Question

The root mean square velocity of a gas is doubled when the temperature is
(a) increased four times
(b) increased two times
(c) reduced to half
(d) reduced to one fourth

Answer 1

The option ( B ) increased two times is the answer which I think.

Answer 2

answer : option (a) increased four times.

explanation : root mean square velocity of a gas is given by, $v_{rms}=\sqrt{\frac{3RT}{M}}$

where R is universal gas constant, T is temperature in Kelvin and M is molecular weight of gas.

here, it is clear that root mean square velocity is directly proportional to square root of T.

e.g., $v_{rms}\propto\sqrt{T}$

so, rms velocity will be doubled when temperature of is increased four times.

hence, option (a) is correct choice.