Question

A railway line is laid with 10m length of rail on a day when the temperature is 2.50°C. There is a gap of 0.5cm between the rails. Find the temperature at which the gap will close.

Answer 1

Let: $l = 10m = 1000 \, \text{cm}$

$$\Delta l = 0.5 \, \text{cm}$$ $$t1 = 2.5{}^{\circ} \text{C}$$ $$\alpha(\text{iron}) = 1.13 \times 10^{-5} \, \text{K}^{-1}$$ $$\Delta l = l \times \alpha(t2 - t1)$$ $$t2 = t1 + \frac{\Delta l}{l \times \alpha}$$

Enter the data:

$$t2 = 2.5 + \frac{0.5}{1000 \times 1.13 \times 10^{-5}} = 46.75{}^{\circ} \text{C}$$

Answer:

The temperature at which the gap will close is: $46.75{}^{\circ} \text{C}$