In the temperature changes from `27^(@)C` to `127^(@)C`, the relative percentage change in RMS velocity is

Options

A. 1.56
B. 2.56
C. 15.6
D. 82.4

Answer

C

Explanation

`v_(rms)=sqrt((3RT)/(M))` fo a particular gas,
M is constant `v_(rms)propsqrt(T)`
`v_(rms)propsqrt(T)impliesv_(rms)=x xxsqrt(T)` (where `x=sqrt((3R)/(M))`)
So, at `27^(@)(300K)` ltBrgt `v_(rms)=xsqrt(300)=17.3x`
at `127^(@)C(400K)`
`v_(rms)=xsqrt(400)=20x`
`therefore`Percentage increase
`=((20x-17.3x))/(17.3)xx100=15.6%`
At `27^(@)C,v_(rms)` will be `sqrt(400)=20`
Percentage increase
`=((20-17.3))/(17.3)xx100`
`=15.6%`