Question

It has been considered that during the formation of earth,$H_2$ gas was available on our planet.Due to excessively high temperature during the formation of earth, $H_2$ gas escaped out of the planet.If average escaping velocity of $H_2$ is $1.1\times {10}^{6}cm/sec$, what was the temperature at the time of earth formation.

Answer 1

Velocity due to thermal energy is considered to be the root mean square velocity given as $V_{rms}=\sqrt[2]{23RT/M}$ where $R=8.31J/Mole-Kelvin$ is gas constant, $T$ is temperature and $M$ is atomic weight for $H_2$, $M=2$

So for escaping from environment the average escape velocity should be provided by $V_{rms}$ so $V_{rms}=1.1\times {10}^{4}m/s$ so $1.1\times {10}^4=\sqrt[2]{23RT/M}$ after putting all value we get temperature of earth at time of formation as $T=9.7\times {10}^{6}Kelvin$