Thermal expansion stretches a heated rod by ΔL = α·L0·ΔT. Pick a material and drag the sliders below to change the temperature change and original length, then watch the change in length respond — the drawing is exaggerated, but the readouts are true.
Thermal Expansion of a Metal Rod
Clamp a rod at one end, pick a material, then heat or cool it. It stretches by ΔL = α·L0·ΔT. The dashed ghost marks the original length; the gold band is the change ΔL — drawn exaggerated so you can see it, while the readouts stay true.
What Is the Thermal Expansion Simulator?
The thermal expansion simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Pick a metal, change the temperature and original length, and watch a rod stretch through ΔL = α·L0·ΔT. It reports change in length δl as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Temperature change Celsius | -50 – 200 °C | 1 |
| Original length of the rod | 0.5 – 3 m | 0.05 |
How One Number, α, Sets Each Rod's Stretch in the Thermal Expansion Sim
Heat a rod of aluminium and a rod of Invar by the same amount, and one lengthens while the other hardly stirs. That difference lives in a single material constant, α, the coefficient of linear expansion. This simulation lets you pick that constant from six buttons and watch it steer everything else. Choose Aluminium (α = 23), Brass (19), Copper (17), Steel (12), Glass (about 8), or Invar (1.2, in units of 10-6 per °C) and the rod's response resets instantly — aluminium expanding roughly 19 times as much as Invar for identical settings.
Two sliders supply the rest of the recipe. Temperature change ΔT can run positive for heating or negative for cooling, and Original length L0 sets the starting metre-scale. The readouts return the change in length ΔL, the original L0, and the final length L = L0 + ΔL. Everything traces to ΔL = α·L0·ΔT, a product of three factors: double either ΔT or L0 and ΔL doubles, while a negative ΔT contracts the rod.
Because α itself is only about 10-5 per °C, a real ΔL is tiny — a fraction of a millimetre up to a few millimetres per metre — so the drawing magnifies the motion ×200 while the numbers stay honest. Since ΔL grows with L0, long rails and bridge spans, not short offcuts, are what earn expansion gaps. Run the numbers in the thermal expansion calculator, then open the next experiment in our physics lab collection.
Frequently asked questions
What is linear thermal expansion?
When a solid is heated it lengthens by ΔL = α·L0·ΔT, where α is the coefficient of linear expansion, L0 the original length and ΔT the temperature change. Cooling reverses it.
Why do different materials expand by different amounts?
Each material has its own coefficient α. Invar (about 1.2 ×10^-6 per °C) barely moves, while aluminium (about 23) expands roughly nineteen times as much for the same length and temperature change.
Does a longer rod expand more?
Yes. The change in length is proportional to the original length L0, so a 2 m rod expands twice as much as a 1 m rod of the same material and temperature change — which is why long rails and bridges are built with expansion gaps.
What happens if the rod is cooled instead of heated?
A negative ΔT gives a negative ΔL, so the rod contracts, shrinking by the same rule ΔL = α·L0·ΔT. Heating and cooling are two directions of the same relation.
References & formula source
- Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 18 (Temperature, Heat), thermal expansion.
- Young & Freedman — University Physics with Modern Physics, §17.4 (Thermal Expansion).
- R. Nave — HyperPhysics, Georgia State University, "Thermal Expansion" section.
- Further reading: Thermal expansion — Wikipedia