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For a non-linear N-atomic ideal gas molecule with all degrees of freedom (translational, rotational, and vibrational) fully excited, find the value of Cp/Cv - 1.

1. 1 / (3N - 3)
2. 1 / N
3. 1 / (3N - 3) only (without the leading 1+)
4. 1 / (N - 1)

Correct answer: 1 / (3N - 3)

Solution

With all modes excited, Cv = (3N-3)R and Cp = (3N-2)R for a non-linear N-atom molecule, giving Cp/Cv - 1 = R/Cv = 1/(3N-3).

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