The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root mean square velocity of the gas molecules is v, at 480 K it becomes

Options

A. `4 v`
B. `2v`
C. `(v)/(2)`
D. `(v)/(4)`

Answer

B

Explanation

The root mean square volocity is given by
`v"rms"=sqrt((3RT)/(M))`
`So " "(v_(1))/(v_(2))=sqrt((T_(1))/(T_(2)))`
Now , `T_(1)=120K,T_(2)=480K,v_(1)=v`
`so, " " (v_(1))/(v_(2))=sqrt((120)/(480))=sqrt((1)/(4))=(1)/(2)`
`rArr" " (v)/(v_(2))=(1)/(2)`
`rArr" "v_(2)=2v`