According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant \(\gamma=\frac{C_{\mathrm{p}}}{C_{\mathrm{v}}}\) is (where \(C_p\) and \(C_v\) are the specific heat capacities of the gas at constant pressure and constant volume, respectively):
1. \(\frac{4+3\gamma}{\gamma-1}\)
2. \(\frac{3+4\gamma}{\gamma-1}\)
3. \(\frac{4-3\gamma}{\gamma-1}\)
4. \(\frac{3-4\gamma}{\gamma-1}\)
Subtopic:  Law of Equipartition of Energy |
From NCERT
NEET - 2024
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The value \(\gamma = \dfrac{C_P}{C_V}\) for hydrogen, helium, and another ideal diatomic gas \(X\) (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:
1. \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{9}{7}\)
2. \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{9}{7}\)
3. \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{7}{5}\)
4. \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{7}{5}\)

Subtopic:  Law of Equipartition of Energy |
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From NCERT
NEET - 2019
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