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?
do this the same way as the baseball bat
I did I multiply by the coefficent of steel which is 12*10^-6 and the chang e in temp. which is 16--39 got 55 but I'm getting the wrong answer.
delta L/L = alpha (-39 -16)
delta L/65 = 12*10^-6 * 55
delta L = 43900 * 10^-6 = .0439
Oh, remember it shrunk. It is -.0439
To find the change in length of the steel section of the Alaskan pipeline, we can use the coefficient of linear expansion for steel and the formula:
ΔL = α * L * ΔT
Where:
ΔL = change in length
α = coefficient of linear expansion
L = original length
ΔT = change in temperature
First, we need to look up the coefficient of linear expansion for steel. The coefficient varies with different types of steel, so let's assume the coefficient for carbon steel, which is approximately 12 x 10^-6 (1/°C).
Next, let's convert the temperatures from Celsius to Kelvin since the coefficient of linear expansion is usually expressed in terms of Kelvin.
Original temperature (T1) = 16°C + 273.15 = 289.15 K
Final temperature (T2) = -39°C + 273.15 = 234.15 K
Change in temperature (ΔT) = T2 - T1 = 234.15 K - 289.15 K = -55 K
Now we can substitute the values into the formula and calculate the change in length (ΔL):
ΔL = (12 x 10^-6) * 65 m * -55 K
Calculating the change in length:
ΔL = -42.9 x 10^-3 m
Therefore, the steel section of the Alaskan pipeline will contract by approximately 42.9 mm (or 0.0429 meters) when the temperature drops from 16°C to -39°C.