Energy Contribution of Vibrational Mode – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

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 Explained:

To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:

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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