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Four molecules of a gas have speeds 1,2,...

Four molecules of a gas have speeds 1,2,3 and `4 km//s`. Find the rms speed of the gas molecule.

Text Solution

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Given `C_(1) = 1 km//s , C_(2) = 2 km//s`
`C_(3) = 3km//s , C_(4) = 4 km//s`
The root mean square speed of molecules is
`C_(rms) = sqrt((C_(1)^(2)+C_(2)^(2)+C_(3)^(2)+C_(4)^(2))/(4))`
`= sqrt((1^(2)+2^(2)+3^(2)+4^(2))/(4))`
`= sqrt((1+4+9+16)/(4)) = sqrt(7.5)`
`C_(rms) = 2.74 km//s`.
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