22}$ gas molecules,each having a mass of $5.3 \times 10^{-26} \ kg$. If the $rms$ speed of the molecules is $400 \ m/s$,calculate the pressure exerted by the gas.