Question

A steel railroad track has a length of 33 m when the temperature is −2 ◦C. What is the increase in the length of the rail on a hot day when the temperature is 39 ◦C? The linear expansion coefficient of steel is 11 × 10−6 ( ◦C)−1 . Answer in units of m.

Answer 1

0.0149 m

Step-by-step explanation:

When a solid material is heated, it expands; in particular, its length increases according to the equation:

`\Delta L=\alpha L \Delta T`

where

`\Delta L` is the increase in length

`\alpha` is the linear expansion coefficient

`L` is the original length of the material

`\Delta T` is the increase in temperature

In this problem:

`L=33 m` is the original length of the steel railroad track

`\alpha=11\cdot 10^(-6) ^(\circ)C^(-1)` is the linear expansion coefficient of steel

`\Delta T=39-(-2)=41^(\circ)C` is the change in temperature of the track

Therefore, the increase in length is:

`\Delta L=(11\cdot 10^(-6))(33)(41)=0.0149 m`