The root mean square speed $v_{rms}$ of gas molecules at a temperature $T$ is proportional to which of the following?

Solution

1. The formula for root mean square speed is $v_{rms}=\sqrt{\frac{3RT}{M}}$.
2. Here $R$ is the gas constant, $T$ is temperature, and $M$ is molar mass.
3. Since $R$ and $M$ are constants, $v_{rms}\propto \sqrt{T}$.
4. Hence the answer is (B).