Objectives (5 minutes)

1. Understand the concept of thermal expansion of liquids: Students should be able to understand what thermal expansion is and how it applies to liquids. They should be able to explain the change in volume of a liquid in a container due to an increase in temperature.

2. Calculate the expansion of a liquid in a container: Students should be able to apply the necessary formulas to calculate the expansion of a liquid in a container. They should be able to solve problems involving the expansion of liquids using the appropriate formulas.

3. Relate the expansion of liquids to everyday life: Students should be able to identify everyday situations where the expansion of liquids occurs and explain the phenomenon. They should be able to relate what they have learned in the classroom to the real world, making the concept more meaningful and applicable.

Secondary Objectives:

• Develop problem-solving skills: Through the practice of calculating the expansion of liquids, students should enhance their problem-solving skills, which is a valuable skill in many aspects of life.

• Foster scientific curiosity: By exploring the expansion of liquids, students should be encouraged to ask questions, investigate, and explore the phenomenon more deeply, thus developing their scientific curiosity.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts (5 minutes): The teacher should start the lesson by briefly reviewing the concepts of thermal expansion of solids and gases, which were studied in previous classes. This will provide a solid foundation for the new topic of expansion of liquids. The teacher can ask quick questions to check students' understanding of these concepts.

2. Problem Situations (5 minutes): The teacher should propose two problem situations involving the expansion of liquids. For example:

   • If a container contains 1 liter of water at 20°C and is heated to 40°C, what will be the new volume of the water?
   • If a container contains 500 ml of oil at 30°C and is cooled to 10°C, what will be the new volume of the oil?

3. Contextualization (2 minutes): The teacher should explain that the expansion of liquids is a common phenomenon and is present in many aspects of everyday life, from reading thermometers to the expansion of fuels in car engines.

4. Introduction to the Topic (3 minutes): The teacher should introduce the topic of the lesson, highlighting the importance of the expansion of liquids and how it applies in various situations. For example, the teacher may mention how the expansion of liquids is fundamental for the construction of thermometers and other temperature measuring instruments. The teacher may also mention that the expansion of liquids is used in industry, for example, in the construction of bridges and roads, where it is necessary to take into account the expansion and contraction of liquids, such as water, due to temperature changes.

Development (20 - 25 minutes)

1. Theory (10 - 12 minutes): The teacher should present the theory of the expansion of liquids, explaining the following points:

   a. Definition (2 minutes): Expansion of liquids is the increase in the volume of a liquid when its temperature is increased. Expansion occurs because, when the temperature of the liquid increases, its molecules gain kinetic energy and move more rapidly, occupying a larger volume.

   b. Linear Expansion (3 minutes): The teacher should explain that, unlike the expansion of solids, the expansion of liquids occurs isotropically, that is, in all directions. Therefore, there is no specific formula to calculate the linear expansion of a liquid in a container. The teacher should emphasize that the expansion of liquids is generally expressed in terms of volumetric expansion coefficient, which is a characteristic constant of each liquid.

   c. Volumetric Expansion Coefficient (3 minutes): The teacher should explain that the volumetric expansion coefficient (β) of a liquid is defined as the relative variation of its volume for a unit variation of temperature. The teacher should provide the formula for calculating the volumetric expansion of a liquid: ΔV = V₀ * β * ΔT, where ΔV is the volume variation, V₀ is the initial volume, β is the volumetric expansion coefficient, and ΔT is the temperature variation.

   d. Units (2 minutes): The teacher should explain the units of measurement used for the expansion of liquids. For example, volume can be measured in liters (L) or cubic meters (m³), temperature in degrees Celsius (°C) or Kelvin (K), and the volumetric expansion coefficient in 1/°C or 1/K.

2. Calculations (5 - 7 minutes): The teacher should demonstrate step by step how to calculate the expansion of a liquid in a container. Using the problem situations proposed in the Introduction, the teacher should guide the students through the calculation process.

   a. Example 1 (3 minutes): The teacher should calculate the expansion of water in example 1, where the initial volume is 1 liter, the temperature variation is 20°C, and the volumetric expansion coefficient of water is 0.00021/°C. The teacher should show how to substitute the values into the formula and solve the equation to find the expansion.

   b. Example 2 (3 minutes): The teacher should do the same for example 2, where the initial volume is 500 ml, the temperature variation is -20°C, and the volumetric expansion coefficient of oil is 0.0007/°C.

3. Practice (5 - 6 minutes): After the demonstration, students should solve the problem situations on their own, with the teacher's guidance. The teacher should move around the classroom, providing help as needed. After the Conclusion, the teacher should review the answers with the class, ensuring that everyone understood the calculation process.

4. Discussion (3 - 4 minutes): The teacher should promote a discussion on how the expansion of liquids applies in the real world. The teacher should ask students to share examples of everyday situations where the expansion of liquids is relevant. For example, students may mention reading thermometers, the expansion of fuels in car engines, the construction of bridges and roads, among others.

Return (10 - 15 minutes)

1. Group Discussion (5 minutes): The teacher should promote a group discussion on the solutions or answers found by students for the proposed problem situations. The teacher may ask some students to share their answers with the class and explain how they arrived at them. This discussion will allow students to see different approaches to solving a problem and learn from their peers.

2. Connection with Theory (5 minutes): After the group discussion, the teacher should connect the practice with the theory. The teacher should explain how the calculations performed by students relate to the theoretical concepts presented at the beginning of the lesson. The teacher should highlight how the expansion of liquids is calculated using the volumetric expansion coefficient and the temperature variation, and how this concept is applied in different situations.

3. Individual Reflection (5 minutes): The teacher should propose that students reflect individually on what they learned in the lesson. The teacher may ask questions such as:

   • What was the most important concept learned today?
   • What questions have not been answered yet?
   • How could you apply what you learned today in real-life situations?

   The teacher should give a minute for students to think about each question. After the reflection time, the teacher may ask some students to share their answers with the class. This activity will help the teacher assess students' understanding of the topic and identify any points that may need reinforcement in future classes.

4. Feedback and Closure (2 - 3 minutes): To conclude the lesson, the teacher should provide feedback on students' performance and reinforce the main points of the topic. The teacher should praise students' efforts and highlight the improvements that were made during the lesson. The teacher may also suggest extra resources for students who wish to deepen their knowledge of the expansion of liquids. For example, the teacher may recommend books, websites, videos, or practical experiments related to the topic.

5. Preparation for the Next Lesson (1 minute): The teacher should inform students about the topic of the next lesson and any homework or readings they will need to complete before the lesson. The teacher may also remind students of any important concepts that will be covered in the next lesson, so that students can review them at home if necessary.

Conclusion (5 - 7 minutes)

1. Review of Contents (2 minutes): The teacher should start the Conclusion by recapping the main points covered during the lesson. The definition of expansion of liquids, isotropic expansion of liquids, volumetric expansion coefficient, and the formula to calculate the expansion of a liquid in a container should be reiterated. The teacher may ask quick questions to check students' understanding of these concepts.

2. Connection between Theory, Practice, and Applications (2 minutes): The teacher should highlight how the lesson connected theory, practice, and applications. The teacher should emphasize how the theory of expansion of liquids was applied in solving the problem situations, and how this concept applies to real situations, such as the construction of thermometers and the expansion of liquids in car engines. The teacher may also recall the calculations and discussions carried out during the lesson to reinforce the connection between theory and practice.

3. Extra Materials (1 minute): The teacher should suggest extra materials for students who wish to deepen their knowledge of the expansion of liquids. These materials may include books, websites, videos, or practical experiments. The teacher should encourage students to explore these materials on their own to strengthen their understanding of the topic.

4. Applications in Everyday Life (1 minute): To conclude, the teacher should once again highlight the importance of the expansion of liquids in everyday life. Everyday situations where this phenomenon is relevant, such as reading thermometers and the expansion of liquids in car engines, may be mentioned again. The teacher should emphasize that understanding the expansion of liquids is not only useful for the classroom but also for everyday life, as it allows a better understanding of the behavior of different substances with temperature variation.

5. Closure (1 minute): The teacher should end the lesson by thanking the students for their participation and reinforcing the importance of the topic studied. The teacher may remind students about the topic of the next lesson and any homework or readings they will need to complete before the lesson. The teacher should also encourage students to ask questions if they have any doubts after the lesson.