A double-glazed window consists of two panes of glass, each of thickness t = 6 mm. The inside room temperature is T_i = 20°C with h_i = 7.7 W/m² · K, while the outside temperature is T_o = –10°C with h_o = 25 W/m² · K. The gap between the glass sheets is of thickness L = 5 mm and is filled with a gas. The glass surfaces may be treated with a low-emissivity coating to reduce their emissivity from ε = 0.95 to ε = 0.95. Determine the heat flux through the window for case 1: ε₁ = ε₂ = 0.95, case 2: ε₁ = ε₂ = 0.05, and case 3: ε₁ = 0.05, ε₂ = 0.95. Consider either air or argon of thermal conductivity k_Ar = 17.7 X 10^–3 W/m
· K to be within the gap. Radiation heat transfer occurring at the external surfaces of the two glass sheets is negligible, as is free convection between the glass sheets.