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

Options

A. `37%`
B. `11%`
C. `33%`
D. `15.5%`

Answer

D

Explanation

We know `v_("rms") = sqrt((3RT)/(M))`
`implies` % increase 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) xx 100`
`=15.5% `