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JEE Main 202311 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
11 April
Shift
Morning Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2023 · 11 April · Morning Shift · Physics · Kinetic Theory of Gases

Three vessels of equal volume contain gases at the same temperature...

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 (vrms)\left({v}_{rms}\right) and choose the correct answer from the options given below:

Options

  1. Avrms(mono)>vrms(dia)>vrms(poly){v}_{rms} ( mono ) > {v}_{rms} ( dia ) > {v}_{rms} ( poly )
  2. BVrms(mono)=Vrms(dia)=Vrms(poly){V}_{rms} ( mono ) = {V}_{rms} ( dia ) = {V}_{rms} ( poly )
  3. Cvrms(mono)<vrms(dia)<vrms(poly){v}_{rms} ( mono ) < {v}_{rms} ( dia ) < {v}_{rms} ( poly )
  4. Dvrms(dia)<vrms(poly)<vrms(mono){v}_{rms} ( dia ) < {v}_{rms} ( poly ) < {v}_{rms} ( mono )

Correct answer

A. vrms(mono)>vrms(dia)>vrms(poly){v}_{rms} ( mono ) > {v}_{rms} ( dia ) > {v}_{rms} ( poly )

Step-by-step solution

The RMS speed is given vrms{v}_{rms} =3RTM= \sqrt{\dfrac{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.

vrms(mono)=3RT4×10−3vrms(dia)=3RT71×10−3vrms(poly)=3RT352×10−3{v}_{rms} ( mono ) = \sqrt{\dfrac{3RT}{4 \times {10}^{- 3}}}{v}_{rms} ( dia ) = \sqrt{\dfrac{3RT}{71 \times {10}^{- 3}}}{v}_{rms} ( poly ) = \sqrt{\dfrac{3RT}{352 \times {10}^{- 3}}}

vrms∝1M{v}_{\text{rms}} ∝ \dfrac{1}{\sqrt{M}}

Hence,

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

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