Question

A 160.0 km long electric power line made out of copper is installed during the Spring months at an average temperature of 10.2 °C.

1) What is the change in the length of the power line on a hot summer day, when the temperature is 32.1 °C? The coefficient of linear expansion for copper is 1.62×10^(-5) 1/C°. Use a positive sign for an increase in length and negative for a decrease.
2) What is the change in the length of the cable on a -28.7 °C cold Winter day?

Answer 1

1.+160.0567km

2.-0.102km

Step-by-step explanation:

Given initial length L1=160Km

L2=?

Initial temperature=10.2°C

Final temperature=32.1°c

Coefficient of linear expansivity a= 1.62*10^-5per Celsius

1: a=L2-L1/L1*∆T

(L2-160/160*21.9)=1.62*10^-5

L2-160=0.0567

L2= 0.0567+160

L2=160.0567Km

2.∆L=? at -28.7°C

Also a=∆L/L1∆T

We're ∆L= aL1∆T

1.65*10^-5*160*(-28.7-10.2)

=-0.102km