Question

Solve the problem with complete solution. A brass wire is .500 m long at 43 degree Celsius. If heated at 70 degree Celsius, what is the change in length?

Answer 1

Given

Initial length: $L_0=0.5\text{ m}.$

Initial temperature: $t_1=43°\text C.$

Final temperature: $t_2=70°\text C.$

Coefficient of thermal expansion for brass: $\alpha=18·10^{-6}/°\text C.$

Solution

Write the equation for thermal expansivity:

$\Delta L=L_0\alpha \Delta t=L_0\alpha(t_2-t_1),\\ \Delta L=0.5(18·10^{-6})(70-43)=2.43·10^{-4}\text{ m}.$

Answer

0.243 mm.