Linear Thermal Expansion
Calculate the change in length of a material due to temperature change.
Results
Area Thermal Expansion
Calculate the change in area of a material due to temperature change.
Results
Volumetric Thermal Expansion
Calculate the change in volume of a material or liquid due to temperature change.
Results
(For solids, β ≈ 3α)
Material Database
Thermal expansion coefficients for common materials.
Solids
| Material | α (10⁻⁶/°C) | β (10⁻⁶/°C) |
|---|---|---|
| Aluminum | 23.1 | 69.3 |
| Brass | 19.0 | 57.0 |
| Copper | 17.0 | 51.0 |
| Steel | 12.0 | 36.0 |
| Stainless Steel | 10.4 | 31.2 |
| Glass (ordinary) | 9.0 | 27.0 |
| Glass (Pyrex) | 3.3 | 9.9 |
| Concrete | 12.0 | 36.0 |
| Wood (pine) | 5.0 | 15.0 |
Liquids
| Material | β (10⁻⁴/°C) |
|---|---|
| Water (20°C) | 2.07 |
| Ethanol | 7.50 |
| Glycerin | 4.85 |
| Mercury | 1.82 |
| Gasoline | 9.50 |
| Olive Oil | 7.00 |
Thermal Expansion Formulas
Key equations for thermal expansion calculations.
Linear Thermal Expansion
Where:
- ΔL: Change in length
- α: Coefficient of linear thermal expansion (per °C or per K)
- L₀: Original length of the object
- ΔT: Change in temperature (in °C or K)
This formula is used for rods, beams, wires, and other one-dimensional objects.
Area Thermal Expansion
Where:
- ΔA: Change in area
- α: Coefficient of linear thermal expansion
- A₀: Original area
- ΔT: Change in temperature
This approximation works well for small temperature changes and isotropic materials.
Volumetric Thermal Expansion
Where:
- ΔV: Change in volume
- β: Coefficient of volumetric expansion (for solids, β ≈ 3α)
- V₀: Original volume
- ΔT: Change in temperature
For solids, the volumetric coefficient is approximately three times the linear coefficient. For liquids, β must be measured directly.
Example Calculations
Practical examples of thermal expansion calculations.
Example 1: Steel Rail Expansion
A steel railroad track is 10 meters long at 20°C. How much does it expand when the temperature reaches 40°C?
Given:
- L₀ = 10 m
- ΔT = 20°C (from 20°C to 40°C)
- α (steel) = 12 × 10⁻⁶ /°C
ΔL = (12 × 10⁻⁶) × 10 × 20
ΔL = 0.0024 m = 2.4 mm
Example 2: Glass Window Expansion
A glass window pane measures 1m × 1.5m at 10°C. What is its area at 30°C?
Given:
- A₀ = 1.5 m²
- ΔT = 20°C
- α (glass) = 9 × 10⁻⁶ /°C
ΔA ≈ 2 × (9 × 10⁻⁶) × 1.5 × 20
ΔA ≈ 0.00054 m² = 5.4 cm²
Final area ≈ 1.50054 m²
Example 3: Aluminum Ball Expansion
An aluminum ball has a diameter of 10 cm at 25°C. What is its new volume at 75°C?
Given:
- Diameter = 10 cm → V₀ = (4/3)π(5)³ ≈ 523.6 cm³
- ΔT = 50°C
- α (aluminum) = 23 × 10⁻⁶ /°C → β ≈ 69 × 10⁻⁶ /°C
ΔV = (69 × 10⁻⁶) × 523.6 × 50
ΔV ≈ 1.806 cm³
Final volume ≈ 525.406 cm³
Example 4: Gasoline Expansion
A car's gas tank holds 50 liters of gasoline at 15°C. How much gasoline will overflow if the temperature rises to 35°C?
Given:
- V₀ = 50 L
- ΔT = 20°C
- β (gasoline) = 950 × 10⁻⁶ /°C
ΔV = (950 × 10⁻⁶) × 50 × 20
ΔV = 0.95 L
Final volume ≈ 50.95 L