A copper telephone wire has essentially no sag between poles 35.0 m apart on a
winter day when the temperature is -20.0°C. How much longer is the wire on
a summer day when TC=35.0°C?
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To find the difference in length between the wire on a winter day and a summer day, we can use the formula for the change in length of a material with temperature:
ΔL = LαΔT
Where:
ΔL = change in length
L = original length of the wire
α = coefficient of linear expansion for copper (16.7 x 10^-6 /°C)
ΔT = change in temperature
First, we need to find the original length of the wire. Since there is no sag between the poles when the temperature is -20.0°C, the length between the poles is equal to the straight-line distance of 35.0 m.
Now we can calculate the change in length when the temperature changes from -20.0°C to 35.0°C:
ΔT = 35.0°C - (-20.0°C) = 55.0°C
ΔL = (35.0 m)(16.7 x 10^-6 /°C)(55.0°C)
ΔL = 0.030 m or 30 mm
Therefore, the wire will be approximately 30 mm longer on a summer day when the temperature is 35.0°C compared to a winter day when the temperature is -20.0°C.