Thermal Expansion

Most materials expand when heated and contract when cooled. This is called thermal expansion, and it happens because particles vibrate more at higher temperatures.

What Is Thermal Expansion?

When a substance is heated, its particles (atoms or molecules) vibrate more energetically and push each other further apart. This causes the material to expand.

Linear Expansion (Solids)

For a solid rod, the change in length is:

Linear Thermal Expansion

\Delta L = \alpha \cdot L_0 \cdot \Delta T

α = coefficient of linear expansion (1/°C), L₀ = original length (m), ΔT = temperature change (°C).

Common Expansion Coefficients

Material	α (×10⁻⁶ /°C)
Steel	12
Aluminium	23
Glass	9
Concrete	12

Everyday Examples

Railway gaps: small gaps are left between rail sections so they don't buckle in summer heat
Bridges: expansion joints allow for movement
Thermometers: liquid expands up a narrow tube
Bimetallic strips: two metals expand at different rates, causing a strip to bend (used in thermostats)

Note Water is an exception — it expands when it freezes (0°C), which is why ice floats and pipes burst in winter.

A steel rail is 20 m long at 10°C. How much does it expand when heated to 40°C?

$\Delta T = 40 - 10 = 30°\text{C}$

$\Delta L = 12 \times 10^{-6} \times 20 \times 30 = 0.0072 \text{ m} = 7.2 \text{ mm}$

Real world: Steel bridge expansion joints

A 500 m steel bridge (α = 12 × 10⁻⁶/°C) experiences a temperature swing of 40°C between winter and summer. Using ΔL = α · L₀ · ΔT:

$\Delta L = 12 \times 10^{-6} \times 500 \times 40 = 0.24 \text{ m} = 24 \text{ cm}$

That's nearly a quarter of a metre! Expansion joints allow the deck to slide freely, preventing buckling.

Real world: Bimetallic thermostat strip

A home thermostat contains a strip of brass and steel bonded together. Brass expands more than steel (α_brass ≈ 19 × 10⁻⁶/°C vs. α_steel ≈ 12 × 10⁻⁶/°C). As the room warms, the strip bends because the brass side tries to grow longer. At the set temperature, the bending opens the circuit and switches the boiler off automatically.

Real world: Stuck jar lid

Running hot water over a metal lid for 30 seconds heats the metal faster than the glass. The metal expands (α_steel ≈ 12 × 10⁻⁶/°C, α_glass ≈ 9 × 10⁻⁶/°C), loosening the seal just enough to twist the lid off easily.

Tip Where do you see this in real life? Look for expansion joints on bridges, railway lines, and concrete pavements — the small gaps are there by design to allow for thermal expansion!

Practice Problems

Why are gaps left between sections of a concrete footpath?

Show answer

To allow for thermal expansion in hot weather, preventing cracking and buckling.

An aluminium rod (α = 23×10⁻⁶/°C) is 1 m long at 20°C. Find its length at 70°C.

Show answer

ΔL = 23×10⁻⁶ × 1 × 50 = 0.00115 m. New length = 1.00115 m.