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At what temperature will the average vel...

At what temperature will the average velocity of oxygen molecules be sufficient to escape from the earth. Given mass of oxygen molecule `= 5.34 xx 10^(-26) kg`. Boltzmann constant, `k = 1.38 xx 10^(-23) J "molecule"^(-1) K^(-1)`. Escape velocity of earth `= 11.0 km s^(-1)`.

Text Solution

Verified by Experts

The correct Answer is:
`(1452pi)/(25)xx10^(3)K`
At every temperature there will be some molecules with the required escape speed, as theoretically
`0 le |vecV| le prop` at all temperatures.
`V_(arm) = sqrt((8RT)/(piM)) :. sqrt((8RT)/(piM)) = 11 xx 10^(3) m//s`
put `R = 25//3J-mol^(-1)K^(-1)`
`M = 0.032` is `SI` units `(kg//mol)`
`(11^(2) xx 10^(3xx2)) xx (pi)/(8) xx (3)/(25) xx 0.032 = T`
`T = (1452pi)/(25) xx 10^(3)K`
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