JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Heat & Thermodynamics

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Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic). the second contains chlorine (diatomic) and third contains uranium hexafloride polyatomic). Arrange these on the basis of their root mean square speed (

v_{rms}

) and choose the correct answer from the options given below:

(A) $V_{rms} ($ mono $) = v_{rms} ($ dia $) = v_{rms} ($ poly $)$
(B) $v_{rms}$ (mono) $> v_{rms}$ (dia) $> v_{rms}$ (poly)✓ Correct
(C) $v_{rms} ($ dia $) < v_{rms} ($ poly $) < v_{rms} ($ mono $)$
(D) $V_{rms} ($ mono $) < V_{rms} ($ dia $) < V_{rms} ($ poly $)$

Answer: (B)

Solution

The root mean square speed is

v_{r m s} = \frac{3 R T}{M}

, set by temperature and molar mass and independent of pressure. At the common temperature

v_{r m s} \propto \frac{1}{M}

. The molar masses rise in the order neon (

20

g/mol), chlorine (

71

g/mol), uranium hexafluoride (

352

g/mol), so the speeds fall in the reverse order. Hence

v_{r m s} (mono) > v_{r m s} (dia) > v_{r m s} (poly)

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option

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JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Heat & Thermodynamics

Solution

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