Question

A metal wire that is 3m long at 20 degrees Celsius is found to increase in length by 1.5cm when heated to 520 degrees Celsius. Determine the Coefficient of the linear expansion of the metal?

Answer 1

The law of linear expansion with temperature is $L = L_0(1+ \alpha \Delta T)$, where

$\alpha$ - coefficient of linear expansion,

$L_0$ - length at initial temperature $T_0$,

$L$ - length at final temperature $L$,

$\Delta T = T - T_0$ - change in temperature.

Formula can be rewritten as $\frac{\Delta L}{L_0} = \alpha \Delta T$, from where $\alpha = \frac{\Delta L}{\Delta T L_0} = \frac{1.5 \cdot 10^{-2} m}{500 C\cdot 3m} = 1 \cdot 10^{-5} C^{-1}$.