Chapter 3, Problem 39P

Consider a house that has a $10-\text{m }\times 20\text{-m}$ base and a 4-rn-high wall. All four walls of the house have an R-vahie of 2.31 m² °C/W. The two $10-\text{m }\times 4\text{-m}$ walls have no windows. The third wall has five windows made of 0.5-cm-thick glass $(k=0.78\text{ W/niK})$, $1.2\text{m }\times 1.8\text{m}$ 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 $(k=0.026\text{ V/mK)}$ and 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. detenninc the average rate of heat transfer through each wall.

If the house is electrically heated and the price of electricity is $0.08/kVh. determine the amount of money this household will save per heating season by converting the single-pane windows to double-pane windows.