A copper telephone has essentially no sag between poles 35.0 apart on a winter day when the temperature is -20.0 degree celcius ,how much longer a wire in summer season when temperature is 35 degree celcius??
To calculate the change in length of the wire between the winter and summer seasons, we can use the coefficient of linear expansion for copper. The coefficient of linear expansion (α) is a measure of how much a material's length changes in response to a change in temperature.
The formula to calculate the change in length (ΔL) is given by:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the initial length of the wire
α is the coefficient of linear expansion for copper
ΔT is the change in temperature
Let's calculate the change in length for the copper wire.
Step 1: Determine the initial length (L) of the wire.
The distance between the poles is given as 35.0 meters.
Step 2: Find the coefficient of linear expansion (α) for copper.
The coefficient of linear expansion for copper is approximately 0.000016 (1/°C). This means that for every 1 degree Celsius change in temperature, the length of the wire changes by 0.000016 times its initial length.
Step 3: Calculate the change in temperature (ΔT).
The change in temperature is the difference between the summer temperature (35°C) and the winter temperature (-20°C).
ΔT = 35°C - (-20°C) = 55°C
Step 4: Calculate the change in length (ΔL).
Using the formula:
ΔL = L * α * ΔT
Since we don't know the initial length of the wire, we will assume it to be 35 meters (as stated in the question).
ΔL = 35 * 0.000016 * 55
ΔL ≈ 0.0308 meters
So, the wire will be approximately 0.0308 meters (or 30.8 millimeters) longer in the summer season when the temperature is 35°C compared to the winter temperature of -20°C.