Consider a house that has a 10-m × 20-m base and a 4-m-high wall. All four walls of the house have an R-value of 2.31m²⋅°C/ W . The two 10-m × 4-m walls have no windows. The third wall has five windows made of 0.5-cm-thick glass (k = 0.78 W/m⋅K), 1.2 m × 1.8 m in size. The fourth wall has the same size and number of windows, but they are double paned with a 1.5-cm-thick stagnant airspace (k = 0.026 W/m⋅K) enclosed between two 0.5-cm-thick glass layers. The thermostat in the house is set at 24° C, and the average temperature outside at that location is 8° C during the seven-month-long heating season. Disregarding any direct radiation gain or loss through the windows and taking the heat transfer coefficients at the inner and outer surfaces of the house to be 7 and 18 W/m²⋅K, respectively, determine the average rate of heat transfer through each wall.
If the house is electrically heated and the price of electricity is $0.08/kWh, determine the amount of money this household will save per heating season by converting the single-pane windows to double-pane windows.