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Match the C_p/C_v ratio for ideal gases with different type of molecules : Molecule Type | C_p/C_v (A) Monoatomic | (I) 7/5 (B) Diatomic rigid molecules | (II) 9/7 (C) Diatomic non-rigid molecules | (III) 4/3 (D) Triatomic rigid molecules | (IV) 5/3

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

Correct answer: (1) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Solution

The correct option matches the specific heat ratios for different types of molecules based on their degrees of freedom. Monoatomic gases have a ratio of 5/3 due to their limited motion, diatomic rigid molecules have a ratio of 7/5, diatomic non-rigid molecules can have more vibrational modes leading to a ratio of 9/7, and triatomic rigid molecules have a ratio of 7/5 as well.

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