If the absolute temperature of a sample of gas in a fixed volume container is quadrupled, then the root mean square speed in the initial state `u_(i)` and that in the final stage `u_(f)` be related as .

Options

A. `u_(f)=u_(i)//4`
B. `u_(f)=u_(i)//2`
C. `u_(f)= 2u_(i)`
D. `u_(f)= 4u_(i)`

Answer

C

Explanation

`u_(i) prop sqrtT_(1)`
`u_(f) prop sqrtT_(2)`
`(u_(i))/(u_(f)) = sqrt(T_(1)/(T_(2))) = sqrt(T_(1)/(4T_(1))) = (1)/(2)` .