Thermal Expansion Calculator
Enter original length, expansion coefficient and temperature change to get linear, area and volume expansion. Steel rail L₀=10 m, ΔT=50°C → ΔL=6 mm.
Input Data
Results
At a glance:Thermal expansion: an object's volume grows as temperature rises. Linear expansion ΔL=α·L₀·ΔT (α linear coefficient); area expansion ΔA≈2α·A₀·ΔT and volume expansion ΔV≈3α·V₀·ΔT (isotropic approximation). Properties: (1) metals α≈10⁻⁵/°C; (2) liquids expand more than solids (water 2.1e-4); (3) anomaly — water between 0–4°C contracts on heating; (4) platinum–iridium alloys have tiny α, used for standards. Applications: (1) rail expansion joints; (2) bridge expansion joints; (3) bimetallic temperature sensors; (4) mercury thermometers; (5) thermostats.
Formula
Linear: ΔL = α·L₀·ΔT
Final length: L = L₀·(1 + α·ΔT)
Area: ΔA ≈ 2α·A₀·ΔT
Volume: ΔV ≈ 3α·V₀·ΔT
$$\Delta L = \alpha L_0 \Delta T, \quad L = L_0(1 + \alpha\,\Delta T), \quad \Delta A \approx 2\alpha A_0 \Delta T, \quad \Delta V \approx 3\alpha V_0 \Delta T$$How to Use
- Enter original length L₀ (m).
- Enter linear coefficient α (1/°C).
- Enter temperature change ΔT (°C).
- The tool gives linear, area and volume expansion.
Case Studies
Buildings and railways
Rail joint: 25 m steel rail, summer 60°C, winter 0°C, ΔT=60 → ΔL=18 mm. A 6 mm gap isreserved to avoid buckling (Hong Kong rail standard).
Bridge expansion: Tsing Ma Bridge 1377 m steel, ΔT=40 → ΔL=0.66 m; joints absorb it.
Building joints: a tall building every 30–50 m; concrete α=1e-5, ΔT=30 → 30 m expands 9 mm.
Bimetallic strip and thermometer
Bimetallic strip: two metals of different α bonded. On heating it bends (different expansion); used in thermostats, fluorescent starters, overload protectors.
Mercury thermometer: mercury α=1.8e-4, glass α=…; a 100°C span gives a readable expansion.
Glass cracking: sudden hot–cold shock; borosilicate (α=3.3e-6) is heat-resistant, ordinary glass cups crack easily.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.