Liquid nitrogen is stored in the thin-walled inner sphere of the vacuum-jacketed vessel in Figure 6; the radii, surface temperatures and emissivities are marked on the figure. Heat reaches the nitrogen by radiation only. Take σ = 5.67 × 10^{−8} W/m²·K⁴ and the latent heat of vaporisation of nitrogen as 199 kJ/kg. Determine (a) the view factor F_{21} from the outer shell to the inner sphere (answer as a fraction), (b) the net radiation heat transfer to the nitrogen (in W) and (c) the mass of nitrogen boiled off per day (in kg/day).