By what factor the rms velocity will change, if the temperature s raised from `27^(@)C` to `327^(@)C`?

Options

A. `sqrt2` times
B. 2 times
C. `2sqrt2`times
D. 4 times

Answer

A

Explanation

Root mean square velocity `(V"rms")` given by
`v" rms"=sqrt((3RT)/(M))` where , R is gas constant , M the molecular weight and T the temperature.
Given , `T_(1)=27^(@)C=273+27=300K`
`T_(2)=327^(@)C=273+327=600K`
`therefore(v"rms")_(1)/(v"rms")_(2)=sqrt((300)/(600))=sqrt((1)/(2))rArr(v"rms")_(2)=sqrt2(v"rms")_(1)`
Hence ,rms speed increases `sqrt2` times.