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

Explanation

Let , `T=T_1=273K`
RMS velocity,
`C=sqrt((3RT_1)/m)" "...(1)`
When the RMS velocity is tripled,
`3C=sqrt((3RT_2)/M)" "...(2)`
Dividing equation (2) by (1) we get
`(3C)/C=sqrt((3RT_2//M)/(3Rxx273//M))`
`3=sqrt((T_2)/(273))`
Squaring on both side
`9 = T_2/273`
`:. T_2 = 273xx9=2457K`
Temperature
`T_2= 2457K`