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The average velocity of CO(2) at the tem...

The average velocity of `CO_(2)` at the temperature `T_(1)K` and maximum (most) proable velocity of `CO_(2)` at the temperature `T_(2) K` is `9xx10^(4) cm s^(-1)`. Calculate the values of `T_(1)` and `T_(2)`.

Text Solution

Verified by Experts

The correct Answer is:
(1682.5 k , 2142 k)
`u_(av)`(average velocity) `=sqrt((8RT_(1))/(pi M)) rArr (9 xx 10^(4))/(100) ms^(-1) = sqrt((8 xx 8.314 T_(1))/(3.14 xx 44 xx 10^(-3))) rArr T_(1) = 1682.5 K`
Also, for the same gas `(u_(av))/(u_(m ps)) = sqrt((8RT_(1))/(pi M)): sqrt((2RT_(2))/(M)) = sqrt((8T_(1))/(pi) xx (1)/(2T_(2))) = sqrt((4T_(1))/(pi T_(2))) rArr 1 = sqrt((4T_(1))/(pi T_(2)))`
`rArr T_(2) = (4T_(1))/(pi) = (4 xx 1682.5)/(3.14) = 2124K`, Hence, `T_(1) = 1682.5 K and T_(2) = 2142K`
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