Question

A rod of metal is measured at 12 °C and is 3.521 m long. At 100 °C the rodis 3.523 m long. Determine the value of the coefficient of linear expansionfor the metal.

Answer 1

In order to determine the coefficient of linear expansion of this metal, we can use the following formula:

$\Delta L=\alpha\cdot L_0\cdot\Delta T$

Where DeltaL is the change in length, alpha is the coefficient, L0 is the initial length and DeltaT is the change in temperature.

So, for DeltaL = 0.002 m, L0 = 3.521 m and DeltaT = 88°C , we have:

$\begin{gathered} 0.002=\alpha\cdot3.521\cdot88 \\ \alpha=\frac{0.002}{3.521\cdot88} \\ \alpha=6.45\cdot10^{-6} \end{gathered}$

Therefore the coefficient is 6.45 * 10^-6 °C^-1.