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

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)`.

Text Solution

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`"Average velocity"=sqrt((8RT)/(piM))`
`"Most probable velocity"=sqrt((2RT)/(M))`
`"Average velocity at "T_(1)K="Most probable velocity at "T_(2)K`
`=9.0xx10^(4)" cm s"^(-1)`
`R=8.314xx10^(7)" ergs K"^(-1)"mol"^(-1),M=44`
`"Average velocity at "T_(1)K`
`sqrt((8xx8.314xx10^(7)xxT_(1))/(3.143xx44))=9.0xx10^(4)`
`T_(1)=(81xx10^(8)xx3.143xx44)/(8xx8.314xx10^(7))=1682.5K`
`"Similarly, "sqrt((2xx8.314xx10^(7)xxT_(2))/(44))=9.0xx10^(4)`
`T_(2)=(81xx10^(8)xx44)/(2xx8.314xx10^(7))`
`=2143K.`
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