The molecules of a given mass of a gas have rms velocity of `200ms^(-1)` at ` 27^(@)C` and `1.0xx10^(5)Nm^(-2)` perssure. What the temperature and perssure of the gas are respectively.
`127^(@)C and 0.05xx10^(5)Nm^(-2)`
Find the rms velocity of its molecules in `ms^(-1)`

Explanation

`T_(1)=27^(@)+273=300K, T_(2)=127^(@)C+273=400K`
rms speed of molecules is `nu_(rms)=sqrt((3RT)/M)` So it depends only on temperature,
`nu_(rms) propto sqrtT`
`nu_(1)/nu_(2)=sqrt(T_(1)/T_(2))implies 200/V_(2)=sqrt((300)/(400)),200/nu_(2)=sqrt3/2`
`nu_(2)=400/sqrt3`
`nu_(2)=231ms^(-1)`