Problem — Aluminium with doubled lambda

Problem

Suppose the linear expansion coefficient of aluminium were suddenly doubled, becoming $\lambda'_{\text{Al}} = 48 \cdot 10^{-6} \ \text{K}^{-1}$. What are the three most visible practical consequences in everyday life? Consider bridges, cans and electrical wires.

Solution

The change in length $\Delta \ell = \lambda \, \ell_0 \, \Delta T$ is proportional to $\lambda$: doubling the coefficient, for the same $\Delta T$, doubles every expansion. Bridges and structures: expansion joints would need to be doubled to absorb the elongation and avoid dangerous deformation and internal stresses. Cans and containers: they would undergo larger dimensional changes with temperature, making seals and closures less stable and increasing the risk of deformation. Overhead wires and cables: in the heat they would stretch more, sagging further between one pylon and the next, especially in summer. Doubling $\lambda$ doubles all expansions, requiring larger margins and joints in every aluminium structure (Bloomfield 2016) Riferimenti bibliografici.

Collegamenti

Argomenti: Termologia Concetti: Dilatazione termica