Question

A 145.0 km long electric power line made out of copper is installed during the Spring months at an average temperature of 13.7 °C. What is the change in the length of the power line on a hot Summer day, when the temperature is 42.0 °C? The coefficient of linear expansion for copper is 1.62×10-5 1/C°. Use positive sign for an increase in length and negative for a decrease.

Answer 1

66.4767 m

Step-by-step explanation:

`L_0` = Original length of power line = 145 km

`\alpha` = Coefficient of linear expansion =
`1.62* 10^(-5)\ /^(\circ)C`

Initial temperature = 13.7°C

Final temperature = 42°C

Change in length of a material is given by

`\Delta L=\alpha L_0\Delta T\\\Rightarrow \Delta L=1.62* 10^(-5)* 145000* (42-13.7)\\\Rightarrow \Delta=66.4767\ m`

The change in length will be 66.4767 m