WBJEE · Physics · Kinetic Theory of Gases
Six molecules of an ideal gas have velocities \(1,3,5,5,6\) and \(5 \mathrm{~m} / \mathrm{s}\) respectively. At any given temperature, if \(\overline{V}\) and \(V_{\mathrm{rms}}\) represent average and rms speed of the molecules, then
- A \(\overline{V}=5 \mathrm{~m} / \mathrm{s}\)
- B \(V_{r m s} > \overline{V}\)
- C \(V_{\text {rms }}^2 < \overline{V}^2\)
- D \(V_{r m s}=\overline{V}\)
Answer & Solution
Correct Answer
(B) \(V_{r m s} > \overline{V}\)
Step-by-step Solution
Detailed explanation
Hint : \(\overline{V}=\frac{1+3+5+5+6+5}{6}=\frac{25}{6}=4.16\) \(\begin{aligned} & \overline{V}_{\mathrm{ms}}=\sqrt{\frac{1+9+25 \times 3+36}{6}}=\sqrt{\frac{121}{6}}=\frac{11}{\sqrt{6}}=4.48 \\ & \mathrm{~V}_{\mathrm{rms}} > \overline{V} \end{aligned}\)
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