Match the List I with List II
Choose the correct answer from the options given below:

Solution

Physics sir · 3 steps

Count the degrees of freedom f for each gas, then γ = 1 + 2/f matches it in one line.

1. The one formula. By equipartition, Cᵥ = f/2R and Cₚ = Cᵥ + R. Dividing gives γ = Cₚ/Cᵥ = 1 + 2/f, so you only need f for each gas.
2. Counting f. Every molecule has 3 translational modes. A diatomic molecule adds 2 rotational modes, and a rigid non-linear triatomic molecule adds 3. If the molecule is non-rigid, each vibrational mode adds 2, one for kinetic energy and one for potential energy.

   Gas	Degrees of freedom f	γ = 1 + 2/f	Match
   (A) Triatomic rigid	3 + 3 = 6	4/3	III
   (B) Diatomic non-rigid	3 + 2 + 2 = 7	9/7	IV
   (C) Monoatomic	3	5/3	I
   (D) Diatomic rigid	3 + 2 = 5	7/5	II

3. So. The matching is A-III, B-IV, C-I, D-II, which is option (a).

The idea to keep. For any ideal gas, γ = 1 + 2/f. Get f right: 3 for translation, 2 or 3 for rotation, and 2 for each vibrational mode.

Answer from the NTA final answer key. Solution by PrepWiser.