Calculate the temperature at which the rms velocity of a gas triples its value at S.T.P. `[T_(1)=273K]`

Explanation

At STP temperature `T_(1)=273K`
RMS velocity of a gas `(nu(rms))_(1)=nu`
New RMS velocity of a gas, at temperature `(T_(2))`
`(nu_(rms))_(2)=3nu`
New tempertaure `T_(2)=?`
`nu _(rms)=sqrt((3RT)/M)`
`(nu_(rms))_(1)/(nu_(rms))_(2)=sqrt(T_(1)/T_(2)`
`T_(2)=(nu_(rms))_(2)/(nu_(rms))_(1)^(2)xxT_(1)=((3nu)/nu)^(2)xx273`
`T_(2)=9xx273=2457K`