Third-law perspective: At a temperature of absolute zero (0 K), what kind of molecular energy does a classical ideal gas possess?

Introduction / Context:
Absolute zero (0 K) is a limiting concept where thermal motion ceases. In classical thermodynamics and kinetic theory, the internal energy of an ideal gas is purely kinetic; at 0 K, that kinetic energy vanishes. This question checks conceptual understanding across translational, rotational, and vibrational modes.

Given Data / Assumptions:

• Classical ideal-gas model.
• Temperature is exactly 0 K.
• No quantum zero-point corrections are considered in this introductory context.

Concept / Approach:
For an ideal gas, mode energies scale with temperature: translational, rotational, and vibrational energies all go to zero as T → 0 K in the classical limit. Therefore, the gas possesses no thermal energy in any mode at 0 K.

Step-by-Step Solution:

Verification / Alternative check:
Quantum mechanics introduces zero-point energy in bound systems (e.g., vibrations), but the classical ideal-gas model used in basic thermodynamics ignores such effects for free molecules.

Why Other Options Are Wrong:

• Translational/Rotational/Vibrational only: Each implies residual thermal energy at 0 K, which is not the classical result.

Common Pitfalls:
Conflating classical and quantum results; for basic chem eng thermodynamics, the classical “no thermal energy at 0 K” framing is intended.

Final Answer:
None of these