How Materials Expand with Temperature
Every solid material expands when heated. Engineers must account for this in bridge expansion joints, pipeline loops, and precision machined parts.
Formulas
Linear: ΔL = α × L₀ × ΔT
Area: ΔA = 2α × A₀ × ΔT
Volume: ΔV = 3α × V₀ × ΔT
(for isotropic solids)
α = coefficient of linear thermal expansion (1/°C)Worked Example
Steel rail: L=25m, ΔT=60°C, α=12×10⁻⁶/°C
ΔL = 12×10⁻⁶ × 25 × 60 = 0.018 m = 18 mm
→ Rail gap must be ≥18mm to prevent bucklingExpansion Coefficients (α × 10⁻⁶/°C)
- Steel: 11-13
- Aluminium: 22-24
- Copper: 16-17
- Concrete: 10-12
- Glass (borosilicate): 3.3
- Invar (low-expansion): 1.5
Practical Rules
- Steel pipe 100m run: allow ~70mm expansion loop per 100°C change
- Bridge expansion joint every ~60m
- Bimetallic strips use mismatched α to create controlled bending
Calculate thermal expansion: Free Thermal Expansion Calculator
Linear Thermal Expansion Formula
ΔL = α × L₀ × ΔT, where α = coefficient of linear thermal expansion (1/°C or 1/K), L₀ = original length, ΔT = temperature change. Common values: steel α ≈ 12×10⁻⁶/°C, aluminium α ≈ 23×10⁻⁶/°C, concrete α ≈ 10×10⁻⁶/°C, glass α ≈ 8×10⁻⁶/°C, copper α ≈ 17×10⁻⁶/°C, nylon α ≈ 80×10⁻⁶/°C. Example: a 100 m steel rail with ΔT = 30°C expands by 12×10⁻⁶ × 100 × 30 = 0.036 m = 36 mm.
Engineering Applications
- Railway tracks: Rail joints or continuous welded rail (CWR) expansion gaps are sized for expected temperature range. CWR is pre-stressed (destressed at a reference temperature) to prevent buckling in summer and cracking in winter.
- Bridges: Expansion joints at deck ends accommodate 50–200 mm of movement over seasonal temperature cycles. Older bridges without joints suffered cracking from restrained thermal movement.
- Pipework: Expansion loops, bellows joints, and sliding supports allow piping to expand without stressing connections. Steam piping at 200°C may see ΔT = 170°C from ambient — movement can be 30–50 mm per 30 m of pipe.
- Glass facades: Curtain wall systems must accommodate differential thermal movement between glass, aluminium framing, and concrete structure.
Frequently Asked Questions
Why does a bimetallic strip bend when heated?
A bimetallic strip consists of two metals with different thermal expansion coefficients bonded together. When heated, the metal with higher α expands more than the other — since they are bonded, the strip bends towards the lower-expansion metal. This bending is used to actuate thermostats, automatic chokes, and circuit breakers. Invar (Fe-Ni alloy, α ≈ 1×10⁻⁶/°C) is used where minimal thermal expansion is critical — precision instruments, telescope mirrors.
How is thermal expansion handled in tall buildings?
A 300 m steel-framed skyscraper with ΔT = 40°C between summer sun and winter night expands vertically by 12×10⁻⁶ × 300 × 40 ≈ 144 mm (14 cm). Interior columns are shielded from exterior temperature swings, so differential expansion between perimeter and core columns must be accommodated in floor and facade connections. The Empire State Building reportedly sways up to 2.5 cm due to thermal effects alone.
Does volume also change with temperature?
Yes. Volumetric expansion: ΔV = γ × V₀ × ΔT where γ ≈ 3α (for isotropic materials). This is critical for liquid containment — a sealed tank of hydraulic oil cannot expand in volume when heated; pressure builds rapidly. Hydraulic systems include thermal relief valves and expansion tanks. Water's anomalous behaviour (maximum density at 4°C, expands on freezing) is why ice floats and frozen pipes burst.