Thermal expansion is the tendency of matter to change size when its temperature changes. Most solids, liquids, and gases expand when heated because their particles move more vigorously and, on average, spread farther apart. This effect matters in bridges, railroad tracks, thermometers, engines, pipelines, and electronic devices.
Engineers must allow for expansion so materials do not buckle, crack, or lose calibration.
In solids, expansion is often measured as a change in length, area, or volume using a coefficient of expansion. Liquids usually expand more than solids, which is why liquid thermometers can show temperature changes. Gases expand strongly, and at constant pressure their volume is proportional to absolute temperature.
Devices such as expansion joints and bimetallic strips use thermal expansion to prevent damage or convert temperature changes into motion.
Key Facts
- Linear expansion: ΔL = αL0ΔT
- Area expansion: ΔA = 2αA0ΔT for an isotropic solid with small temperature changes
- Volume expansion: ΔV = βV0ΔT, where β is about 3α for many isotropic solids
- Final length after heating: L = L0 + ΔL = L0(1 + αΔT)
- For an ideal gas at constant pressure: V1/T1 = V2/T2, with T in kelvins
- Thermal stress can occur when expansion is blocked, causing large forces in rails, bridges, pipes, or glass
Vocabulary
- Thermal expansion
- Thermal expansion is the increase in the size of a material when its temperature rises.
- Coefficient of linear expansion
- The coefficient of linear expansion, α, is the fractional change in length per degree of temperature change.
- Expansion joint
- An expansion joint is a gap or flexible section that lets a structure expand and contract without damage.
- Bimetallic strip
- A bimetallic strip is two bonded metals that bend when heated because the metals expand by different amounts.
- Thermal stress
- Thermal stress is internal force per area produced when a material is heated or cooled but cannot freely expand or contract.
Common Mistakes to Avoid
- Using Celsius instead of kelvins for gas law temperatures is wrong because gas volume relationships depend on absolute temperature, not relative temperature scales.
- Forgetting the original length in ΔL = αL0ΔT is wrong because a longer object expands more than a shorter object made of the same material for the same temperature change.
- Assuming every material expands by the same amount is wrong because different materials have different expansion coefficients.
- Ignoring constraints is wrong because an object that cannot expand freely may develop thermal stress instead of simply changing length.
Practice Questions
- 1 A 12.0 m steel rail has α = 1.2 × 10^-5 per °C. How much does its length increase when its temperature rises from 10°C to 45°C?
- 2 A 250 mL liquid sample has β = 9.5 × 10^-4 per °C. What is its volume increase when it is heated by 30°C?
- 3 A bimetallic strip is made of brass on top and steel on the bottom. Brass has a larger coefficient of linear expansion than steel. When the strip is heated, which way does it bend, and why?