Question

As the sun shines on a snow-capped mountain, much of the snow sublimes instead of melts. How is this favored by entropy?

Short answer

Sublimation is favored by entropy because it increases molecular disorder.

Step-by-step solution

Understand the Process of Sublimation

Sublimation is the process where a solid changes directly into a gas without passing through the liquid state. In this scenario, the snow (solid) is directly turning into water vapor (gas) as the sun shines on the mountain.

Analyze Entropy Change

Entropy is a measure of the randomness or disorder in a system. When snow sublimes, it transforms from a highly ordered solid state, where molecules are tightly packed, to a more disordered gaseous state, where molecules are far apart and move freely. This transition increases the randomness of the molecules.

Apply the Second Law of Thermodynamics

According to the Second Law of Thermodynamics, processes that increase the entropy of a system are favored. Since sublimation results in increased molecular randomness and disorder, there is an increase in entropy.

Conclude the Effect of Entropy

Since sublimation increases the entropy of the system, it is thermodynamically favored. The natural tendency towards higher entropy supports the process of subliming snow on the mountain.

Key concepts

Sublimation

Sublimation is a fascinating process where a solid turns directly into a gas, skipping the liquid phase entirely. This can happen under specific conditions, usually involving changes in temperature or pressure. For a practical example, consider snow or ice on a mountain. When the sun shines, instead of turning into liquid water, some of the snow vaporizes directly into water vapor. One might wonder why this happens. The conditions on the mountain, such as lower air pressure and increased energy from the sun, facilitate this direct transition.
Sublimation is a common phenomenon in nature and even in everyday life. Think about dry ice, which is solid carbon dioxide. When exposed to air, it doesn't melt, but instead changes from a solid to a gas - sublime!
In sublimation, the molecules of a solid absorb energy sufficient to break the strong bonds holding them in a definite shape, allowing them to disperse as gas molecules.

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle in physics that helps to explain why certain processes occur naturally. It states that the total entropy of an isolated system can never decrease over time. Entropy can be thought of like a measure of disorder or randomness in a system, and according to this law, systems naturally progress toward greater disorder.
In the context of sublimation, when snow sublimates into water vapor, the process aligns with this law because it results in an increase in entropy. More molecular disorder means more entropy. Thus, because sublimation increases entropy, it is thermodynamically favorable.
This principle plays out in countless processes in the universe, illustrating the natural tendency towards chaos rather than order. It's why ice cubes melt, why gases mix, and even why energy spreads out over time.

Molecular Disorder

Molecular disorder refers to the arrangement and freedom of movement of molecules within a substance. In a solid state like snow, molecules are closely packed in a regular arrangement, which means there is low disorder or low entropy.
However, when a solid sublimates and becomes a gas, the molecules are no longer constrained to fixed positions. They are free to move around and spread out, leading to more disorder and higher entropy.
This increase in molecular freedom and randomness is a hallmark of gaseous states. It ties directly into why the process of sublimation is favored in terms of entropy. In essence, molecular disorder is a driving factor in many natural processes and is a critical component of understanding the behavior of substances as they change states.