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Steel rails, each 18.0 m long, are laid at 12 °C.

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Steel rails, each $18.0\ \text{m}$ long, are laid at $12\ ^\circ\text{C}$ . The hottest they get is $52\ ^\circ\text{C}$ . What gap must be left between them? ( $\alpha = 1.2 \times 10^{-5}\ \text{K}^{-1}$ .)

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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