Lesson Plan | Traditional Methodology | Linear Expansion

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to establish a clear and structured foundation for what students should learn during the lesson. By defining the main objectives, the teacher can guide the explanation in a focused manner, ensuring that all essential points are addressed. This also helps students understand what is expected of them and the importance of the topic in the context of its practical applications.

Main Objectives

1. Understand the concept of linear expansion and how it occurs in solid materials.

2. Learn the mathematical formula that describes linear expansion and how to apply it.

3. Solve practical problems involving the linear expansion of objects, such as iron bars.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to capture the students' attention by establishing a connection between theoretical content and its practical applications in the real world. By presenting curiosities and everyday examples, students are encouraged to recognize the relevance of the theme, becoming more engaged and receptive to learning.

Context

Explain to the students that the phenomenon of linear expansion is a physical effect observed in solid materials when there is a variation in temperature. Start by mentioning that all bodies are made up of atoms and molecules, which are in constant motion. This movement is intensified with the increase in temperature, causing the atoms and molecules to move apart, resulting in the expansion of the material. Cite practical examples from everyday life, such as the expansion of train tracks on hot days, which can cause deformation if there is not enough space for expansion.

Curiosities

Did you know that thermal expansion is a crucial factor in the construction of bridges and buildings? The metal structures of these constructions need expansion joints to allow for the expansion and contraction of materials, preventing structural damage. Another interesting example is mercury in thermometers, which expands with heat, allowing for accurate temperature measurement.

Development

Duration: (45 - 60 minutes)

The purpose of this stage is to deepen students' understanding of the concept of linear expansion, ensuring that they comprehend both the theory and practical application. Through detailed explanations of the topics and problem-solving, students will be able to apply the formula for linear expansion in real situations and solve problems involving the expansion of materials due to temperature changes.

Covered Topics

1. Definition of Linear Expansion: Explain that linear expansion refers to the change in length of a solid material when there is a change in temperature. Highlight that this change is directly proportional to the change in temperature and the initial length of the material. 2. Formula for Linear Expansion: Present the mathematical formula for linear expansion: ΔL = L₀ * α * ΔT, where ΔL is the change in length, L₀ is the initial length, α is the linear expansion coefficient of the material, and ΔT is the change in temperature. 3. Linear Expansion Coefficient: Explain that the linear expansion coefficient, α, is a constant that depends on the material. Different materials have different values of α, which means they expand at different rates when subjected to the same temperature change. 4. Practical Applications: Detail some practical applications of linear expansion, such as in train tracks, bridges, and thermometers. Explain how engineers and scientists utilize the knowledge of linear expansion to design structures that can accommodate the expansion and contraction of materials without causing damage.

Classroom Questions

1. An iron bar has an initial length of 2 meters at 20°C. If the temperature increases to 50°C, what will be the change in length of the bar? (The linear expansion coefficient of iron is 12 x 10⁻⁶ °C⁻¹) 2. A steel rail 10 meters long expands 5 mm when the temperature increases by 30°C. What is the linear expansion coefficient of steel? 3. An aluminum ruler is 1 meter long at 25°C. If the temperature drops to -10°C, what will be the new length of the ruler? (The linear expansion coefficient of aluminum is 24 x 10⁻⁶ °C⁻¹)

Questions Discussion

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate the knowledge acquired by the students, allowing them to check their answers and understand the necessary steps for solving the problems. Additionally, the proposed discussions and reflections encourage critical thinking and practical application of the learned content, promoting a deeper and more lasting understanding of the topic.

Discussion

• Discussion of the Questions Solved by Students 

1. Question 1:

   • Statement: An iron bar has an initial length of 2 meters at 20°C. If the temperature increases to 50°C, what will be the change in length of the bar? (The linear expansion coefficient of iron is 12 x 10⁻⁶ °C⁻¹)
   • Resolution:
     • Step 1: Identify the given data: L₀ = 2 meters, ΔT = 50°C - 20°C = 30°C, α = 12 x 10⁻⁶ °C⁻¹.
     • Step 2: Apply the formula for linear expansion: ΔL = L₀ * α * ΔT.
     • Step 3: Calculate: ΔL = 2m * 12 x 10⁻⁶ °C⁻¹ * 30°C = 0.00072 meters or 0.72 mm.
     • Conclusion: The iron bar will have a change in length of 0.72 mm.

2. Question 2:

   • Statement: A steel rail 10 meters long expands 5 mm when the temperature increases by 30°C. What is the linear expansion coefficient of steel?
   • Resolution:
     • Step 1: Identify the given data: L₀ = 10 meters, ΔL = 5 mm = 0.005 meters, ΔT = 30°C.
     • Step 2: Rearrange the formula for linear expansion to find α: ΔL = L₀ * α * ΔT, then α = ΔL / (L₀ * ΔT).
     • Step 3: Calculate: α = 0.005m / (10m * 30°C) = 0.005 / 300 = 1.67 x 10⁻⁵ °C⁻¹.
     • Conclusion: The linear expansion coefficient of steel is 1.67 x 10⁻⁵ °C⁻¹.

3. Question 3:

   • Statement: An aluminum ruler is 1 meter long at 25°C. If the temperature drops to -10°C, what will be the new length of the ruler? (The linear expansion coefficient of aluminum is 24 x 10⁻⁶ °C⁻¹)
   • Resolution:
     • Step 1: Identify the given data: L₀ = 1 meter, ΔT = -10°C - 25°C = -35°C, α = 24 x 10⁻⁶ °C⁻¹.
     • Step 2: Apply the formula for linear expansion: ΔL = L₀ * α * ΔT.
     • Step 3: Calculate: ΔL = 1m * 24 x 10⁻⁶ °C⁻¹ * -35°C = -0.00084 meters or -0.84 mm.
     • Conclusion: The aluminum ruler will shrink by 0.84 mm, resulting in a new length of 0.99916 meters.

Student Engagement

1. ### Student Engagement 樂

• Question 1: Why is it important to consider thermal expansion in the construction of bridges and train tracks?
• Question 2: How does the linear expansion coefficient vary among different materials and why is this relevant?
• Reflection 1: Think of other everyday examples where thermal expansion can have visible effects. How do these examples influence our daily lives?
• Reflection 2: Discuss how thermal expansion can be a problem in electronic components and how engineers can mitigate these effects.

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to recap the main points of the lesson, reinforcing the connection between theory and practice, and highlighting the relevance of the topic for everyday life. This helps consolidate the acquired knowledge and the importance of the subject, preparing students to apply what they have learned in real situations and future lessons.

Summary

• Linear expansion refers to the change in length of a solid material due to changes in temperature.
• The formula for linear expansion is ΔL = L₀ * α * ΔT.
• The linear expansion coefficient, α, is specific to each material.
• Practical applications include train tracks, bridges, and thermometers.

The lesson connected the theory of linear expansion with practical applications by demonstrating how temperature variation affects the length of solid materials, using examples such as train tracks and bridges. This allowed students to visualize the importance of the phenomenon in daily life and in engineering contexts.

Understanding linear expansion is crucial for various areas of daily life and engineering. For example, expansion joints in bridges prevent structural damage caused by thermal expansion. Additionally, the phenomenon is visible in mercury thermometers, which expand with heat, allowing for precise measurements.