JEE Physics 2023 Question with Solution

Given: Two lists are to be matched using the degrees of freedom of different gases.

Find: The correct correspondence between List I and List II.

Use the standard classification of molecular degrees of freedom:

• Monoatomic gases have only translational degrees of freedom.
• Rigid diatomic gases have translational and rotational degrees of freedom.
• Nonrigid diatomic gases also include vibrational motion.
• Polyatomic gases have translational, rotational, and multiple vibrational modes.

From the given data:

1. (A) $3$ Translational degrees of freedom corresponds to monoatomic gases, so (A) \rightarrow (I).
2. (B) $3$ Translational, $2$ rotational degrees of freedom corresponds to rigid diatomic gases, so (B) \rightarrow (III).
3. (C) $3$ Translational, $2$ rotational, and $1$ vibrational degrees of freedom corresponds to nonrigid diatomic gases, so (C) \rightarrow (IV).
4. (D) $3$ Translational, $3$ rotational, and more than one vibrational degrees of freedom corresponds to polyatomic gases, so (D) \rightarrow (II).

Therefore, the correct matching is (A)-(I), (B)-(III), (C)-(IV), (D)-(II).

The solution states that the correct option is B, but this does not agree with the listed option values. The option text matching the worked solution is Option A.

Therefore, the most defensible correct option is A.

Given:

• Monoatomic gases
• Rigid diatomic gases
• Nonrigid diatomic gases
• Polyatomic gases

Find: Which gas type matches each degree-of-freedom description.

The extracted table from the solution gives:

Matching term by term:

• (A) matches (I)
• (B) matches (III)
• (C) matches (IV)
• (D) matches (II)

Hence the correct mapping is (A)-(I), (B)-(III), (C)-(IV), (D)-(II), which corresponds to Option A among the listed options.

Thus, although the page labels the correct option as B, the worked explanation supports Option A.