A spherical habitat is built under the Martian surface. There is power generation in the habitat. This causes the surface to be at a uniform temperature of 30°C. The Martian surface is at a uniform temperature of 10°C. Calculate the heat loss. Assume the habitat is 10m in diameter. The distance from the center of the habitat to the Martian surface is 6m in diameter. An aerogel is put on the surface above the habitat acting as insulation.
Assume the Martian surface has a thermal conductivity of k=0.8 W/m.°C.
