Lesson Plan | Traditional Methodology | Thermodynamics: Entropy

Objectives

Duration: (10 - 15 minutes)

This stage aims to prepare students to understand the concept of entropy, its importance in thermodynamics, and how it applies to physical processes. By clearly defining the objectives, it ensures that the focus of the lesson is aligned with the skills that students should acquire, facilitating understanding and learning of the content in a structured manner.

Main Objectives

1. Explain the concept of entropy and its relation to disorder in physical systems.

2. Demonstrate how to calculate the change in entropy in different thermodynamic processes.

3. Analyze and verify the behavior of entropy in closed and open systems.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to provide students with an initial understanding of the concept of entropy and its practical relevance. With a well-defined context and practical examples, students will be more prepared and motivated to delve into the calculations and analyses of changes in entropy in thermodynamic processes.

Context

To begin the lesson on entropy, explain to the students that thermodynamics is a field of physics that studies the laws governing energy transformations. Within thermodynamics, entropy is a fundamental concept related to disorder and the irreversibility of natural processes. Emphasize that understanding entropy is crucial for understanding how energy is distributed and transformed in physical systems, and how this affects everything from car engines to the expansion of the universe.

Curiosities

An interesting curiosity to engage students is that entropy is present in their daily lives in ways they might not imagine. For example, when mixing a glass of hot water with a glass of cold water, the tendency is for the temperature to stabilize, which is an example of increasing entropy. Another example is the melting of ice in a glass of water, where the ordered structure of the ice transforms into a more disordered structure of water molecules.

Development

Duration: (45 - 50 minutes)

The purpose of this stage is to deepen students' understanding of the concept of entropy, its importance in thermodynamics, and how to calculate the change in entropy in different processes. Through detailed explanations, practical examples, and problem-solving, students will be able to apply the concept of entropy in various situations and verify the increase or decrease of the entropy of a system.

Covered Topics

1. Definition of Entropy: Explain that entropy is a measure of the disorder or randomness of a system. Discuss how entropy is related to the second law of thermodynamics, which states that the entropy of the universe tends to increase. 2. Entropy in Reversible and Irreversible Processes: Detail the difference between reversible processes (where the total entropy of the system and the environment is constant) and irreversible processes (where the total entropy increases). Use examples such as free expansion of a gas and reversible adiabatic compression to illustrate these concepts. 3. Calculation of Change in Entropy: Show how to calculate the change in entropy (ΔS) in different processes. Exemplify with the formula ΔS = Q/T for isothermal processes and discuss how to integrate the equation dS = dq/T for adiabatic processes and other types of transformations. 4. Entropy and the Second Law of Thermodynamics: Reinforce the idea that the second law of thermodynamics implies that the total entropy of an isolated system never decreases. Use the example of a thermal engine to explain how efficiency is limited by the second law due to the increase in entropy. 5. Practical Applications and Everyday Examples: Discuss some practical applications of entropy, such as in thermal engines, refrigerators, and the expansion of the universe. Show everyday examples of increasing entropy, such as mixing substances and dissolving solids in liquids.

Classroom Questions

1. Calculate the change in entropy when 500 J of heat is reversibly transferred to a system at a constant temperature of 300 K. 2. A block of ice at 0°C melts to form water at 0°C. If the enthalpy of fusion of ice is 334 J/g, calculate the change in entropy when melting 100 g of ice. 3. Explain why the total entropy of the universe increases in an irreversible process, using the example of free expansion of a gas.

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to review and consolidate students' learning, ensuring that they well understand the discussed concepts and know how to apply the formulas and principles of entropy in different situations. Through detailed discussion of the resolved questions, the teacher can clarify doubts, reinforce important points, and stimulate students' critical thinking, promoting a deeper and more lasting understanding of the content.

Discussion

• Calculate the change in entropy when 500 J of heat is reversibly transferred to a system at a constant temperature of 300 K:

To calculate the change in entropy (ΔS), use the formula ΔS = Q/T.

Substituting the provided values, we have ΔS = 500 J / 300 K = 1.67 J/K. Therefore, the change in entropy is 1.67 J/K.

• A block of ice at 0°C melts to form water at 0°C. If the enthalpy of fusion of ice is 334 J/g, calculate the change in entropy when melting 100 g of ice:

First, calculate the total amount of heat required to melt 100 g of ice: Q = mass * enthalpy of fusion = 100 g * 334 J/g = 33400 J.

Now, use the formula ΔS = Q/T. The temperature should be converted to Kelvin: 0°C = 273.15 K.

Substituting the values, we have ΔS = 33400 J / 273.15 K ≈ 122.2 J/K. Therefore, the change in entropy is approximately 122.2 J/K.

• Explain why the total entropy of the universe increases in an irreversible process, using the example of free expansion of a gas:

In an irreversible process, such as the free expansion of a gas, the entropy of the system increases because the gas disperses to occupy a larger volume, increasing molecular disorder. The entropy of the environment does not decrease enough to compensate for this increase, resulting in an overall increase in the total entropy of the universe. According to the second law of thermodynamics, in any irreversible process, the total entropy of the universe always increases, reflecting the natural tendency of closed systems to move towards the greatest possible disorder.

Student Engagement

1. How is entropy related to the irreversibility of natural processes? Give examples from everyday life. 2. Why is the change in entropy an important measure in analyzing thermodynamic processes? 3. If the entropy of the universe is always increasing, what does this imply about the direction of time and the evolution of physical systems? 4. How would you explain the relationship between entropy and the second law of thermodynamics to someone who does not know physics? 5. Think of a thermal engine. How does entropy influence its efficiency and operation?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main points addressed during the lesson, ensuring that students have a clear and organized view of the concepts and applications of entropy. In addition, the conclusion reinforces the importance of the topic for understanding natural and technological processes, ensuring that students leave the lesson with a solid and practical understanding of the content.

Summary

• Explanation of the concept of entropy and its relation to disorder in physical systems.
• Demonstration of how to calculate the change in entropy in different thermodynamic processes.
• Analysis of entropy in reversible and irreversible processes.
• Application of the second law of thermodynamics and understanding of the increase in the entropy of the universe.
• Practical examples of the increase of entropy in everyday situations.

The lesson connected theory with practice by presenting practical and everyday examples of entropy, such as the mixing of hot and cold water and the melting of ice, in addition to solving real problems of change in entropy in different thermodynamic processes. This allowed students to visualize how theoretical concepts apply to concrete and relevant situations in their daily lives and to understanding natural and technological phenomena.

Entropy is a fundamental concept that affects various aspects of daily life, from the efficiency of engines and refrigerators to understanding natural phenomena such as the expansion of the universe. Knowing how to calculate and understand the change in entropy enables students to analyze and predict the behavior of physical systems, reflecting on the irreversibility of natural processes and the tendency toward increased disorder.