The absolute temperature of the gas is increased 3 times. What will be the increases in root mean square velocity of the gas molecules?

Options

A. `upsilonsqrt(2)`
B. `upsilon//sqrt(3)`
C. `sqrt(3) upsilon`
D. same

Answer

C

Explanation

[`upsilon` is the root mean square velocity of gas molecules at temperature T]
`upsilon_(rms)=sqrt(((3RT)/(M)))`
`rArr upsilon_(rms) prop sqrt(T)`
`:. (upsilon'_(rms))/(upsilon'_(rms))=sqrt(((T')/T))`
Here `upsilon_(rms)=upsilon, T'=3T`
`:. upsilon'_(rms) =sqrt(((3T)/T)) upsilon`
`=sqrt(3) upsilon`