Consider a \(400 \mathrm{~mm} \times 400 \mathrm{~mm}\) window in an aircraft. For a temperature difference of \(90^{\circ} \mathrm{C}\) from the inner to the outer surface of the window, calculate the heat loss rate through \(L=12\)-mm-thick polycarbonate, soda lime glass, and aerogel windows, respectively. The thermal conductivities of the aerogel and polycarbonate are \(k_{\mathrm{ag}}=0.014 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(k_{\mathrm{pc}}=0.21 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), respectively. Evaluate the thermal conductivity of the soda lime glass at \(300 \mathrm{~K}\). If the aircraft has 130 windows and the cost to heat the cabin air is \(\$ 1 / \mathrm{kW} \cdot \mathrm{h}\), compare the costs associated with the heat loss through the windows for an 8-hour intercontinental flight.