Question

    In a diatomic gas at ordinary temperatures, how many

    degrees of freedom contribute to internal energy?
    A 3 Correct Answer Incorrect Answer
    B 5 Correct Answer Incorrect Answer
    C 6 Correct Answer Incorrect Answer
    D 7 Correct Answer Incorrect Answer

    Solution

    In thermodynamics, the degrees of freedom of a gas molecule are the independent ways it can store energy. For a diatomic gas (e.g., O₂, N₂) at ordinary temperatures:

    • 3 translational degrees of freedom (motion along x, y, z axes)
    • 2 rotational degrees of freedom (about two perpendicular axes perpendicular to the bond axis)
    Thus, at ordinary temperatures, a diatomic molecule has: 5 degrees of freedom These 5 modes contribute to the internal energy, according to the equipartition theorem. The vibrational degrees of freedom (which would increase total to 7) are not active at ordinary temperatures due to quantum restrictions — they become significant only at high temperatures.

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