Problem — Aluminium bar

Problem

An aluminium bar ($\ell_0=1{,}50$ m, $\lambda_{Al}=24\cdot10^{-6}\ \mathrm{K}^{-1}$) expands by $\Delta\ell=1$ mm. Find the temperature change it underwent.

The aluminium bar lengthens by $\Delta\ell$ as the temperature increases.

Solution

Setup. From the linear expansion law $\Delta\ell=\ell_0\,\lambda\,\Delta T$ we get $\Delta T=\dfrac{\Delta\ell}{\ell_0\,\lambda}$. Substitution ($\Delta\ell=0{,}001$ m): $\Delta T=\frac{0{,}001}{1{,}50\cdot 24\cdot10^{-6}}=\frac{0{,}001}{3{,}6\cdot10^{-5}}\approx 27{,}8\ \mathrm{K}$ $\ev{\Delta T\approx 27{,}8\ \mathrm{K}}$

Links

Topics: Termologia Concepts: Dilatazione termica