A long power transmission cable is buried at a depth (ground-to-cable-centerline distance) of \(1 \mathrm{~m}\). The cable is encased in a thin-walled pipe of \(0.05-\mathrm{m}\) diameter, and, to render the cable superconducting (with essentially zero power dissipation), the space between the cable and pipe is filled with liquid nitrogen at \(77 \mathrm{~K}\). If the pipe is covered with a superinsulator \(\left(k_{i}=0.005 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\right)\) of \(0.05-\mathrm{m}\) thickness and the surface of the earth \(\left(k_{g}=\right.\) \(1.2 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) is at \(300 \mathrm{~K}\), what is the cooling load (W/m) that must be maintained by a cryogenic refrigerator per unit pipe length?