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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.

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Answer:

66.4767 m

Explanation:

[tex]L_0[/tex] = Original length of power line = 145 km

[tex]\alpha[/tex] = Coefficient of linear expansion = [tex]1.62\times 10^{-5}\ /^{\circ}C[/tex]

Initial temperature = 13.7°C

Final temperature = 42°C

Change in length of a material is given by

[tex]\Delta L=\alpha L_0\Delta T\\\Rightarrow \Delta L=1.62\times 10^{-5}\times 145000\times (42-13.7)\\\Rightarrow \Delta=66.4767\ m[/tex]

The change in length will be 66.4767 m

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