At what temperature , will the root mean square velocity on hydrogen be double of its value at `S.T.P`., pressure remaining constant ?

Explanation

Let `V _(1)` be the r.m. s. belocity at S.T.P. and `V_(2)` be the r.m.s. velocity at unknown temperature `T_(2).`
Here `T_(1) =273 K, T_(2) = ? (V_(2))/(V_(1)) =2` We know , `V ^(2) prop T`
`therefore (V_(1) ^(2))/(V _(2) ^(2)) = (T_(1))/( T_(2)) or T_(2) = T_(1) ((V_(2))/(V_(1))) ^(2)`
`= 273 xx(2) =273 xx 4= 1092K`
`T_(2) = (1092-273) =819^(@)C`