Question:
A polyatomic ideal gas has 24 vibrational modes. What is the value of \(\gamma\)?
A polyatomic ideal gas has 24 vibrational modes. What is the value of \(\gamma\)?
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Each vibrational mode contributes 2 degrees of freedom (kinetic and potential); a non-linear polyatomic gas has 3 translational + 3 rotational; then \(\gamma = 1 + 2/f\).
Updated On: Nov 4, 2026
- \(1.37\)
- \(1.30\)
- \(1.03\)
- \(10.3\)
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The Correct Option is C
Solution and Explanation
Degrees of freedom of a polyatomic gas with vibrational modes: \(f = 3\ (\text{translational}) + 3\ (\text{rotational}) + 2\times 24\ (\text{vibrational}) = 54\).
\(\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{54} = 1.037\approx 1.03\).
Answer: (3) 1.03
\(\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{54} = 1.037\approx 1.03\).
Answer: (3) 1.03
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