Energy Contribution of Vibrational Mode – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Energy Contribution of Vibrational Mode

For an ideal gas, total energy is equally distributed in all possible energy modes, with each mode has an average energy equal to \(\frac{1}{2} k_B T\), and each vibrational mode has energy contribution of
\(\frac{1}{3} k_B T\)
\(k_B T\)
\(\frac{3}{2} k_B T\)
\(\frac{1}{4} k_B T\)

Solution:

Each vibrational mode has both kinetic energy and potential energy modes, thus having two degrees of freedom. Therefore, the average energy per vibrational mode is \(2 \times \frac{1}{2} k_B T = k_B T\).

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