Linear Thermal Expansion
Change in length due to temperature change.
Formula
Variables
Example
A 10 m steel rail (α≈12×10⁻⁶) warmed 30 °C grows about 3.6 mm.
How it works
This formula predicts how much a solid object gets longer when its temperature changes. Most materials expand because their atoms vibrate more at higher temperature, so the average spacing between them increases; for small temperature changes, that increase is proportional to the original length and the temperature change. The coefficient of expansion, α, tells you how strongly a material responds to heating or cooling.
When to use it
Use this for long, thin, or uniform objects like rods, rails, wires, bridge components, and precision machine parts when only a temperature change and a change in length are needed. It is especially useful when the temperature change is moderate and the material can be treated as expanding linearly.
Worked example, step by step
A copper wire is 2.5 m long at 20 °C. Its linear expansion coefficient is α = 16.5 × 10^-6 /°C, and its temperature rises by 50 °C. ΔL = αL0ΔT ΔL = (16.5 × 10^-6)(2.5)(50) ΔL = 2062.5 × 10^-6 m ΔL = 0.0020625 m ΔL ≈ 2.06 mm So the wire increases in length by about 2.06 mm.
Common mistakes to avoid
- Using the final length instead of the original length L0 in the formula
- Forgetting that ΔT is the temperature change, not the final temperature
- Mixing up units, such as leaving α in per °C while length is in mm without converting consistently
Did You Know?
Bridges have expansion joints because steel grows measurably longer on a hot day.
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