Question

The molecules of a given mass of a gas have rms velocity of `200 m//s at 27^(@)C and 1.0 xx 10^(5) N//m_(2)` pressure. When the temperature and pressure of the gas are respectively `127^(@)C and 0.05 xx 10^(5) Nm^(-2)`, the rms velocity of its molecules in `ms^(-1)` is
A. `(400)/(sqrt(3))`
B. `(100sqrt(2))/(3)`
C. `(100)/(3)`
D. `100sqrt(2)`

Answer 1

Correct Answer - a
It is given that
`v_(rms) = 200 ms^(-1), T_(1) = 300K, P_(1) = 10^(5) N//m^(2)`
`T_(2) = 400 K, P_(2) = 0.05 xx 10^(5) N//m^(2)`
As, rms velocity of gas molecules.
`because v_(rms) prop sqrt(T) " " (because v_(rms) = sqrt((3RT)/(m)))`
For two different cases
`rArr ((v_(rms))_(1))/((v_(rms))_(2)) = sqrt((T_(1))/(T_(2))) rArr (200)/((v_(rms))_(2)) = sqrt((300)/(400)) = sqrt((3)/(4))`
`rArr (v_(rms))_(2) = (2)/(sqrt(3)) xx 200 = (400)/(sqrt(3))ms^(-1)`