The root mean square velocity of a gas is doubled when the temperature is

Options

A. Reduced to half
B. Reduced to one-fourth
C. Increased four times
D. Increased two times

Answer

c

Explanation

`U_(rms) propto sqrt(T)`
` therefore U_(rms1)/ U_(rms2)=sqrt(T_(1)/T_(2))`
`U/(2U) = sqrt(T_(1)/T_(2))`
` T_(1)/T_(2)= 1/4`
`implies T_(2)= 4T_(1)`
`therefore` The root mean square velocity of a gas usually doubles when the temperature increases four times.