Thermal Expansion

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THERMAL EXPANSION — Edwin Ogie Library

Linear, area & volume expansion • Worked examples • 30-question CBT quiz

THERMAL EXPANSION

A concise illustrated e-note for students — Edwin Ogie Library

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Highlights & Objectives

Highlights

• Clear explanations of linear, area and volume expansion.
• Microscopic origin and practical engineering examples.
• Three worked examples per subtopic and a 30-question CBT quiz.

Objectives

• Explain why materials expand on heating.
• Use ΔL = αL₀ΔT, ΔA = βA₀ΔT, ΔV = γV₀ΔT correctly.
• Apply knowledge to simple engineering calculations and design allowances.

Basic Concepts

Thermal expansion: materials change size as temperature changes. Atoms vibrate more when heated; due to the anharmonic nature of interatomic potentials the average interatomic spacing increases, producing expansion.

Microscopic origin

• Anharmonic potential → asymmetric energy well → bond lengths increase with temperature.
• Bond type matters: metallic, covalent and ionic bonds give different α values.
• Gases expand much more because molecules are far apart.

Example (qualitative): Aluminium expands more than steel because its effective α is larger due to bonding and crystal structure differences.

Thermal Expansion in Solids

We commonly measure linear (1D), area (2D) and volume (3D) expansion in solids.

Linear formula: ΔL = α · L₀ · ΔT

Area formula: ΔA = β · A₀ · ΔT (for isotropic solids β ≈ 2α)

Volume formula: ΔV = γ · V₀ · ΔT (for isotropic solids γ ≈ 3α)

Thermal Expansion in Liquids

Liquids expand mainly in volume. Coefficients vary strongly with temperature and substance.

Formula: ΔV = γ · V₀ · ΔT

Example: Fuel tank headspace must account for ΔV (can be many litres for large tanks).

Thermal Expansion in Gases

Gases: use ideal gas law PV=nRT. At constant pressure V ∝ T(K). Fractional changes can be large.

Example: Hot air balloon — heating air lowers density and increases volume, producing lift.

Worked Linear Examples

1. Rail gap: L₀=20 m, α=12×10⁻⁶, ΔT=40 °C → ΔL=12×10⁻⁶×20×40=0.0096 m = 9.6 mm.
2. Aluminium member: L₀=5 m, α=23×10⁻⁶, ΔT=35 °C → ΔL≈4.03 mm.
3. Precision rod: L₀=0.2 m (glass), α=8.5×10⁻⁶, ΔT=10 °C → ΔL≈0.017 mm.

Worked Area & Volume Examples

1. Panel area: A₀=1.5 m², α=12×10⁻⁶, ΔT=40 °C → β≈24×10⁻⁶ → ΔA=24×10⁻⁶×1.5×40=0.00144 m².
2. Fuel tank: V₀=2.0 m³, γ=950×10⁻⁶, ΔT=25 °C → ΔV=0.0475 m³ (47.5 L).
3. Glass block: cube 0.5 m side, V₀=0.125 m³, γ≈27×10⁻⁶, ΔT=20 °C → ΔV≈0.0000675 m³ (67.5 mL).

Applications & Tips

• Bridges & rails: use expansion joints.
• Thermostats: bimetallic strips exploit different α.
• Electronics: plan solder & PCB tolerances for thermal cycling.

Common Pitfalls & Advanced Notes

• Don't assume α is constant for very large ΔT — use α(T) or integrate.
• Anisotropic materials expand differently along axes.
• Phase changes invalidate small-ΔT linear formulas during the transition.

Summary & Checklist

• Linear: ΔL = α L₀ ΔT
• Area: ΔA = β A₀ ΔT, β ≈ 2α
• Volume: ΔV = γ V₀ ΔT, γ ≈ 3α
• Gases: PV=nRT, use Kelvin for T.

CBT Quiz — 30 Questions

This is a 30-question multiple-choice quiz (15 minutes). Press Start Quiz below to begin.

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Thermal Expansion — Quiz

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