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Show that the root mean square velocity ...

Show that the root mean square velocity of an `O_(2)` molecule at `54^(@)C` is not twice its root mean square velocity at `27^(@)C`.

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At `54^(@)C`, i.e., at (273+54)K=327K the root mean square velocity of `O_(2)` molecule,
`(c_(rms))_(1)=sqrt((3RT)/(M))=sqrt((3xx8.314xx10^7 xx327)/(32))`
`=5.048xx10^(4)cm*s^(-1)`
and at `27^(@)C` i.e., at `(273+27)K=300K`
`(c_(rms))_(2)=sqrt((3RT)/(M))=sqrt((3xx8.314xx10^(7)xx300)/(32))`
`=4.835xx10^(4)cm*s^-1`
`therefore (c_(rms))_(1)ne2(c_(rms))_(2)`
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