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Formulas

Thermal Expansion (Linear)

Change in length due to temperature change.

Physics
Subject
Thermodynamics
Sub Subject
Thermal Properties
Chapter
Expansion
Topic

Thermal Expansion (Linear)

📊 beginner
$$\Delta L = \alpha L_0 \Delta T$$
Change in length due to temperature change.
Variables & Units
$\Delta L$
Change in length
Unit: $\text{m}$
$\alpha$
Coefficient of linear expansion
Unit: $\text{K}^{-1}$
$L_0$
Original length
Unit: $\text{m}$
$\Delta T$
Temperature change
Unit: $\text{K}$ or $^\circ\text{C}$
Key Information
📐 Derived From
Empirical observation
💡 Example
Aluminum rod $L_0=1\,\text{m}$, $\alpha=23\times10^{-6}\,\text{K}^{-1}$, heated $\Delta T=50\,\text{K}$: $\Delta L = (23\times10^{-6})(1)(50) = 0.00115\,\text{m} = 1.15\,\text{mm}$.
🔧 Applications
Bridge expansion joints, thermostats, railway tracks
⚠️ Constraints
Isotropic material, small $\Delta T$

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