Question

The mean square speed of the molecules of a gas at absolute temperature T is proportional to
(a) $\frac{1}{T}$
(b) $\sqrt{T}$
(c) T
(d) T².

Answer 1

Root mean squared velocity is given by
$$\begin{gathered} v_{rms}=\sqrt{\frac{3RT}{M}} \\ \Rightarrow {\left(v_{rms}\right)}^2=\frac{3RT}{M} \\ \Rightarrow {\left(v_{rms}\right)}^2\alpha T \end{gathered}$$

Thus, (c) is the correct answer.