The temperature of an ideal gas is increased from `27^(@)C to 127^(@)C`, the percentage increase in `V_(rms)` is [2013]

Options

A. 0.37
B. 0.11
C. 0.33
D. `15.5`%

Answer

D

Explanation

We know, `v_(rms)=sqrt(3RT)/(M)`
`rArr`%increse in
`v_(rms)=sqrt((3RT_(2))/(M)-sqrt(3RT_(1)/(M))/sqrt(3RT_(1))/(M)xx100`
`=sqrt(T_(2)-sqrt(T_(1))/(sqrt(T_(1))xx100`
`=sqrt((400)-sqrt(300))/sqrt(300)xx100`
`=(20-17.32)/(17.32)xx100`
=15.5%