Vibrational Energy and Degrees of Freedom – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Vibrational Energy and Degrees of Freedom

Assertion (A): Vibrational energy of molecule at temperature \(T\) is \(kT\).
Reason (R): For every molecule, vibrational degree of freedom is 2.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true as each vibrational mode contributes \(kT\) to the internal energy. Reason (R) is false; vibrational degrees of freedom vary by molecular structure (e.g., diatomic molecules have 1). Thus, (A) is true and (R) is false.

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