A steel section of the Alaskan pipeline had a length of 65.1 m and a temperature of 15.8 °C when it was installed. What is its change in length when the temperature drops to a frigid -31.2 °C?
Change in L = Lo * a*(T-To)
= 65.1 * 10^-5 * (-31.2-15.8) = -0.030597 m.
To calculate the change in length of the steel section of the Alaskan pipeline due to temperature change, you need to use the coefficient of linear expansion of steel. The coefficient of linear expansion represents the fractional increase in length for each degree Celsius increase in temperature.
The formula to calculate the change in length is given by:
ΔL = (α * L * ΔT)
Where:
ΔL is the change in length
α is the coefficient of linear expansion of steel
L is the original length of the steel section
ΔT is the change in temperature
Firstly, you need to identify the coefficient of linear expansion of steel. The coefficient of linear expansion for steel is typically around 12 x 10^-6 per degree Celsius.
Now, we can substitute the given values into the formula to find the change in length:
ΔL = (12 x 10^-6 / °C) * (65.1 m) * (-31.2 °C - 15.8 °C)
ΔL = (12 x 10^-6 / °C) * (65.1 m) * (-47 °C)
Calculating the change in length:
ΔL = -0.037 mm
Therefore, the steel section of the Alaskan pipeline will contract by approximately 0.037 mm when the temperature drops to -31.2 °C.