A steel section of the Alaskan pipeline had a length of 73.8 m and a temperature of 15.7 °C when it was installed. What is its change in length when the temperature drops to a frigid -45.3 °C?
To calculate the change in length of the steel section of the Alaskan pipeline, we can use the coefficient of linear expansion (α) of steel and the formula:
ΔL = L * α * ΔT
Where:
ΔL represents the change in length
L is the original length of the steel section
α is the coefficient of linear expansion of steel
ΔT is the change in temperature
First, we need to find the value of the coefficient of linear expansion (α) for steel. The coefficient of linear expansion represents how much a material expands per degree Celsius change in temperature. Let's assume the coefficient of linear expansion for steel as 12 × 10^(-6) 1/°C.
Now we can substitute the given values into the formula:
L = 73.8 m (original length of the steel section)
α = 12 × 10^(-6) 1/°C (coefficient of linear expansion of steel)
ΔT = (final temperature - initial temperature) = (-45.3 °C - 15.7 °C) = -61.0 °C (change in temperature)
ΔL = 73.8 m * 12 × 10^(-6) 1/°C * -61.0 °C
Simplifying the equation, we get:
ΔL = -0.0669 m
Therefore, when the temperature drops from 15.7 °C to -45.3 °C, the steel section of the Alaskan pipeline changes in length by -0.0669 meters.
L = Lo + Lo*(T-To)oC*u.
L = 73.8 + 73.8(-45.3-15.7)1.24*10^-5.
L = 73.8 + (-.0558) = 73.74 m.