According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant γ = C v C p is ( C P where C v are the specific heat capacities of the gas at

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According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant γ = C v ​ C p ​ ​ is ( C P ​ where C v ​ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):NEET 2024 (Re-NEET)

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A polygamic gas has 3 translational, 3 rotational and f vibration modes U = 2 3 ​ k B ​ T + 2 3 ​ k B ​ T + f k B ​ T U = ( 3 + f ) k B ​ T C V ​ = ( 3 + f ) R C p ​ = ( 4 + f ) R C v ​ C p ​ ​ = 3 + f 4 + f ​ = γ 4 + f = 3 γ + f γ 4 − 3 γ = f ( γ − 1 ) ⇒ f = γ − 1 4 − 3 γ ​

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