Answer
$68.00^{\circ}C$
Work Step by Step
Given/Known: $L_{new}=10.009\,cm$, $L=10.000\,cm$,
$\alpha=1.875\times10^{-5}/C^{\circ}$ (obtained in part a) and $T_{i}=20.000^{\circ}C$
Recall: $L_{new}=L+\Delta L=L+L\alpha\Delta T$
$\implies T_{f}-T_{i}=\frac{L_{new}-L}{L\alpha}$
$\implies T_{f}=\frac{L_{new}-L}{L\alpha}+T_{i}$
Result: $T_{f}=\frac{10.009\,cm-10.000\,cm}{10.000\,cm\times1.875\times10^{-5}/C^{\circ}}+20.000^{\circ}C=68.00^{\circ}C$
