Chapter 6, Problem 58TS

Imagine people breathing on the length of a $40,000-\text{km}$-long steel pipe that forms a ring to smoothly fit snugly entirely around the circumference of Earth so as to raise its temperature by $1°\text{C}$. The pipe gets longer and is no longer snug. Show that it then stands an astounding $70\text{ m}$ above ground level! (To simplify, consider only the expansion of the pipe’s radial distance from Earth’s center, Earth’s radius, which is $6370\text{ km}$.)