A steel section of the Alaskan pipeline had a length of 65.9 m and a temperature of 21.4 °C when it was installed. What is its change in length when the temperature drops to a frigid -43.3 °C?
To find the change in length of the steel section of the Alaskan pipeline when the temperature drops, we can use the coefficient of linear expansion formula. This formula relates the change in length (∆L) of a material to its original length (L₀), the coefficient of linear expansion (α), and the change in temperature (∆T).
The formula is given by:
∆L = α * L₀ * ∆T
1. First, let's convert the temperatures from Celsius to Kelvin, as the coefficient of linear expansion is typically given in terms of Kelvin. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature.
Initial temperature (T₁) = 21.4 °C + 273.15 = 294.55 K
Final temperature (T₂) = -43.3 °C + 273.15 = 229.85 K
2. Next, we need to find the coefficient of linear expansion for steel. The coefficient of linear expansion (α) is a property of the material and represents how much the material expands or contracts per unit change in temperature.
For steel, the coefficient of linear expansion is typically around 12 x 10^(-6) per Kelvin (12 * 10^(-6) / K).
3. Now we can substitute the values into the formula and calculate the change in length (∆L):
∆L = α * L₀ * ∆T
∆L = (12 * 10^(-6) / K) * 65.9 m * (229.85 K - 294.55 K)
Calculating the change in length (∆L) gives us the final answer.