KinexiaLEARN PHYSICS

Thermal Expansion — Steel Bridge in Summer (Worked Example)

Easy
Problem

A 200 m steel bridge deck warms from −10 °C on a winter night to 30 °C on a summer afternoon. How much does it lengthen? (α_steel = 12 × 10⁻⁶ /°C.)

Given

  • L₀ = 200 m

  • ΔT = 30 − (−10) = 40 °C

  • α = 12 × 10⁻⁶ /°C

Find

Change in length ΔL.

Principle

Most solids expand in proportion to their original length and the temperature change, scaled by the material's expansion coefficient.

Formula

Solution

  1. Write the formula: ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T

  2. Substitute: ΔL=(12×10−6)×200×40\Delta L = (12 \times 10^{-6}) \times 200 \times 40

  3. Calculate: ΔL=0.096 m=9.6 cm\Delta L = 0.096\ \mathrm{m} = 9.6\ \mathrm{cm}

≈ 9.6 cm longer

Unit check

(1/°C) × m × °C = m. Temperature units cancel — correct.

What this means physically

Nearly 10 cm of growth — which is why bridges have expansion joints with visible gaps. Without them, the deck would buckle or tear its supports apart.

Common mistake

Using the final temperature instead of the change, or dropping the 10⁻⁶ and getting an absurd 96 km answer. Always sanity-check the magnitude.