To solve the problems below, you will need to know the average coefficient of linear expan...

To solve the problems below, you will need to know the average coefficient of linear expansion, a, which differs for different materials. We define L to be the length of the object, and a to be the fractional change per unit length for a temperature change of 1°C. For aluminum, α = 24 × 10-6/°C, and for steel, a = 11 × 10-6/°C. The change in length ΔL of a material is given by ΔL = LαΔT. Imagine a 40,000-km steel pipe that forms a ring to fit snugly entirely around the circumference of Earth. Suppose that people along its length breathe on it so as to raise its temperature by 1°C. The pipe gets longer—and is also no longer snug. How high does it stand above ground level? Show that the answer is an astounding 70 m higher! (To simplify, consider only the expansion of its radial distance from the center of Earth, and apply the geometry formula that relates circumference C and radius r, C = 2πr.)