Answer :

In kinetic theory of ideal gas mean speed also known as average speed is given as



Where R=gas constant=8.31Jmol-1K-1


T-temperature of gas


M=molar mass of gas


Molar mass of hydrogen=2amu=2g/mol=2kg/mol


Escape speed of earth is the speed given to projectile so that it escapes the gravitational field of earth. It is given by formula



Where G=universal gravitational constant


ME=mass of earth


R=radius of earth


We also know that acceleration due to gravity g is



Multiplying and dividing equation (II) by R



Putting the value of g from equation (III) to above equation we get



According to question vmean is equal to ve


So, from equation (I) and (IV) we get



Radius of earth R=6400km=6400000m


g=9.8m/s



Squaring both sides




Temperature at which the mean sped of the molecules of hydrogen gas equals the escape speed from the earth is 11800K.


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