• id: JME-10-N01
• title: Linear Expansion of Solids
• tags: expansion, linear, alpha

When a solid is heated, its length increases: $L = L_0(1 + \alpha\Delta T)$, where $\alpha$ is the coefficient of linear expansion (K$^{-1}$). This coefficient is a material property — steel ($12 \times 10^{-6}$ K$^{-1}$), aluminium ($23 \times 10^{-6}$ K$^{-1}$), Invar ($0.9 \times 10^{-6}$ K$^{-1}$). Invar (Iron-Nickel alloy) has the lowest $\alpha$ among common metals — used in clock pendulums and precision instruments. The formula is valid for small temperature changes. For large ranges, $\alpha$ itself varies with temperature, and integration is needed: $L = L_0 \exp(\int \alpha \, dT)$.