Lesson Note on Thermal Expansivity for SS1 (SSS 1)

Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Second Term
Week: 2
Age: 15 years
Duration: 45 minutes
Subject: Physics
Curriculum Theme: Physics
Previous Lesson: Heat Energy.
Topic: THERMAL EXPANSIVITY
Subject Matter: Meaning of thermal expansivity, linear expansivity, area expansivity, volume or cubic expansivity, using expansivity coefficients, solving simple problems involving linear, area and volume expansion

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define thermal expansivity.
• State and explain the three types of thermal expansivity.
• State the formulas and S.I. units for linear, area, and volume expansivity.
• Recall the relationship between linear, area, and volume expansivities.

Affective Domain:

• Appreciate the importance of understanding thermal expansivity in everyday life and engineering.
• Show interest in solving problems related to thermal expansion.

Psychomotor Domain:

• Identify the given quantities in problems involving thermal expansion.
• Apply the correct formulas to solve simple problems on linear, area, and volume expansion.
• Use appropriate units in stating answers to expansion problems.

Social Domain:

• Collaborate effectively with peers during problem-solving activities.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum
• State Unified Scheme of Work
• New School Physics by M.W. Anyakoha

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing expansion formulas
• Sample data tables for coefficients of expansivity
• Calculator (optional)
• Ruler
• Chalkboard

Rationale for the Lesson

Understanding thermal expansivity helps pupils to explain common phenomena such as gaps left in railway tracks and bridges, and how thermometers work. This knowledge is important for designing structures and devices that experience changes in temperature, preventing damage or malfunction.

Prerequisite/Previous Knowledge

Pupils are expected to have basic knowledge of heat, temperature, and measurement from previous lessons.

Lesson Content/Board Summary

THERMAL EXPANSIVITY

Meaning of Thermal Expansivity

Thermal expansivity is the property of matter to change in size (length, area, or volume) in response to a change in temperature.

Types of Thermal Expansivity

There are three main types of thermal expansivity:

• Linear Expansivity
• Area Expansivity
• Volume or Cubic Expansivity

Linear Expansivity (α)

Linear expansivity is the fractional change in length per unit rise in temperature. It applies to solids that are long and thin, like rods or wires.

The formula for linear expansion is:

ΔL = L₀αΔT

Where:

• ΔL = change in length
• L₀ = original length
• α = coefficient of linear expansivity
• ΔT = change in temperature

The S.I. unit for the coefficient of linear expansivity (α) is per Kelvin (K⁻¹) or per degree Celsius (°C⁻¹).

Area Expansivity (β)

Area expansivity is the fractional change in area per unit rise in temperature. It applies to flat objects like metal sheets.

The formula for area expansion is:

ΔA = A₀βΔT

Where:

• ΔA = change in area
• A₀ = original area
• β = coefficient of area expansivity
• ΔT = change in temperature

The S.I. unit for the coefficient of area expansivity (β) is per Kelvin (K⁻¹) or per degree Celsius (°C⁻¹).

Volume/Cubic Expansivity (γ)

Volume expansivity is the fractional change in volume per unit rise in temperature. It applies to solids, liquids, and gases.

The formula for volume expansion is:

ΔV = V₀γΔT

Where:

• ΔV = change in volume
• V₀ = original volume
• γ = coefficient of volume expansivity
• ΔT = change in temperature

The S.I. unit for the coefficient of volume expansivity (γ) is per Kelvin (K⁻¹) or per degree Celsius (°C⁻¹).

Relationship between α, β, and γ

For isotropic materials (materials that expand equally in all directions):

• β ≈ 2α
• γ ≈ 3α

Solving Simple Problems

To solve problems involving thermal expansion:

• Identify the type of expansivity required (linear, area, or volume).
• List the given quantities (original length/area/volume, change in temperature, coefficient of expansivity).
• Select the appropriate formula.
• Substitute the values into the formula and calculate the unknown quantity.
• Ensure correct S.I. units are used for all quantities.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them questions about what happens to objects when heated or cooled, linking to everyday examples like railway tracks or boiling water. The teacher then introduces the topic: Thermal Expansivity.
Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction of the new topic.
Learning Point: Pupils recall prior knowledge on heat and temperature effects and are introduced to the lesson topic.

Step 2: Meaning of Thermal Expansivity

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains the meaning of thermal expansivity, defining it as the change in size of a material due to temperature change. The teacher explains that materials generally expand when heated and contract when cooled.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification.
Learning Point: Pupils understand the general concept of thermal expansivity.

Step 3: Linear Expansivity

Time: 7 minutes
Teaching Skill: Explanation/Formula Introduction
Teacher’s Activity: The teacher explains linear expansivity, its formula (ΔL = L₀αΔT), and its S.I. unit (K⁻¹ or °C⁻¹). The teacher may show a chart illustrating linear expansion.
Pupils’ Activity: Pupils copy notes, observe the chart, and ask questions.
Learning Point: Pupils learn about linear expansivity, its formula, and unit.

Step 4: Area Expansivity

Time: 7 minutes
Teaching Skill: Explanation/Formula Introduction
Teacher’s Activity: The teacher explains area expansivity, its formula (ΔA = A₀βΔT), and its S.I. unit (K⁻¹ or °C⁻¹). The teacher also introduces the relationship β ≈ 2α.
Pupils’ Activity: Pupils listen, take notes, and understand the concept of area expansion and its relation to linear expansion.
Learning Point: Pupils learn about area expansivity, its formula, unit, and relationship with linear expansivity.

Step 5: Volume Expansivity and Relationships

Time: 7 minutes
Teaching Skill: Explanation/Formula Introduction
Teacher’s Activity: The teacher explains volume/cubic expansivity, its formula (ΔV = V₀γΔT), and its S.I. unit (K⁻¹ or °C⁻¹). The teacher also introduces the relationship γ ≈ 3α.
Pupils’ Activity: Pupils listen, take notes, and grasp the concept of volume expansion and its relation to linear expansivity.
Learning Point: Pupils learn about volume expansivity, its formula, unit, and relationship with linear expansivity.

Step 6: Problem Solving

Time: 7 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: The teacher works through one or two simple examples on the chalkboard involving linear expansion, guiding pupils on how to identify given values, apply the formula, and state the answer with correct units. The teacher encourages pupils to attempt a similar problem in class.
Pupils’ Activity: Pupils observe the worked examples, ask questions, and attempt to solve a simple problem.
Learning Point: Pupils learn how to apply the expansion formulas to solve problems.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define thermal expansivity.
2. Mention the three types of thermal expansivity.
3. State the formula for linear expansivity and its S.I. unit.
4. What is the relationship between linear expansivity (α) and volume expansivity (γ)?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the definitions, formulas, and practical applications of thermal expansivity. The teacher assigns homework involving simple calculation problems.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their learning and prepare for further practice.

Lesson Keywords

• Thermal expansivity – The property of matter to change in size with temperature.
• Linear expansivity – Fractional change in length per unit temperature change.
• Area expansivity – Fractional change in area per unit temperature change.
• Volume expansivity – Fractional change in volume per unit temperature change.
• Coefficient – A multiplying factor or constant in a formula.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide more complex problems or encourage them to research practical applications of thermal expansion. For pupils needing extra support, the teacher will provide simplified examples, one-on-one guidance, and peer tutoring opportunities.

Note for teachers using this lesson plan

Teachers should ensure that pupils understand the concept of ‘change in temperature’ (ΔT) and how to calculate it. Emphasize the importance of using consistent units throughout calculations. Practical demonstrations, even simple ones like heating a metal rod, can enhance understanding if resources are available.