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On a scorching summer day in Paris, the 330-meter iron Eiffel Tower grows up to 15 centimeters taller than it is in mid-winter.
When atoms absorb thermal energy, their asymmetric vibrations push neighboring bonds farther apart, stretching the macroscopic material in every dimension.
In 1731, Dutch scientist Pieter van Musschenbroek invented the pyrometer to measure this exact elongation of heated metal rods under precise temperature changes.
How do we quantify this one-dimensional stretch using a single material constant?

Linear Thermal Expansion

The fractional change in length Ξ”LL0\frac{\Delta L}{L_0} is directly proportional to temperature change Ξ”T\Delta T, scaled by the linear expansion coefficient Ξ±\alpha.
We calculate this elongation with the linear expansion formula: Ξ”L=Ξ±L0Ξ”T\Delta L = \alpha L_0 \Delta T where L0L_0 is initial length, and Ξ±\alpha has units of Kβˆ’1\text{K}^{-1} or ∘Cβˆ’1^{\circ}\text{C}^{-1}.
Consider a 50.0-meter steel bridge girder (Ξ±steel=1.20Γ—10βˆ’5Β Kβˆ’1\alpha_{\text{steel}} = 1.20 \times 10^{-5}\text{ K}^{-1}) experiencing a temperature swing from βˆ’10.0∘C-10.0^{\circ}\text{C} to 35.0∘C35.0^{\circ}\text{C}.
With Ξ”T=35.0βˆ’(βˆ’10.0)=45.0Β K\Delta T = 35.0 - (-10.0) = 45.0\text{ K}, the elongation is: Ξ”L=(1.20Γ—10βˆ’5Β Kβˆ’1)(50.0Β m)(45.0Β K)=0.027Β m=2.7Β cm\Delta L = (1.20 \times 10^{-5}\text{ K}^{-1})(50.0\text{ m})(45.0\text{ K}) = 0.027\text{ m} = 2.7\text{ cm} Engineers install comb-shaped expansion joints to absorb this 2.7 cm growth without buckling the road.
What happens when a flat surface expands in two dimensions at the same time?

Areal Thermal Expansion

When a two-dimensional sheet heats up, its area changes according to Ξ”A=Ξ²A0Ξ”T\Delta A = \beta A_0 \Delta T, where Ξ²\beta is the areal expansion coefficient.