Q.A steel railway rail is $20\ \text{m}$ long at $10\,^\circ\text{C}$. If the rail is heated to $40\,^\circ\text{C}$ on a hot afternoon, find the increase in its length. Take the coefficient of linear expansion of steel as $\alpha = 1.2\times10^{-5}\ {}^\circ\text{C}^{-1}$.

Almost every solid expands on heating because its constituent atoms vibrate with a larger average amplitude about their lattice positions, pushing neighbouring atoms slightly farther apart on average. The coefficient of linear expansion $\alpha$ ($L=L_0(1+\alpha\Delta T)$), coefficient of superficial expansion $\beta$, and coefficient of cubical expansion $\gamma$ describe the change in length, area, and volume respectively; for an isotropic solid, $\beta = 2\alpha$ and $\gamma = 3\alpha$. Applications include railway-track gaps, bridge roller supports, and the bimetallic strip used in thermostats.