An ideal gas is made of polyatomic molecules. | vedclass

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(A) For a polyatomic gas molecule, the total degrees of freedom $F$ is given by the sum of translational, rotational, and vibrational modes.Given: Tra

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$4$

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(A) For a polyatomic gas molecule, the total degrees of freedom $F$ is given by the sum of translational, rotational, and vibrational modes.Given: Translational modes = $3$, Rotational modes = $3$, Vibrational modes = $f$.Each vibrational mode contributes $2$ degrees of freedom (one for kinetic energy and one for potential energy).So, the total degrees of freedom $F = 3 + 3 + 2f = 6 + 2f$.The ratio of heat capacities $\gamma = C_p/C_v = 1 + 2/F$.Given $\gamma = 8/7$, we have $8/7 = 1 + 2/F$.$8/7 - 1 = 2/F \implies 1/7 = 2/F \implies F = 14$.Equating the two expressions for $F$: $6 + 2f = 14$.$2f = 8 \implies f = 4$.

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_p/C_v$ of the gas is $8/7$, then the value of $f$ is:

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