Question

What is the unit of linear expansion coefficient of a solid? Which expands more, iron or brass?

Answer 1

Linear expansion:

1. If the solid is in the form of a rod or a wire then with the rise in temperature its length increases, this is called linear expansion.
2. If a metal rod of length L has a rise in temperature $∆\mathrm{T}$ and due to the rise in temperature the rise in length is $∆\mathrm{L}$ then, it is observed that,
3. Linear expansion coefficient is given by,

$\mathrm{\alpha }=\frac{∆\mathrm{L}}{\mathrm{L}∆\mathrm{T}}$

Now the unit of coefficient of linear expansion is:

$$\begin{gathered} \mathrm{Unit}\mathrm{of}\mathrm{\alpha }=\frac{\mathrm{Unit}\mathrm{of}∆\mathrm{L}}{\mathrm{unit}\mathrm{of}\mathrm{L}\times \mathrm{unit}\mathrm{of}∆\mathrm{T}} \\ \mathrm{Unit}\mathrm{of}\mathrm{\alpha }=\frac{\mathrm{metre}\left(\mathrm{m}\right)}{\mathrm{metre}\left(\mathrm{m}\right)\times {}^0\mathrm{C}} \\ \mathrm{Unit}\mathrm{of}\mathrm{\alpha }=\frac{1}{{}^0\mathrm{C}} \\ \mathrm{Unit}\mathrm{of}\mathrm{\alpha }={/}^0\mathrm{C} \\ {=}^0{\mathrm{C}}^{-1} \end{gathered}$$

It is observed that when an iron strip and a brass strip both in form of a bimetallic strip are heated to the same temperature, the thermal expansion of brass is more than the iron strip.

This suggests that brass expands more than iron.