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Polyatomic gas with a given number of vibrational modes: find Cp/Cv

The same question, asked 2 times: 2021 Paper 7*, 2021 Paper 8. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 7

    3
    A polyatomic (non-linear) ideal gas has 24 vibrational modes. What is the value of γ=CpCv\gamma=\frac{C_p}{C_v} for this gas?

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  2. Question 2

    2021 Paper 8

    2
    If one mole of the polyatomic gas is having two vibrational modes and β\beta is the ratio of molar specific heats for polyatomic gas (β=CPCV)\left( \beta=\frac{C_{P}}{C_{V}} \right) then the value of β\beta is:

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