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?
The pipe shortens. That is a -55 C temperature change.
length change =
L*alpha*(delta T)
-(65 m)*(thermal expansion coefficient of steel)* (55 C)
Look up the thermal expansion coefficient of steel for that temperature range. It is about 12*10^-6 per degree C
To determine the change in length of the steel section of the Alaskan pipeline, we can use the linear coefficient of thermal expansion (α) of steel. The linear coefficient of thermal expansion represents the change in length of a material per degree Celsius change in temperature.
First, let's find the linear coefficient of thermal expansion for the steel material. The linear coefficient of thermal expansion for steel can differ slightly depending on the specific type of steel, but as an approximation, we can use the value of 12 × 10^(-6) per °C.
The formula for calculating the change in length of a material due to a temperature change is:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the linear coefficient of thermal expansion
L is the original length
ΔT is the change in temperature
Now let's plug in the values to calculate the change in length:
ΔL = (12 × 10^(-6) per °C) * (65 m) * (16°C - (-39°C))
Simplifying the formula:
ΔL = (12 × 10^(-6) per °C) * (65 m) * (55°C)
Calculating the result:
ΔL = 0.000012 * 65 * 55
ΔL = 0.000012 * 3575
ΔL = 0.0429 m (rounded to four decimal places)
Therefore, the change in length of the steel section of the Alaskan pipeline is approximately 0.0429 meters when the temperature drops from 16°C to -39°C.