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Cp/Cv or molar specific heat from the degrees of freedom (including vibrational modes)

This type of question, asked 9 times: 2021 Paper 7, 2021 Paper 8, 25 Jun 2022, 26 Jul 2022, 24 Jan 2023, 25 Jan 2023, 22 Jan 2025, 2 Apr 2025, 7 Apr 2025. All 9 questions 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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  3. Question 3

    25 Jun 2022

    96
    The ratio of specific heats (CPCV)\left( \frac{C_{P}}{C_{V}} \right) in terms of degree of freedom (f) is given by:

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  4. Question 4

    26 Jul 2022

    102
    A gas has nn degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be:

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  5. Question 5

    24 Jan 2023

    102
    Let γ1\gamma_{1} be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and γ2\gamma_{2} be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, γ1γ2\frac{\gamma_{1}}{\gamma_{2}} is:

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  6. Question 6

    25 Jan 2023

    91
    According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is: -

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  7. Question 7

    22 Jan 2025

    83
    For a diatomic gas, if γ1=(CpCv)\gamma_{1}=\left( \frac{Cp}{Cv} \right) for rigid molecules and γ2=(CpCv)\gamma_{2}=\left( \frac{Cp}{Cv} \right) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

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  8. Question 8

    2 Apr 2025

    24
    γA\gamma_{A} is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. γB\gamma_{B} is the specific heat ratio of polyatomic gas BB having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If γAγB=(1+1n)\frac{\gamma_{A}}{\gamma_{B}} = \left( 1 + \frac{1}{n} \right), then the value of nn is .
  9. Question 9

    7 Apr 2025

    13
    Match the List-I with List-II
    List-IList-II
    A. Triatomic rigid gasI. CPCV=53\frac{C_{P}}{C_{V}} = \frac{5}{3}
    B. Diatomic non-rigid gasII. CPCV=75\frac{C_{P}}{C_{V}} = \frac{7}{5}
    C. Monoatomic gasIII. CPCV=43\frac{C_{P}}{C_{V}} = \frac{4}{3}
    D. Diatomic rigid gasIV. CPCV=97\frac{C_{P}}{C_{V}} = \frac{9}{7}
    Choose the correct answer from the options given below :

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