Compute the ratio of the rate of heat loss through a...

Compute the ratio of the rate of heat loss through a single-pane window with area $0.15 \mathrm{~m}^{2}$ to that for a double-pane window with the same area. The glass of a single pane is $4.2 \mathrm{~mm}$ thick, and the air space between the two panes of the double-pane window is $7.0 \mathrm{~mm}$ thick. The glass has thermal conductivity $0.80 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. The air films on the room and outdoor surfaces of either window have a combined thermal resistance of $0.15 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}$.

Key Concepts

Thermal Conduction

Thermal conduction is the process by which heat energy is transferred through a material due to a temperature gradient. It is governed by Fourier's law, where the rate of heat transfer is proportional to the material's thermal conductivity and the temperature difference, and inversely proportional to the thickness of the material.

Thermal Resistance

Thermal resistance is a measure of a material's opposition to the flow of heat. It is calculated by dividing the thickness of the material by the product of its thermal conductivity and cross-sectional area. This concept is essential for evaluating and comparing the insulating properties of different materials.

Series Combination of Thermal Resistances

When heat flows through multiple layers of different materials, each layer offers its own thermal resistance. These resistances add up in series, much like electrical resistors, to give a total thermal resistance for the entire system. This approach is crucial for analyzing complex structures where multiple layers, such as glass and air, work together in insulating applications.

Heat Transfer Rate Comparison

Comparing the heat transfer rate across different configurations involves analyzing how differences in material properties and layer thicknesses affect the overall thermal resistance. By understanding this concept, one can determine the efficiency of various designs, such as single-pane versus double-pane windows, in reducing heat loss.

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