Heat Loss through a Window
A small office has a 3 × 4-ft window on one wall. The window is made from single-pane glass that is \frac{1}{8} in. thick. While evaluating the building’s heating and ventilation system, an engineer needs to calculate the heat loss through the window on a winter day. Although the temperature difference of the air inside and outside the office is much larger, the two surfaces of the glass differ by only 3^\circ F. In units of watts, what quantity of heat is lost through the window each hour?
Approach
To calculate the conductive flow of heat through the window, we apply Equation (7.9).
Q=\frac{kA\Delta t}{L}(T_h-T_1) (7.9)
The thermal conductivity of glass is listed in Table 7.5
Table 7.5
Thermal Conductivity of Certain Materials
| Thermal Conductivity, _{k} | ||
| Material | W/(m .^\circ C) | (Btu/h)/(ft .^\circ F) |
| Steel | 45 | 26 |
| Copper | 390 | 220 |
| Aluminum | 200 | 120 |
| Glass | 0.85 | 0.50 |
| Wood | 0.3 | 0.17 |
as 0.50 (Btu/h)/(ft.^\circ F). After calculating the energy loss in the USCS dimensions of Btu, we will convert to the SI unit of watt by applying the conversion factor 1 Btu = 1055 J from Table 7.1.
Table 7.1
Conversion Factors Between Various Units for Energy and Work in the USCS and SI
| (ft . lb) | J | Btu | kW.h |
| 1 | 1.356 | 1.285×10^{-3} | 3.766×10^{-7} |
| 0.7376 | 1 | 9.478×10^{-4} | 2.778×10^{-7} |
| 778.2 | 1055 | 1 | 2.930×10^{-4} |
| 2.655×10^{6} | 3.600×10^{6} | 3413 | 1 |
