Thermal Expansion Calculator
Calculate thermal expansion of materials when subjected to temperature changes. Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature.
Linear Expansion
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What Is Thermal Expansion?
Thermal expansion is a fundamental property of materials that describes how their dimensions change in response to temperature variations. When a material is heated, its molecules gain energy and vibrate more vigorously, increasing the average distance between them. This microscopic change manifests as a measurable expansion at the macroscopic level.
Types of Thermal Expansion
Thermal expansion occurs in three forms, depending on the dimensions being considered:
Linear Expansion
Change in length along one dimension (1D)
Area Expansion
Change in surface area (2D) - approximately twice the linear expansion
Volumetric Expansion
Change in volume (3D) - approximately three times the linear expansion
Key Formulas
- 1Linear expansionΔL = α × L₀ × ΔT
- 2New lengthL = L₀ × (1 + α × ΔT)
- 3Required temperature changeΔT = ΔL / (α × L₀)
- 4Thermal expansion coefficientα = ΔL / (L₀ × ΔT)
- 5Area expansionΔA = 2α × A₀ × ΔT (approximate)
- 6Volume expansionΔV = 3α × V₀ × ΔT (approximate)
Where:
Material Behavior
Different materials expand at different rates when heated. This is quantified by the coefficient of thermal expansion (CTE):
- Most materials expand when heated and contract when cooled
- Metals typically have higher CTEs than ceramics
- Water is a notable exception - it expands when cooled below 4°C
- Some specialized materials like Invar (nickel-iron alloy) have near-zero thermal expansion
- Thermal expansion is usually linear for small temperature changes
- Materials like glass can shatter due to thermal shock from rapid temperature change
Thermal Expansion Coefficients
| Material | Linear CTE (µm/(m·K)) | Notes |
|---|---|---|
| Aluminum | 23.1 | High expansion - used in heat sinks |
| Steel (Carbon) | 11.7 | Moderate expansion - structural applications |
| Copper | 16.5 | Used in electrical and heat transfer applications |
| Glass (Borosilicate) | 3.3 | Low expansion - laboratory glassware |
| Concrete | 12.0 | Why expansion joints are necessary in structures |
| Invar (36% Ni-Fe) | 1.2 | Extremely low expansion - precision instruments |
| Titanium | 8.6 | Aerospace and biomedical applications |
| PVC | 52.0 | High expansion - plumbing consideration |
Engineering Applications
Expansion Joints
Allow structures to safely expand and contract with temperature changes, preventing buckling and cracking.
Bimetallic Strips
Used in thermostats - two metals with different CTEs bend when heated due to uneven expansion.
Interference Fits
Parts are heated to expand before assembly, creating tight mechanical connections when cooled.
Thermal Stresses
When expansion is constrained, thermal stresses develop that can lead to material failure.
Piping Systems
Require expansion loops or flexible connections to accommodate thermal movement.
Precision Instruments
Specialized low-expansion materials like Invar are used where dimensional stability is critical.
Interesting Facts
The Eiffel Tower can be up to 15 cm taller in summer due to thermal expansion
Railroad tracks include small gaps to prevent buckling on hot days
Dental fillings must match the thermal expansion of teeth to prevent cracks
Water reaches its maximum density at 4°C and expands when cooled further
Car engines would seize without proper thermal expansion allowances in their design
Some cooking techniques leverage thermal expansion - like using hot water to loosen a tight jar lid