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 (essentially zero power dissipation), the space between the cable and pipe is filled with liquid nitrogen at 77 K. If the pipe is covered with a super insulator (kR = 0.005 W/m ∙ K) of 0.05-m thickness and the surface of the earth (kg = 1.2 W/m ∙ K) is at 300 K. what is the cooling load in Wm that must be maintained by a cryogenic refrigerator per unit pipe length?