Problem 69 - Pearson Physics

Question

If you clean up a messy room, putting things back where they belong, you decrease the room's entropy. Does this violate the second law of thermodynamics? Explain.

Step-by-Step Solution

Answer

No, cleaning a room doesn't violate the second law of thermodynamics because the total entropy of the system (room plus person) doesn't decrease.

Step 1: Understanding the Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. Entropy, often associated with disorder, will tend to decrease in any spontaneous process, causing the system to become more disordered unless energy is added.

Step 2: Identifying the System Involved

Consider the room as part of a larger system that includes the person cleaning it. The room itself is not an isolated system because it interacts with the surroundings, such as the person cleaning it.

Step 3: Energy and Entropy changes due to Cleaning

When you clean a room, you expend energy. This energy comes from your body and transfers to the room, allowing you to decrease the room's entropy by organizing it. Meanwhile, your body (and the overall environment) experiences an increase in entropy.

Step 4: Considering Overall Entropy Change

While the room's entropy decreases, the entropy increase in your body and the surroundings (due to energy expenditure and heat generation) compensates for this decrease. Thus, the total entropy of the combined system (room plus person) either stays the same or increases.

Step 5: Conclusion

Cleaning the room does not violate the second law of thermodynamics because, even though the room's entropy decreases, the total entropy of the system (including the person and their interactions with the surroundings) does not decrease.

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics, playing a crucial role in understanding how energy and disorder interact. It's often described as a measure of disorder or randomness within a system. The second law of thermodynamics revolves around this concept, stating that the entropy of an isolated system tends to increase or remain constant over time. This principle implies that natural processes tend to progress toward a state of maximum entropy. For instance, a messy room represents a higher entropy state than when it is clean and organized. Removing clutter means decreasing the room's entropy, but this action does not violate thermodynamic laws because the decrease in the room's entropy is offset by entropy increases elsewhere. This highlights that entropy balances changes across the entire system.

Isolated System

An isolated system in thermodynamics is one that has no interaction with its surroundings. This means it cannot exchange energy nor matter with anything outside its boundaries. The concept is crucial in applying the second law of thermodynamics, as it sets conditions where the law holds its strictest form: in an isolated system, total entropy cannot decrease. The house in the messy room problem isn't isolated; it includes the person cleaning it. Since energy is added to the room through human effort, it interacts with its surroundings, making it a non-isolated system. The concept of an isolated system helps us comprehend why cleaning does not infringe upon thermodynamic laws; the person's interaction with the room and their energy expenditure are key to understanding the broader system's entropy changes.

Energy Transfer

Energy transfer plays a critical role in changes in entropy. When a person cleans a messy room, they are transferring energy from their body to the room. This energy comes from metabolic processes, which themselves generate entropy. When a room is organized, its entropy decreases, seemingly contradicting the second law. However, the process of cleaning involves energy transfer that increases entropy elsewhere, such as in the person's body through heat production and in the air via breathing. This change maintains or increases the total entropy of the combined person-room system, in alignment with the thermodynamic principle that mandates entropy increase or stability in isolated systems.

• Energy applied to the system results in decreased local entropy.
• Surrounding environment absorbs leftover energy, increasing its own entropy.

Disorder

Disorder is intricately linked to entropy. In thermodynamics, a system with high entropy is usually more disordered, such as a scattered pile of books. Organizing a room reduces its local disorder, seemingly suggesting a decrease in entropy. However, thanks to energy input from cleaning, disorder is only reduced locally while increased energetically elsewhere. When you tidy up, you're temporarily reducing disorder. This is possible because the energy invested in organizing is transformed into heat and other forms of energy, spreading disorder throughout other areas. This counters the temporary decrease in local disorder, ensuring that the overall disorder according to the second law doesn’t decline.

• Local disorder can decrease with energy input.
• Overall disorder, including wider environmental considerations, remains constant or increases.