Liquid oxygen (LOX) is being shipped through interstellar space in a spherical tank, constructed of several layers of material. The tank has an inner diameter of 5m, and the LOX is contained in a 15cm-thick shell of polycrystalline fused silicon dioxide, which is sheathed in a 3cm-thick pressure-bearing shell of 2024-T6 aluminum. The polished aluminum of the shell has an emissivity of 0.05, space may be assumed to be at 3K. Data for the solid materials may be evaluated at 100K, due to the table limitations.
To avoid expansion stresses on the shell, the LOX (melting point 54.9K) is kept from freezing by a small heater internal to the tank. How much heat must be supplied by this heater?