WBJEE · Physics · Kinetic Theory of Gases
Let \(\overline{\mathrm{V}}, \mathrm{V}_{\mathrm{rms}}, \mathrm{V}_{\mathrm{p}}\) denotes the mean speed, root mean square speed and most probable speed of the molecules each of mass \(m\) in an ideal monoatomic gas at absolute temperature T Kelvin. Which statement(s) is/are correct?
- A No molecules can have speed greater than \(\sqrt{2} V_{r m s}\)
- B No molecules can have speed less than \(V_p / \sqrt{2}\)
- C \(V_p \lt \bar{V} \lt V_{r m s}\)
- D Average kinetic energy of a molecule is \(\frac{3}{4} m V_p^2\)
Answer & Solution
Correct Answer
(D) Average kinetic energy of a molecule is \(\frac{3}{4} m V_p^2\)
Step-by-step Solution
Detailed explanation
\(V_{r m s}=\sqrt{\frac{3 R T}{M}}\) \(V_{a v g}=\sqrt{\frac{8 R T}{\pi M}}\) \(\mathrm{V}_{\mathrm{mp}}=\sqrt{\frac{2 R T}{\mathrm{M}}}, \mathrm{~V}_{\mathrm{p}} \lt \overline{\mathrm{V}} \lt \mathrm{V}_{\mathrm{rms}}\)…
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