A copper telephone wire has essentially no sag between poles 34.0 m apart on a winter day when the temperature is −20.0°C. How much longer is the wire on a summer day when the temperature is 32.0°C? (Note: Table 19.1 is available for use in solving this problem.)
To calculate the change in length of the wire between the two given temperatures, we can use the formula:
ΔL = αLΔT
Where:
ΔL = Change in length
α = Coefficient of linear expansion
L = Original length
ΔT = Change in temperature
To find the coefficient of linear expansion (α), we need to refer to Table 19.1. The coefficient for copper is usually provided in the table.
Looking at Table 19.1, we find that the coefficient of linear expansion for copper is approximately 0.0000160 per degree Celsius.
Now, we can calculate the change in length (ΔL) of the telephone wire.
Given data:
Original length (L): 34.0 m
Change in temperature (ΔT): (32.0°C) - (-20.0°C) = 52.0°C
Coefficient of linear expansion (α) for copper: 0.0000160 per degree Celsius
Substituting the values into the formula:
ΔL = (0.0000160 per °C) * (34.0 m) * (52.0°C)
Calculating the result:
ΔL ≈ 0.028m
Therefore, the wire will be approximately 0.028 meters longer on a summer day when the temperature is 32.0°C compared to a winter day when the temperature is -20.0°C.