Question

Which of the following is not accompanied by an increase in the entropy of the system: (a) mixing of two gases at the same temperature and pressure, (b) mixing of ethanol and water, (c) discharging a battery, (d) expansion of a gas followed by compression to its original temperature, pressure, and volume?

Short answer

Option (d): Expansion and compression of a gas does not increase entropy.

Step-by-step solution

Understand the Concept of Entropy

Entropy is a measure of the disorder or randomness in a system. Generally, when a system becomes more disordered, its entropy increases. We'll examine each option to determine which scenario does not result in increased entropy.

Evaluate Mixing of Two Gases

When two gases are mixed, even if they are at the same temperature and pressure, the entropy increases due to the increase in disorder. Each gas's molecules are spread out more randomly after mixing.

Evaluate Mixing of Ethanol and Water

Mixing ethanol and water results in increased entropy. The liquids' molecules intermingle, increasing disorder compared to the separated pure substances.

Evaluate Discharging a Battery

Discharging a battery increases entropy as it converts chemical energy into electrical energy and heat, dispersing energy and increasing system randomness.

Evaluate Expansion and Compression of a Gas

For the expansion of a gas followed by compression back to its original temperature, pressure, and volume, the entropy of the system does not increase. The process is cyclic and reversible, effectively returning the system to its initial state, maintaining its original entropy.

Key concepts

Entropy Increase

Entropy, a fundamental concept in thermodynamics, measures the level of disorder or randomness in a system. When a system moves towards a state of higher disorder, such as when substances mix or energy is dispersed, its entropy rises. This increase is a reflection of the tendency of energy and matter to spread out in a given space. For instance:

• Mixing two different gases or liquids enhances the disorder at a molecular level, thus increasing entropy.
• In batteries, the conversion of stored chemical energy to other forms during discharge leads to a rise in entropy.
• However, entropy does not increase in cyclic and reversible processes where the system returns to its original state.

Understanding the principle of entropy increase is crucial as it underlies many natural and artificial processes.

Entropy and Disorder

The relationship between entropy and disorder can be likened to rearranging a deck of cards. When ordered, there's low entropy; scrambled, entropy is high. This analogy applies broadly in nature. When we consider systems like gases or liquids, the randomness of their molecules reflects high entropy states. Examples include:

• Gases mixing where molecules distribute randomly across the volume, enhancing disarray.
• During battery discharge, new products form and energy disperses, leading to increased disorder.

Disorder isn't inherently "bad." It's a natural progression in many processes, showcasing energy's inherent tendency to spread out.

Cyclic and Reversible Processes

Not all processes lead to a change in entropy, as seen in cyclic and reversible processes. In these scenarios, systems undergo changes but ultimately return to their starting conditions. When a gas expands and is then compressed back to the original state, we have a cyclic process. Key attributes:

• The entropy of the system remains unchanged because it is reversible.
• Reversibility suggests the process can run backwards precisely, maintaining disorder levels.
• No net energy is dispersed, so no lasting increase in entropy occurs.

Understanding these processes helps in designing more efficient systems where energy conservation is essential.

Mixing and Entropy

Mixing different substances typically results in an increase in entropy. This is largely due to the increased degree of randomness as distinct molecules intermingle. Consider these scenarios:

• When two gases mix, each type of molecule occupies new positions, enhancing the overall disorder.
• Mixing liquids like ethanol and water allows molecules to intermingle, surpassing their initial ordered structures.

This behavior illustrates the universality of entropy increase in mixing, governed by the second law of thermodynamics, emphasizing the inherent drive towards disorder.

Battery Discharge and Entropy

Battery discharge is a practical demonstration of entropy increase. As the battery converts chemical energy into electrical energy and heat:

• The chemical reactions progress, creating products that increase the system's disorder.
• Energy disperses from concentrated forms to more spread-out forms, elevating system entropy.

This discharge exemplifies the inevitable trend towards energy dispersion and disorder characteristic of real-world systems. Understanding this concept is vital for improving battery technologies, focusing on energy efficiency and performance enhancement.