Kinetic Theory of Gases: JEE Main Physics Question with Solution
Match List I with List II :List-I(A)(B)(C)(D)3 Translational degrees of freedom3 Translational, 2 rotational degrees of freedoms3 Translational, 2 rotational and 1 vibrational degrees of freedom3 Translational, 3 rotational and more than one vibrational degrees of freedomList II(I)(II)(III)(IV)Monoatomic gasesPolyatomic gasesRigid diatomic gasesNonrigid diatomic gases
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Hint 1 of 3
How many translational, rotational, and vibrational degrees of freedom does an ideal monoatomic gas possess?
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Correct answer
The correct matching is (A) - (I), (B) - (III), (C) - (IV), and (D) - (II).
Inverting the degree-of-freedom ordering by incorrectly assigning high vibrational degrees of freedom to monoatomic gases. Recall that point-like monoatomic gas particles have only 3 translational degrees of freedom with no rotational or vibrational modes.
Confusing nonrigid diatomic gases with monoatomic gases and polyatomic gases with rigid diatomic gases. Associate the basic 3 translational modes with monoatomic gases, and assign non-zero vibrational modes to nonrigid or complex molecules.
C · (A) - (I), (B) - (III), (C) - (IV), (D) - (II)
None. This correctly maps translational, rotational, and vibrational modes to their corresponding molecular geometries. This is correct: monoatomic has 3 translational, rigid diatomic adds 2 rotational, nonrigid diatomic adds 1 vibrational mode, and non-linear polyatomic adds 3 rotational plus multiple vibrational modes.
D · (A) - (I), (B) - (IV), (C) - (III), (D) - (II)
Swapping the properties of rigid and nonrigid diatomic gases. A rigid diatomic gas has fixed bond lengths and zero vibrational modes, whereas a nonrigid diatomic gas includes active vibrational modes.
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Solution
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Recall standard degrees of freedom: monoatomic gas has only 3 translational modes (A → I); rigid diatomic adds 2 rotational modes (B → III); non-rigid diatomic includes 1 additional vibrational mode (C → IV); non-linear polyatomic has 3 translational, 3 rotational, and multiple vibrational modes (D → II), giving (A)-(I), (B)-(III), (C)-(IV), (D)-(II).