To determine the coefficient of linear expansion, we can use the formula:
ΔL = α * L0 * ΔT
Where: ΔL is the change in length α is the coefficient of linear expansion L0 is the initial length ΔT is the change in temperature
In this case, we have: ΔL = 1.5 cm = 0.015 m (converted from centimeters to meters) L0 = 10 m ΔT = 90 °F
Plugging in these values into the formula, we can solve for α:
0.015 m = α * 10 m * 90 °F
First, let's convert the temperature from Fahrenheit to Celsius, as the coefficient of linear expansion is usually given in terms of degrees Celsius:
ΔT_Celsius = (ΔT_Fahrenheit - 32) * (5/9) ΔT_Celsius = (90 - 32) * (5/9) ≈ 27.8 °C
Now, let's rearrange the formula to solve for α:
α = ΔL / (L0 * ΔT_Celsius)
α = 0.015 m / (10 m * 27.8 °C)
Calculating this expression, we find:
α ≈ 0.00005396 m/°C
Therefore, the coefficient of linear expansion for the given pipe is approximately 0.00005396 m/°C.