In this problem, we will consider a half spherical igloo of radius R = 2m. The wall of the igloo consists of 30 cm of thickly compressed snow blocks. The heat conductivity of the compressed snow is 0.3 W/(m*K). If the outside temperature is -20oC and the inside needs to be at +20oC: how many humans need to be inside the igloo to achieve this with only the heat produced by the humans? Use the following data and assumptions: the situation is steady state heat is only lost through the wall of the igloo (so we ignore the floor) the only resistance against the heat flow is in the walls of the igloo a human produces about 150 Watt

a. In a steady state, what is the relation between the heat flow through the wall and the temperature difference across the wall?

b. Set up a heat balance for the igloo.

c. Compute how many people are roughly needed for the situation sketched above.