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📘 Lesson 3 of 10 · Thermodynamics

📏 Thermal Expansion

Most materials expand when heated and contract when cooled, as their particles vibrate more (or less) and take up more (or less) space — an effect engineers must always plan around.

Course progress: 30%

01 Key Concepts

Why Materials Expand

As temperature increases, particles vibrate more vigorously and, on average, push each other slightly farther apart, increasing the material's overall size.

Linear Expansion

The change in length of a solid due to temperature change: delta_L = alpha*L0*delta_T, where alpha is the material's coefficient of linear expansion.

Area and Volume Expansion

Area expansion coefficient is approximately 2*alpha; volume expansion coefficient is approximately 3*alpha, for the same material.

Expansion Joints

Gaps deliberately built into bridges, railways, and buildings to allow materials room to expand in heat without buckling or cracking.

Anomalous Expansion of Water

Water is unusual: it expands as it cools from 4°C to 0°C (and freezes), which is why ice floats and pipes can burst in freezing weather.

02 Key Formulas

03 Solved Examples

Example 1 A 10m steel rod (alpha=0.000012 per °C) is heated by 50°C. Find its change in length.
  1. Apply delta_L = alpha*L0*delta_T = 0.000012*10*50.
  2. = 0.000012*500.
Answer: 0.006 m (6 mm)
Example 2 Why are expansion joints built into long bridges?
  1. Bridges experience large temperature swings between seasons.
  2. Without gaps to accommodate expansion, the bridge material could buckle or crack under thermal stress.
Answer: To allow the bridge material room to expand and contract safely with temperature changes
Example 3 Why does an ice cube float on liquid water?
  1. Water is unusual in that it expands slightly as it freezes, becoming less dense than liquid water.
  2. Lower density means ice floats.
Answer: Ice is less dense than liquid water due to water's anomalous expansion upon freezing

04 Practice Questions

1A 5m rod (alpha=0.00002) is heated by 20°C. Find its change in length.
delta_L=0.00002*5*20=0.002m
2What happens to most materials' particles as temperature increases?
They vibrate more vigorously and spread slightly farther apart
3Why are expansion joints used in construction?
To safely accommodate thermal expansion and contraction without damage
4What is unusual about water's behavior between 0°C and 4°C?
It expands as it cools in that range, rather than contracting like most substances
5Is the area expansion coefficient roughly 2x or 3x the linear coefficient?
2x

📄 Thermal Expansion — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet