Chapter 4, Problem 4.24P

A long power transmission cable is buried at a depth (ground-to-cable-centerline distance) of 2 m. The cable is encased in a thin-walled pipe of 0.1-m diameter, and, to render the cable superconducting (with essentially zero power dissipation), the space between the cable and pipe is tilled with liquid nitrogen at 77 K. If the pipe is covered with a superinsulator $\left(k_g=1.2\text{W/m}\cdot \text{K}\right)$ of 0.05-m thickness and the surface of the earth $\left(k_g=1.2\text{W/m}\cdot \text{K}\right)$ is at 300K, what is the cooling load (W/m) that must be maintained by a cryogenic refrigerator per unit pipe length?