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Area and volume expansion
Intermediate
Coefficients are about 2α and 3α.
β = 2α, γ = 3αArea expands by β = 2α and volume by γ = 3α for isotropic solids. Liquids have a larger γ than solids.
A steel sheet heated 50 K: area +0.12%.
Use the right coefficient for area or volume.
In more detail
Area and volume expansion follow linear expansion, with coefficients roughly twice and three times the linear value. For solids, ΔA = 2αAΔT and ΔV = 3αVΔT.
Real-world uses
- Engineers calculate volume changes in tanks and pipes.
- Metal lids loosen when heated because the metal expands.
- Engineers designing a metal lid or a glass container must allow for area and volume expansion when the temperature changes.
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Frequently asked questions
Why does a hole get bigger when heated?
Because the material around it expands, so the hole expands as well.
Which coefficient is used for volume?
The volume coefficient is about three times the linear coefficient for isotropic solids.
Why does a lid loosen when heated?
The lid expands, but the jar may expand less or more, so the fit changes, which is why the lid can be loosened with hot water.
Related topics in Heat & Thermodynamics
Thermometers · Zeroth law · Thermal expansion · Anomalous expansion of water · Heat · Specific heat capacity