Unit 6.6: Coefficient of Thermal Expansion

Definition

Coefficient of Thermal Expansion (CTE):
The coefficient of thermal expansion is the measure of how much a material expands when the temperature changes.

It represents the change in dimension of a material per unit original dimension per degree change in temperature.

For linear expansion:

\alpha = \frac{\Delta L}{L_0 \Delta T}

Where:

• $\alpha$ = Coefficient of linear expansion

• $\Delta L$ = Change in length

• $L_0$ = Original length

• $\Delta T$ = Change in temperature

SI Unit:

per °C (°C⁻¹) or per Kelvin (K⁻¹)

Core Concept Explanation

When temperature increases, atoms in a material vibrate more intensely.

Because of this increased vibration:

1. Distance between atoms increases.

2. The material expands.

3. Dimensions such as length, area, or volume increase.

Thus, thermal expansion occurs in most materials when temperature rises.

Similarly:

• Heating → Expansion

• Cooling → Contraction

Important Classifications

1. Linear Expansion

Expansion occurs in one dimension (length).

Example:

Expansion of railway tracks or metal rods.

2. Area Expansion

Expansion occurs in two dimensions (surface area).

Example:

Expansion of metal plates.

Relation:

Area expansion coefficient ≈ 2α

3. Volume Expansion

Expansion occurs in three dimensions (volume).

Example:

Expansion of liquids and gases.

Relation:

Volume expansion coefficient ≈ 3α

Key Principles / Concepts

1. Temperature Dependence

Thermal expansion is directly proportional to temperature change.

Higher temperature change → greater expansion.

2. Material Dependence

Different materials expand at different rates.

Examples:

3. Atomic Bond Strength

Materials with strong atomic bonds expand less.

Materials with weak bonds expand more.

Important Comparisons

Properties / Characteristics

Typical coefficient of thermal expansion values:

Observations:

• Aluminum expands more than steel.

• Glass has relatively low thermal expansion.

Applications in Engineering

1. Expansion Joints

Used in:

• Bridges

• Railway tracks

• Pipelines

to allow expansion and avoid structural damage.

2. Thermometers

Thermal expansion of liquids like mercury or alcohol is used to measure temperature.

3. Bimetallic Strips

Used in:

• Thermostats

• Temperature control devices

Two metals with different expansion rates bend when heated.

4. Machine Design

Engineers must consider thermal expansion when designing:

• Engines

• Turbines

• Boilers

Exam-Focused Points

Important points frequently asked in JE/AE exams:

• Coefficient of thermal expansion measures change in size due to temperature.

• Linear expansion formula given above.

• Unit = per °C or per Kelvin.

• Volume expansion ≈ 3 × linear expansion.

• Area expansion ≈ 2 × linear expansion.

• Aluminum has higher expansion than steel.

Common Exam Traps

Trap 1

Confusing thermal expansion with thermal conductivity.

• Thermal expansion → change in size

• Thermal conductivity → heat transfer

Trap 2

Forgetting relation between coefficients.

Important relation:

• Area coefficient ≈ 2α

• Volume coefficient ≈ 3α

Trap 3

Ignoring expansion allowance in engineering structures.

Expansion joints are necessary in long structures.

Example Competitive Exam Questions

Question: What is the coefficient of thermal expansion?
Answer: It is the measure of change in dimension of a material per unit original dimension per degree change in temperature.

Question: What happens to most materials when temperature increases?
Answer: They expand.

Question: What is the SI unit of coefficient of thermal expansion?
Answer: Per Kelvin (K⁻¹) or per degree Celsius (°C⁻¹).

Question: What is the relation between linear and volume expansion coefficients?
Answer: Volume expansion coefficient ≈ 3 times the linear expansion coefficient.

Question: Why are expansion joints provided in bridges and railway tracks?
Answer: To accommodate thermal expansion and prevent structural damage.

Quick Revision Summary

• Thermal expansion = increase in size due to temperature rise.

• Coefficient of thermal expansion measures rate of expansion.

• Linear expansion formula shown above.

• Unit = K⁻¹ or °C⁻¹.

• Area expansion ≈ 2α.

• Volume expansion ≈ 3α.

• Important in bridges, railway tracks, and machine design.