A steel section of the Alaskan pipeline had a length of 65 m and a temperature of 22° C when it was installed. What is its change in length when the temperature drops to a frigid -37° C?
Well, I guess the steel section of the Alaskan pipeline is about to experience some serious shrinkage! It's like the steel is hitting the gym and getting all ripped. So, to answer your question, we'll need to use the coefficient of linear expansion for steel, which is roughly 12 x 10^-6 per °C. So, let's do some math!
First, let's calculate the change in temperature: 22°C - (-37°C) = 59°C.
Next, we'll calculate the change in length using the formula: change in length = original length x coefficient of linear expansion x change in temperature.
Plugging in our numbers, we have: change in length = 65m x 12 x 10^-6 per °C x 59°C.
After some number crunching, the change in length of the steel section will be approximately 0.04575 meters, or about 45.75 millimeters. So, hold on tight, because that steel section is going to shrink a little bit! It's like the Alaskan pipeline is turning into a pipeline for miniature-sized oil.
To calculate the change in length of the steel section of the Alaskan pipeline, we can use the coefficient of linear expansion, which is a characteristic property of the material.
1. Determine the coefficient of linear expansion (α) for steel:
The coefficient of linear expansion for steel is typically around 12 x 10^(-6) per degree Celsius (or 12 μm/m/°C).
2. Calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
= (-37°C) - (22°C)
= -59°C
3. Calculate the change in length (ΔL) using the formula:
ΔL = α × L × ΔT
where:
ΔL = change in length
α = coefficient of linear expansion
L = initial length
ΔL = (12 x 10^(-6) / °C) × (65 m) × (-59°C)
= -45.24 mm
Therefore, the steel section of the Alaskan pipeline will contract by 45.24 mm when the temperature drops from 22°C to -37°C.
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 for linear expansion.
First, we need to know the coefficient of linear expansion for steel. The coefficient of linear expansion, denoted by α (alpha), represents how much a material expands or contracts with a change in temperature. For steel, the coefficient of linear expansion is approximately 12 x 10^(-6) per degree Celsius (12 μm/m°C).
Next, we can use the formula for linear expansion:
ΔL = α * L * ΔT
Where:
- ΔL is the change in length
- α is the coefficient of linear expansion
- L is the original length
- ΔT is the change in temperature
Given:
- Original length (L) = 65 m
- Initial temperature (T1) = 22°C
- Final temperature (T2) = -37°C
Now we can substitute the values into the formula:
ΔL = (12 x 10^(-6) /°C) * (65 m) * (-37°C - 22°C)
Calculating this:
ΔL = (12 x 10^(-6) /°C) * (65 m) * (-59°C)
Simplifying:
ΔL = - 0.045 m
Therefore, the change in length of the steel section of the Alaskan pipeline when the temperature drops from 22°C to -37°C is approximately -0.045 meters.
ΔL = αLΔT
α =12 •10⁻⁶ °C⁻¹
ΔL = 12 •10⁻⁶•65•( -37-22) = - 0.046 m