# A railway track (made of iron) is laid in winter when the average temperature is 18 degrees...

## Question:

A railway track (made of iron) is laid in winter when the average temperature is 18 degrees Celsius. The track consists of sections of 12.0 m placed one after the other. How much gap should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48 degrees Celsius? The coefficient of linear expansion of iron = {eq}11 \times 10^{-5} {/eq} degrees Celsius{eq}^{-1} {/eq}.

## Thermal Expansion.

Let's imagine we put the end of a wire into the stove. As the temperature rises, the wire experiences a small increase in length. This phenomenon is called thermal expansion and is very important for designers of bridges and other large structures.

{eq}\text{Known data:}\\ T_1 = 18\,^oC\\ T_2 = 48\,^oC\\ L = 12.0\,m\\ \alpha = \dfrac{11\times{10^{-5}}}{^oC}\\ \text{Unknowns:}\\ \Delta L = ? \\ {/eq}

The thermal expansion of each iron bar is defined by the following expression:

{eq}\Delta L = L\,\alpha\,(T_2 - T_1)\\ \Delta L = {\rm (12.0\,m)\left ( \dfrac{11\times{10^{-5}}}{^oC}\right )(48 - 18)\,^oC = 0.040\,m = 40\,mm}\\ {/eq}

Each iron bar expands 20 mm on each side, therefore the gap between the bars should be 40 mm to avoid compression in the summer.

{eq}\color {blue} { gap ={\rm 40\,mm } } {/eq}