Thermal Expansion of Substances
Simple Explanation
Most substances expand when heated and contract when cooled, because their particles vibrate more (and push each other slightly further apart) at higher temperatures. For a solid, the change in length is given by ΔL = L₀αΔT, where α is a material-specific constant.
Why Do We Need It?
Thermal expansion has to be accounted for in almost all engineering — bridges, railway tracks, and power lines are all deliberately designed with gaps or slack to handle this expansion safely.
Formula
Linear Thermal Expansion
ΔL = L₀αΔT
When a solid is heated, it expands — the amount it expands is proportional to its original length, how much its temperature changes, and a material-specific property called the coefficient of linear expansion.
- ΔL
- — the change in length, in metres (m)
- L₀
- — the original length, in metres (m)
- α
- — the coefficient of linear expansion of the material, in per kelvin (K⁻¹)
- ΔT
- — the change in temperature, in kelvin (K) or degrees Celsius (°C)
When to use it: Whenever the change in length of a solid due to a temperature change needs to be found.
Worked Example
Find the expansion of a steel rail
A steel rail is 20 m long at 10°C. If it heats up to 40°C, find its increase in length. Steel's coefficient of linear expansion α is 1.2 × 10⁻⁵ K⁻¹.
Why Does This Work?
A longer original length has more total material to expand, and a bigger temperature change gives each part of the material more energy to push apart with — both effects multiply together with the material's own expansion tendency (α) to give the total change in length.
Real-Life Example
Gaps in railway tracks and bridges
Railway tracks and long bridges are built with small gaps (expansion joints) between sections.
Without these gaps, thermal expansion on a hot day would cause the rails or bridge sections to push against each other with enormous force, potentially buckling or warping.
Practice
An aluminium rod is 5 m long at 15°C and heats to 35°C. Find its increase in length. (α for aluminium = 2.4 × 10⁻⁵ K⁻¹.)
MediumCommon mistake
Assuming all materials expand by the same amount for the same temperature change — different materials have very different values of α, which is why bimetallic strips (two different metals bonded together) bend when heated, as one side expands more than the other.
Quick Review
- ΔL = L₀αΔT
- Most substances expand when heated, contract when cooled.
- Engineering structures need expansion joints to handle this safely.