Three vessels of equal volume… - JEE Main 2023 Physics PYQ

JEE Main 2023 — Physics 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 hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $({v}_{rms})$ and choose the correct answer from the options given below:

Official previous-year question

Held on 11 Apr 2023 · Verified 6 Jul 2026.

Options

A
${v}_{rms}(\mathrm{mono})>{v}_{rms}(\mathrm{dia})>{v}_{rms}(\mathrm{poly})$
B
${V}_{rms}(\mathrm{mono})={V}_{rms}(\mathrm{dia})={V}_{rms}(\mathrm{poly})$
C
${v}_{rms}(\mathrm{mono})<{v}_{rms}(\mathrm{dia})<{v}_{rms}(\mathrm{poly})$
D
${v}_{rms}(\mathrm{dia})<{v}_{rms}(\mathrm{poly})<{v}_{rms}(\mathrm{mono})$

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Solution

The RMS speed is given ${v}_{rms}$ $=\sqrt{\frac{3RT}{M}}$ .

The temperature and pressure is same for all the gases. So the speed is inversely proportional to the square root of the molar mass of the gases.

${v}_{rms}(mono)=\sqrt{\frac{3RT}{4\times {10}^{-3}}} {v}_{rms}(dia)=\sqrt{\frac{3RT}{71\times {10}^{-3}}} {v}_{rms}(poly)=\sqrt{\frac{3RT}{352\times {10}^{-3}}}$

${v}_{\text{rms }}\propto \frac{1}{\sqrt{M}}$

Hence,

${v}_{rms}(poly)<{v}_{rms}(dia)<{v}_{rms}(mono)$ .

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Options

${v}_{rms}(\mathrm{mono})>{v}_{rms}(\mathrm{dia})>{v}_{rms}(\mathrm{poly})$

${V}_{rms}(\mathrm{mono})={V}_{rms}(\mathrm{dia})={V}_{rms}(\mathrm{poly})$

${v}_{rms}(\mathrm{mono})<{v}_{rms}(\mathrm{dia})<{v}_{rms}(\mathrm{poly})$

${v}_{rms}(\mathrm{dia})<{v}_{rms}(\mathrm{poly})<{v}_{rms}(\mathrm{mono})$

Solution

The RMS speed is given ${v}_{rms}$ $=\sqrt{\frac{3RT}{M}}$ .

The temperature and pressure is same for all the gases. So the speed is inversely proportional to the square root of the molar mass of the gases.

${v}_{rms}(mono)=\sqrt{\frac{3RT}{4\times {10}^{-3}}} {v}_{rms}(dia)=\sqrt{\frac{3RT}{71\times {10}^{-3}}} {v}_{rms}(poly)=\sqrt{\frac{3RT}{352\times {10}^{-3}}}$

${v}_{\text{rms }}\propto \frac{1}{\sqrt{M}}$

Hence,

${v}_{rms}(poly)<{v}_{rms}(dia)<{v}_{rms}(mono)$ .

Options

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Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

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