The temperature of the gas is raised from `27^(@)C` to `927^(@)C`, the root mean square velocity is

Options

A. `sqrt((927)/(27))` times of the earlier value
B. same as before
C. halved
D. doubled

Answer

D

Explanation

Root mean square velocity at `T_(1)` temperature,
`U_(1)=sqrt((3RT_(2))/(M))=sqrt((3R(27+273))/(M))" ...(i)"`
Root mean square velocity at `T_(2)` temperature,
`U_(2)=sqrt((3RT_(2))/(M))=sqrt((3R(927+273))/(M))" ...(ii)"`
Eq. (i) divided by Eq. (ii)
`(U_(1))/(U_(2))=sqrt((27+273)/(927+273))=sqrt((300)/(1200))=(1)/(2)`
`U_(2)=2U_(1)`