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A steel tape is correct at 25 °C. A surveyor uses it at 40 °C and reads 60.00 m.

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A steel tape is correct at $25\ ^\circ\text{C}$ . A surveyor uses it at $40\ ^\circ\text{C}$ and reads $60.00\ \text{m}$ . What is the true distance? ( $\alpha = 1.2 \times 10^{-5}\ \text{K}^{-1}$ .)

Need a reminder? The key ideaShow

Thermal expansion: $\Delta L = \alpha L\,\Delta T$ , $\Delta A = 2\alpha A\,\Delta T$ , $\Delta V = \gamma V\,\Delta T$ with $\gamma = 3\alpha$ for solids. Steel $\alpha = 1.2 \times 10^{-5}\ \text{K}^{-1}$ ; mercury $\gamma = 1.8 \times 10^{-4}\ \text{K}^{-1}$ .

The worked solution

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