A steel section of the Alaskan pipeline had a length of 65 m and a temperature of 16°C when it was installed. What is its change in length when the temperature drops to a frigid -39°C?
m
I will be happy to critique your thinking. This is a standard linear coefficent of expansion problem.
65:18= X:-45
-162,5
To determine the change in length of the steel section of the Alaskan pipeline, we can use the coefficient of linear expansion (α) of steel, which represents how much length a material changes per degree Celsius of temperature change.
First, we need to find the coefficient of linear expansion for steel. The coefficient of linear expansion for steel can vary depending on the specific type of steel, but for general purposes, we can use an average value of 12 x 10^-6 per degree Celsius.
Next, we can calculate the change in temperature. The initial temperature was 16°C, and it dropped to -39°C, resulting in a change of -55°C.
Now, we can use the formula to calculate the change in length:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the initial length of the steel section
ΔT is the change in temperature
Using the given values:
α = 12 x 10^-6 per °C
L = 65 meters
ΔT = -55°C
ΔL = (12 x 10^-6 per °C) * (65 meters) * (-55°C)
Simplifying the equation:
ΔL = (-0.000012) * (65) * (-55)
ΔL ≈ 0.042575 meters
Therefore, the change in length of the steel section of the Alaskan pipeline when the temperature drops to -39°C is approximately 0.042575 meters.