The molecules of a given mass of gas have a rms velocity of `200 m//sec at 127^(@)C and 1.0 xx 10^(5) N//m^(2)` pressure. When the temperature is `127^(@)C` and pressure is `0.5 xx 10^(5) N//m^(2)` the rms velocity in `m//sec` will be

Options

A. `(100 sqrt(2))/(3)`
B. `100sqrt(2)`
C. `(400)/(sqrt(3))`
D. none of the above

Answer

C

Explanation

`(v'_(rms))/(v_(rms)) = sqrt((T')/(T)) sqrt((127+273)/(27+273)) = sqrt((400)/(300))`
`v'_(rms) = sqrt((4)/(3))v_(rms) = sqrt((4)/(3)) xx 200 = (400)/(sqrt(3))m//s`