2010018204

The aluminium rod and brass rod have the same length at a given temperature. The material constants of the rods are: ${\alpha }_{\mathrm{aluminium}}=24\cdot {10}^{-6}{\mathrm{K}}^{-1}$ and ${\alpha }_{\mathrm{brass}}=18\cdot {10}^{-6}{\mathrm{K}}^{-1}$. Suppose both rods are heated to the same higher temperature. Find the true statement about the extensions of both rods. Round the percentage difference in the rods’ extensions to the whole percent. $$$$ Hint: Solid materials expand upon heating. The rod with the initial length $l_0$ is upon the temperature increasing by $\mathrm{\Delta }t$ extended by the value $\mathrm{\Delta }l=l_0\cdot \alpha \cdot \mathrm{\Delta }t$, where $\alpha$ is the material constant (coefficient of linear thermal expansion) that is indicative of the extent to which a material expands upon heating.