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

Explanation

Here, `upsilon_(1) = 200m//s`
`T_(1) = 27^(@)C = (27+273)K = 300K`
`P_(1) = 1 xx 10^(5) N//m^(2)`
`T_(2) = 127^(@)C = (127 + 273)K = 400K`
`P_(2) = 0.5 xx 10^(5) N//m^(2) . Upsilon_(2)=?`
As is known rms velocity of gas molecules does not depend upon pressure, and
`upsilon prop sqrt(T)`
`:. (upsilon_2)/(upsilon_1) = sqrt((T_2)/(T_1))`
`upsilon_(2) = upsilon_(1) sqrt((T_2)/(T_1)) = 200 xx sqrt((400)/(300)) = (200 xx 2)/(sqrt(3)) m//s`
`upsilon_(2) = 230.9 m//s`.