Question

An iron rod with an initial length of 12.62 m has its temperature raised from 19o C to 30.6o C. If iron has a coefficient of thermal expansion of 12x10-6 1/oC, what is the change in length of the rod in mm?

Answer 1

1.757 mm

Explanation:

The coefficient of linear expansion is given by the following formula:

`\alpha=(\Delta L)/(L\Delta T)`

Where α = coefficiente of linear expasion, ΔL = change in lenght, ΔT = change in tempetature

Solving for ΔL:

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

Replacing and we calculate the change in lenght:

`\begin{gathered} \Delta L=12\cdot10^(-6)\cdot12.62\cdot(30.6-19) \\ \Delta L=0.001757\text{ m}\cdot\frac{1000\text{ mm}}{1\text{ m}}=1.757\text{ mm} \end{gathered}`

The change in length is 1.757 mm