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Kinetic Theory
Degrees of freedom and specific heats of gases
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- Degrees of freedom and specific heats of gases
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2024 Re-NEET 1 question
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According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $\gamma=\dfrac{C_p}{C_v}$ is ($C_p$, $C_v$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):A polyatomic gas has 3 translational, 3 rotational, and f vibrational modes. $U=\left(3+f\right)k_BT$ (each vibrational mode contributing $k_BT$). So $C_V=(3+f)R$, $C_P=(4+f)R$, and $\gamma=\dfrac{4+f}{3+f}$. Solving, $4+f=3\gamma+f\gamma\Rightarrow4-3\gamma=f(\gamma-1)\Rightarrow f=\dfrac{4-3\gamma}{\gamma-1}$.