The average velocity of `CO_(2)` at the temperature `T_(1)` Kelvin and the most probable veloctiy at `T_(2)` Kelvin is `9.0xx10^(4)cm s^(-1)`. Calculate the values of `T_(1)` and `T_(2)`.

Explanation

We know
Average speed `u_(AV) =sqrt(((8RT)/(piM)))`
Most probable speed `u_(MP) =u_(MP) = sqrt(((8RT)/(M))`
Average speed at `T_(1) K=MP` speed at `T_(2) K` for `CO_(2)`
`sqrt(((8RT_(1))/(piM))) = sqrt(((2RT_(2))/(M)))`
`(T_(1))/(T_(2)) = (pi)/(4)`
Also for `CO_(2), u_(MP) = sqrt(((2RT_(2))/(M))) = 9 xx 10^(4)`
`:.sqrt((( 2xx8.314 xx10^(7)xxT_(2))/(44)))=9 xx10^(4)`
`T_(2) =2143.37 K`
`:.` By eq (1) `T_(1) = 1684.0 K` .