The molecules of a given mass of gas have a rms velocity of `200 m//sec` at `27^(@)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. `100(sqrt(2))`
C. `400/(sqrt(3))`
D. None of these

Answer

C

Explanation

Change in pressure will not affect the rms velocity of molecules. So we will calculate only the effect of temperature.
As, `v_(rms) prop sqrt(T)`
`:. (v_(300^@))/(v_(400^@)) = sqrt((300)/(400)) = sqrt((3)/(4)) implies (200)/(v_(400)) = sqrt(3/4)`
`implies v_(400) = (200xx2)/(sqrt(3)) = (400)/(sqrt(3)) m//s`.