Match the LIST-I with LIST-II LIST-I A. Triatomic rigid gas B. Diatomic non-rigid gas C. Monoatomic gas D. Diatomic rigid gas LIST-II I. Cp/Cv = 5/3 II. Cp/Cv = 7/5 III. Cp/Cv = 4/3 IV. Cp/Cv = 9/7 Choose the correct answer from the options given below:

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q33 – JEE-MAIN 2025

Match the LIST-I with LIST-II

\begin{array}{lcl} LIST-I & LIST-II \\ A. Triatomic rigid gas & I. \frac{C_{p}}{C_{v}} = \frac{5}{3} \\ B. Diatomic non-rigid gas & II. \frac{C_{p}}{C_{v}} = \frac{7}{5} \\ C. Monoatomic gas & III. \frac{C_{p}}{C_{v}} = \frac{4}{3} \\ D. Diatomic rigid gas & IV. \frac{C_{p}}{C_{v}} = \frac{9}{7} \end{array}

Choose the correct answer from the options given below:

The ratio of specific heats ( $γ$ ) for an ideal gas is directly related to its degrees of freedom ( $f$ ).

🥷

Ninja Strategy•Match known values first

Start by matching the most definitively known $γ$ values (monoatomic and diatomic rigid) to quickly eliminate incorrect options.

Step 1: Recall the formula for the ratio of specific heats✦ Active

The ratio of specific heats, $γ = \frac{C_{p}}{C_{v}}$ , for an ideal gas is related to its degrees of freedom ( $f$ ) by the formula:

γ = 1 + \frac{2}{f}

Step 2: Determine degrees of freedom for each gas type○ Expand

Based on the molecular structure and rigidity:

\begin{array}{ll} Monoatomic gas & f = 3 (3 translational) \\ Diatomic rigid gas & f = 5 (3 translational + 2 rotational) \\ Diatomic non-rigid gas & f = 7 (3 translational + 2 rotational + 2 vibrational) \\ Triatomic rigid gas (non-linear) & f = 6 (3 translational + 3 rotational) \end{array}

💡 Teacher's Secret Hint

For triatomic rigid gas, assume non-linear unless specified otherwise, as it allows for 3 rotational degrees of freedom.

Step 3: Calculate

γ

and match with LIST-II○ Expand

Using $γ = 1 + \frac{2}{f}$ :

\begin{array}{ll} A. Triatomic rigid gas (f = 6) : & γ = 1 + \frac{2}{6} = 1 + \frac{1}{3} = \frac{4}{3} \to III \\ B. Diatomic non-rigid gas (f = 7) : & γ = 1 + \frac{2}{7} = \frac{9}{7} \to IV \\ C. Monoatomic gas (f = 3) : & γ = 1 + \frac{2}{3} = \frac{5}{3} \to I \\ D. Diatomic rigid gas (f = 5) : & γ = 1 + \frac{2}{5} = \frac{7}{5} \to II \end{array}

The correct matching is A-III, B-IV, C-I, D-II, which corresponds to option 2.

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