Question

A carbon monoxide (CO) crystal is found to have entropy greater than zero at absolute zero of temperature. Give two possible explanations for this observation.

Short answer

The carbon monoxide (CO) crystal's entropy is greater than zero at absolute zero due to the potential existence of a degenerate ground state and/or structural disorder.

Step-by-step solution

Concept of residual entropy

In some cases, substances can have what's known as 'residual entropy' at absolute zero (0 K). This most often occurs when a system possesses multiple microscopic arrangements (microstates) that are energetically equivalent. Hence, even at absolute zero, it's unclear which specific microstate the system is in, resulting in an entropy greater than zero.

Outline of Possible Explanation 1: Degenerate ground state

A possible explanation for CO crystal's non-zero entropy at absolute zero could be a degenerate ground state. A degenerate ground state is a state with minimum energy where there exist multiple possible equivalent microstates. In the case of a CO crystal, if the CO molecules can align in multiple possible ways with the same energy, there would be a non-zero entropy at absolute zero. This is because the system doesn't know which specific alignment to adopt as all such configurations are energetically equivalent.

Outline of Possible Explanation 2: Structural disorder

Another potential explanation might be structural disorder. Even if the energy states are not degenerate, if the CO molecules in the crystal do not adopt a fully ordered configuration at T=0 K, it can lead to non-zero entropy. This can occur because of some intrinsic asymmetry in the crystal structure, leading the system to have multiple equivalent (but structurally distinct) ways to arrange the CO molecules.

Key concepts

Exploring Absolute Zero

Absolute zero, or 0 Kelvin, is the theoretical point where a system's thermal motion comes to a halt. At this temperature, complex concepts arise. It's commonly understood that entropy, a measure of a system's disorder, should be zero at absolute zero. This is because there should ideally be only one way to arrange particles in their ground state. Thus, no disorder should remain.
However, situations exist where entropy is not zero at this temperature. This indicates a more intricate structure within the system. Certain factors like residual entropy can contribute to this anomaly, where the existence of multiple microscopic states (microstates) implies that the system is not in a perfectly ordered state. The unusual observation of non-zero entropy at absolute zero in certain materials, like a CO crystal, fascinates scientists, leading them toward a deeper understanding of quantum mechanics and material behavior.

Understanding Degenerate Ground State

A degenerate ground state is an interesting concept where different microstates of a system hold the same minimum energy level. In other words, there are several energetically equivalent ways for particles in a system to arrange at its lowest energy point.
If a system exhibits a degenerate ground state, it can have considerable implications on its entropy. For example, a CO crystal having multiple arrangements of its molecules at the same energy level means these configurations coexist. This multiplicity leads to non-zero residual entropy at absolute zero.
To simplify, imagine multiple parking spots that are all equally close to the store entrance. Each spot is a different microstate, but all provide the same benefits. Hence, even at the lowest energy state, the system has multiple avenues to explore, creating residual entropy by default.

The Role of Structural Disorder

Structural disorder is another phenomenon that can explain residual entropy. Even without energy degeneracy, a system can exhibit a lack of complete order in its molecular arrangements. This could be due to intrinsic asymmetry or irregularities in the crystal structure.
Take a CO crystal as an example. If molecules don't settle into a perfectly ordered pattern, different non-identical but energetically similar microstates arise. This scenario results in multiple ways to configure the molecules while still not influencing the energy significantly. Consequently, the entropy at absolute zero remains greater than zero due to these structural possibilities.
Thus, structural disorder implies a form of chaotic arrangement without necessarily implying high-energy instability. These underlying configurations offer diversity in the arrangement without altering the overall stability, contributing to the residual entropy observed in certain materials.