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JEE Main 202310 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
10 April
Shift
Morning Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2023 · 10 April · Morning Shift · Physics · Kinetic Theory of Gases

Match List I with List II: List I List II (A) 3 Translational...

Match List I with List II:

List I List II
(A) 33 Translational degrees of freedom (I) Monoatomic gases
(B) 33 Translational, 22 rotational degrees of freedoms (II) Polyatomic gases
(C) 33 Translational, 22 rotational and 11 vibrational degrees of freedom (III) Rigid diatomic gases
(D) 33 Translational, 33 rotational and more than one vibrational degrees of freedom (IV) Nonrigid diatomic gases

Choose the correct answer from the options given below:

Options

  1. A(A)−(I),(B)−(III),(C)−(IV),(D)−(II)\left(A\right) - \left(I\right), \left(B\right) - \left(III\right), \left(C\right) - \left(IV\right), \left(D\right) - \left(II\right)
  2. B(A)−(IV),(B)−(III),(C)−(II),(D)−(I)\left(A\right) - \left(IV\right), \left(B\right) - \left(III\right), \left(C\right) - \left(II\right), \left(D\right) - \left(I\right)
  3. C(A)−(IV),(B)−(II),(C)−(I),(D)−(III)\left(A\right) - \left(IV\right), \left(B\right) - \left(II\right), \left(C\right) - \left(I\right), \left(D\right) - \left(III\right)
  4. D(A)−(I),(B)−(IV),(C)−(III),(D)−(II)\left(A\right) - \left(I\right), \left(B\right) - \left(IV\right), \left(C\right) - \left(III\right), \left(D\right) - \left(II\right)

Correct answer

A. (A)−(I),(B)−(III),(C)−(IV),(D)−(II)\left(A\right) - \left(I\right), \left(B\right) - \left(III\right), \left(C\right) - \left(IV\right), \left(D\right) - \left(II\right)

Step-by-step solution

The formula for degree of freedom is given by

f=3N−kf = 3N - k

where NN is the number of particles, kk is the individual relationship in the system.

For a monoatomic gas particle, N=1,k=0N = 1, k = 0. So, f=3f = 3

Hence, monoatomic gas has 33 translational degree of freedom.

For a rigid diatomic gas molecule, there are 55 degrees of freedom, 33 translational and 22 rotational. A diatomic gas can have two extra degrees of freedom due to rotation along two independent axes.

A non rigid diatomic molecule has one extra degree of freedom than a rigid one. This is the vibrational degree of freedom. Hence, it has 66 degrees of freedom.

So, a non rigid diatomic gas has 33 translational, 22 rotational and 11 vibrational degrees of freedom.

A polyatomic gas has more than two atoms per molecule. Hence, the total number of degrees of freedom is 33 translational, 33 rotational and more than one vibrational degree of freedom.

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