Expansion of a 30 m steel rail heating by 35 °C

Answer: change in length = 0.0126 m (change in length 12.6 mm, new length 30.0126 m).

What we know

  • Original length: 30 m
  • Expansion coefficient α: 0.000012 1/K
  • Temperature change: 35 K (or °C)

Step by step

Given
L₀ = 30 m, α = 0.000012 1/K, ΔT = 35 K (or °C)
Formula
ΔL = α × L₀ × ΔT
Substitute
ΔL = 0.000012 × 30 × 35
Result
ΔL = 0.0126 m

All results

Change in length0.0126 m
Change in length12.6 mm
New length30.0126 m

Open the thermal expansion calculator with these numbers → and change any of them.

The physics

Almost everything grows when it warms and shrinks when it cools, because heat makes atoms vibrate harder and sit slightly further apart. Linear thermal expansion captures this for a length: the change equals the coefficient α times the original length times the temperature change. Long objects and big temperature swings give the biggest movements.