For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at `127^(@)C`. At 2 atm pressure and at `227^(@)C`, the rms speed of the molecules will be:

Options

A. `100 m//s`
B. `80sqrt(5)m//s`
C. `100 sqrt(5)m//s`
D. `80 m//s`

Answer

c

Explanation

`V_(rms)= sqrt((2RT)/(M))`
`(v_(1))/(v_(2))= sqrt((T_(1))/(T_(2)))= sqrt(((273+127))/(273+227))`
`= sqrt((400)/(500))= sqrt((4)/(5))= (2)/(sqrt(5))`
`:. v_(2)= (sqrt(5))/(2)v_(1)= (sqrt(5))/(2)xx 200= 100sqrt(5)m//s`