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. `(100sqrt2)/3`
B. `100sqrt2`
C. `(400)/sqrt3`
D. None of the above

Answer

C

Explanation

`v_(rms) prop sqrtT`
`rArr v_1/v_2 = sqrt(T_1/T_2) rArr 200/v_2 = sqrt(((273 + 27))/((273 + 127)))`
`rArr v_2 = 400/sqrt3 m//s`.