Sum

**Solve the following problem.**

In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10^{–5}K^{–1} for the material of the rail section?

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#### Solution

**Given:** T_{1} = 27 °C, T_{2} = 45 °C, L_{1} = 10 m. α = 1.2 × 10^{–5} / K

**To find: **Gap that should be left (L_{2} – L_{1})

**Formula:** L_{2} – L_{1} = L_{1} α (T_{2} - T_{1})

**Calculation:** From formula,

L_{2} - L_{1} = 10 × 1.2 × 10^{–5} × (45 - 27)

= 2.16 × 10^{–3} m

= 2.16 mm

The gap that should be left between rail sections is **2.16 mm**.

Concept: Thermal Expansion

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