Three vessels of equal volume contain gases at the same temperature… | JEE Main 2023 (11 Apr, Shift 1)

Q15JEE Main 2023 · 11 APR · SHIFT 1Easy

Degrees of Freedom & Internal Energy

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 hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $(v_{\text{rms}})$ and choose the correct answer from the options given below:

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Answer: (b)

$v_{rms} = \sqrt{\frac{3RT}{M}} \propto \frac{1}{\sqrt{M}}$ at the same $T$ .
$M$ : Ne $= 20$ , $\text{Cl}_2 = 71$ , $\text{UF}_6 = 352$ g/mol.
So $v_{rms}$ (mono) $> v_{rms}$ (dia) $> v_{rms}$ (poly): answer (b).

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