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Thermodynamics · Quick Reference
Thermal Expansion Cheat Sheet
In one line: 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.
Key Ideas
1Why Materials Expand. As temperature increases, particles vibrate more vigorously and, on average, push each other slightly farther apart, increasing the material's overall size.
2Linear 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.
3Area and Volume Expansion. Area expansion coefficient is approximately 2*alpha; volume expansion coefficient is approximately 3*alpha, for the same material.
4Expansion Joints. Gaps deliberately built into bridges, railways, and buildings to allow materials room to expand in heat without buckling or cracking.
5Anomalous 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.
Worked Examples
A 10m steel rod (alpha=0.000012 per °C) is heated by 50°C. Find its change in length.
0.006 m (6 mm)
Why are expansion joints built into long bridges?
To allow the bridge material room to expand and contract safely with temperature changes
Why does an ice cube float on liquid water?
Ice is less dense than liquid water due to water's anomalous expansion upon freezing
Formulas
delta_L = alpha * L0 * delta_T
Practice Yourself
A 5m rod (alpha=0.00002) is heated by 20°C. Find its change in length.
delta_L=0.00002*5*20=0.002m
What happens to most materials' particles as temperature increases?
They vibrate more vigorously and spread slightly farther apart
Why are expansion joints used in construction?
To safely accommodate thermal expansion and contraction without damage