Question

Which of the following processes results in an increase in entropy of the system? (a) A drop of ink spreading out when it is placed in water (b) Steam condensing into drops on windows (c) Constructing a building from loose bricks

Short answer

(a) A drop of ink spreading out in water increases entropy.

Step-by-step solution

Understanding Entropy

Entropy is a measure of disorder or randomness in a system. A process that increases entropy typically involves spreading out energy or matter, leading to a more disordered state.

Analyzing Process (a)

In process (a), a drop of ink spreads out in water. Initially, the ink is concentrated in a small area, but as it diffuses, it occupies a larger volume. This spreading leads to increased randomness or disorder in the system, thus increasing entropy.

Analyzing Process (b)

Process (b) involves steam condensing into drops on windows. In this phenomenon, water vapor (a more disordered state) converts to liquid water droplets (a more ordered state), which results in a decrease in entropy.

Analyzing Process (c)

For Process (c), constructing a building from loose bricks involves arranging bricks into a structured and orderly form. This transformation from a disordered pile to an ordered structure reduces entropy.

Identifying the Process with Increased Entropy

From the analysis, process (a) leads to increased entropy, as the ink's spreading constitutes a move towards greater disorder compared to processes (b) and (c).

Key concepts

Entropy Increase

Entropy is a fundamental concept in thermodynamics and statistical mechanics. It symbolizes the amount of disorder or random arrangement in a system. When something involves spreading or mixing elements more randomly, its entropy usually increases. For instance, imagine you're watching a drop of ink spreading in a glass of water. At first, the ink is concentrated in one spot, but over time it spreads throughout the water. This spread signifies an increase in entropy, as the ink molecules move from a state of order to a more disordered state, filling a larger volume.

The increase in entropy implies that a system becomes less predictable and its outcomes more varied. Generally, natural processes tend to favor states with higher entropy, because they involve more possible configurations, thus increasing disorder. In the spectrum of processes, those resulting in more dispersal and less organization, such as the spreading of ink, are prime examples of entropy increase.

Disorder in Systems

Disorder in physical systems can be seen as the way in which matter and energy are distributed. When a system moves towards greater disorder, its entropy increases. Consider a box containing gas molecules. If initially, these molecules are all in one corner of the box, the system is in a low entropy state due to its orderliness.

However, over time, these molecules will execute random motion and spread out to fill the entire box. This transformation to a uniform distribution of molecules represents an increase in disorder or chaos, which equals higher entropy. In systems where components, like molecules in a gas, become more evenly and randomly distributed, we witness a natural drift toward disorder. This inclination towards disorder is a crucial element in understanding how energy disperses or how chemical reactions take place.

Randomness

Randomness in systems is deeply tied to the concept of entropy. It describes situations where outcomes are unpredictable due to the large number of possible configurations. Think about flipping a coin multiple times. At first, it’s quite random how many heads or tails you might get. This randomness correlates to entropy because each coin flip increases the possible arrangements, adding to disorder.

In physical systems, randomness is portrayed by the erratic motion of particles. For example, gas molecules bouncing off each other in a container exhibit a high degree of randomness. The more random their motion, the higher the system's entropy. Random motion leads to numerous possibilities in particle distribution, which amplifies entropy. Therefore, randomness and entropy go hand in hand – the more random a process or system, the greater the entropy.

Diffusion Process

The diffusion process is a textbook example of entropy in action, illustrating how substances spread from areas of high concentration to areas of low concentration, leading to increased disorder. Imagine again the ink drop in water. Over time, the ink disperses evenly throughout the liquid due to diffusion.

This process is a result of molecules moving from an ordered, compact state to a random, dispersed state. Diffusion exemplifies nature's preference for increasing disorder, as molecules seek to minimize energy and maximize dispersal. This spreading out is the hallmark of rising entropy – the ink particles become randomly distributed, increasing systemic disorder.

In broader terms, diffusion helps explain not just the physical mixing of substances, but also concepts such as the spreading of heat or the distribution of resources, emphasizing the natural tendency toward disorder and chaos in systems.