Kinetic theory – name the law for energy sharing among degrees of freedom The statement “The total energy of a molecule is shared equally among the various degrees of freedom it possesses” is known as which law?

Introduction / Context:
In kinetic theory and statistical thermodynamics, the equipartition theorem links microscopic degrees of freedom to macroscopic thermodynamic quantities like specific heats. Recognizing the name of the law from its statement is a common conceptual check in exams.

Given Data / Assumptions:

• Classical (high-temperature) limit where quantum effects are negligible for accessible modes.
• Degrees of freedom include translational, rotational, and (at sufficiently high T) vibrational modes.
• Each quadratic degree of freedom carries an average energy of (1/2) * k_B * T per molecule.

Concept / Approach:

The equipartition theorem (law of equipartition of energy) states that, at thermal equilibrium, energy is shared equally among all independent quadratic degrees of freedom. This explains, for example, why ideal monatomic gases have cv = (3/2) * R (per mole), while diatomic gases at moderate temperatures exhibit higher specific heats due to active rotational modes.

Step-by-Step Solution:

Verification / Alternative check:

Measurements of specific heats versus temperature show plateaus corresponding to activation of additional modes (rotational, vibrational), broadly consistent with equipartition in the classical limit.

Why Other Options Are Wrong:

Conservation/degradation laws describe energy conservation and quality, not equal sharing among modes.Third law relates to entropy behavior near absolute zero, not energy partitioning.

Common Pitfalls:

Applying equipartition blindly at low temperatures where quantum freezing occurs; some degrees of freedom do not contribute fully to specific heat until sufficiently excited.

Final Answer:

law of equipartition of energy