(Solved): Find linear expansion coefficient: The center span of a steel bridge is 1,200 meters long on a winte ...

When a metal is heated, it expands. The formula is $\Delta l=\alpha li$ $\Delta T$. Where $\Delta I=$ Ifinal - linitial,$\Delta T=T$ lfinal -Tinitial,$\alpha$ is the coefficient of linear expansion $\alpha$ (unit is $1/{}^{\circ }\mathrm{C}$ ) depends on the material to material. You will find $\alpha$ of the material by provided data. The center span of a steel bridge is 1,200 meters long on a winter day when the temperature is $-5^{\circ }\mathrm{C}$. How much longer is the span on a summer day when the temperature is $35^{\circ }\mathrm{C}$ ? $\begin{array}{rl}& \Delta T=35-(-5)=35+5=40^{\circ }\mathrm{C}\\ \Delta =& \alpha l\Delta T=\left(12\times 10^{-6}/{}^{\circ }\mathrm{C}\right)\times 1,200\mathrm{m}\times 40^{\circ }\mathrm{C}\\ =& \left(12\times 10^{-6}/{}^{\circ }\mathrm{C}\right)\times 48,000{\mathrm{m}}^{\circ }\mathrm{C}\\ =& 576,000\times 10^{-6}\mathrm{m}=0.576\mathrm{m}\end{array}$ (I) Copper rod, $\alpha =17\times 10-6\left(I/{}^{\circ }\mathrm{C}\right)$ - official value $\begin{array}{ll}\mathrm{Li}=185.0\mathrm{cm}=1.850\mathrm{m},& \mathrm{Ti}=20.0^{\circ }\mathrm{C}\\ \mathrm{Lf}=185.51\mathrm{cm}=& \mathrm{m},\mathrm{Tf}=180.{}^{\circ }\mathrm{C}\end{array}$ Find $\alpha$ and $\%$ error. (II) Aluminum rod, $\alpha =24\times 10-6\left(1/{}^{\circ }\mathrm{C}\right)$ - official value $\mathrm{Li}=185.0\mathrm{cm},\mathrm{Lf}=185.81\mathrm{cm}$, $\mathrm{Ti}=20.0^{\circ }\mathrm{C},\mathrm{Tf}=200.0^{\circ }\mathrm{C}$ Find $\alpha$ and $\%$ error.