When temperature of an ideal gas is increased from `27^(@)C" to "227^(@)C` , its rms speed is changed from `400ms^(-1) " to "V_(s)` . Then , the `V_(s)` is

Options

A. `516ms^(-1)`
B. `450ms^(-1)`
C. `350ms^(-1)`
D. `746ms^(-1)`

Answer

A

Explanation

We know that rms speed is directly proportional to square root of temperature.
`v_("rms")propsqrt(T)`
Hence , `v_("rms"_(1))/v_("rms"(2))=sqrt((T_(1))/(T_(2)))rArr(400)/(v_("rms"))=sqrt(27+273)/sqrt(227+273)=sqrt((300)/(500))`
`v_("rms"_(2))=vsqrt((500)/(300))xx400`
`=1.29xx400=516.39ms^(-1)~~516ms^(-1)`