18.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?�
To find out how much longer the copper telephone wire is on a summer day, we can use the formula for thermal expansion:
ΔL = L * α * ΔT
Where:
ΔL is the change in length of the wire,
L is the original length of the wire,
α is the coefficient of linear expansion for copper, and
ΔT is the change in temperature.
First, let's calculate the change in temperature:
ΔT = TC - TW
Where:
ΔT is the change in temperature,
TC is the temperature on a summer day, and
TW is the temperature on a winter day.
Given:
TC = 35.0°C (summer day),
TW = -20.0°C (winter day).
ΔT = 35.0°C - (-20.0°C)
ΔT = 55.0°C
Next, we need to find the coefficient of linear expansion for copper. The coefficient of linear expansion for copper is approximately 0.000016 per degree Celsius.
α = 0.000016 (coefficient of linear expansion for copper)
Now, we can substitute the values into the thermal expansion formula:
ΔL = L * α * ΔT
ΔL = 35.0m * 0.000016 * 55.0°C
Calculating this, we find:
ΔL = 0.0308m
Therefore, on a summer day when the temperature is 35.0°C, the copper telephone wire will be approximately 0.0308 meters (or 30.8 millimeters) longer than on a winter day when the temperature is -20.0°C.