A steel section of the Alaskan pipeline had a length of 58.4 m and a temperature of 24.5 °C when it was installed. What is its change in length when the temperature drops to a frigid -45.7 °C?
Well, that's quite a temperature drop! Let's see what happens to our steel buddy.
First, we need to know the coefficient of linear expansion for the steel used in the Alaskan pipeline. Do you happen to have that information?
To calculate the change in length of the steel section of the Alaskan pipeline, we can use the coefficient of linear expansion, which measures how much a material expands or contracts with a change in temperature.
The formula for calculating the change in length is:
ΔL = α * L * ΔT
Where:
ΔL = Change in length
α = Coefficient of linear expansion
L = Initial length
ΔT = Change in temperature
First, we need to find the coefficient of linear expansion for steel. The average coefficient of linear expansion for steel is approximately 12 x 10^-6 °C^-1.
Using the given values:
L = 58.4 m
Initial temperature (T1) = 24.5 °C
Final temperature (T2) = -45.7 °C
ΔT = T2 - T1
ΔT = -45.7 °C - 24.5 °C
ΔT = -70.2 °C
Now we can calculate the change in length:
ΔL = α * L * ΔT
ΔL = (12 x 10^-6 °C^-1) * 58.4 m * (-70.2 °C)
Calculating this value:
ΔL = -0.00008688 m
Therefore, the change in length of the steel section of the Alaskan pipeline, when the temperature drops to -45.7 °C, is approximately -0.00008688 meters.
To find the change in length of the steel section when the temperature drops, we can use the coefficient of linear expansion. The coefficient of linear expansion for steel is typically given as α = 12 x 10^-6 °C^-1 (per degree Celsius).
The formula for calculating the change in length of a material due to temperature change is:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the original length of the material
ΔT is the change in temperature
Let's plug in the values given in the question:
α = 12 x 10^-6 °C^-1
L0 = 58.4 m
ΔT = -45.7 °C - 24.5 °C = -70.2 °C
ΔL = (12 x 10^-6 °C^-1) * (58.4 m) * (-70.2 °C)
Now we can calculate the change in length.