Question

Windows are a major source of heat loss from a house because glass has a higher thermal conductivity than the other materials typically used in construction and because insulation can be placed inside walls but not windows. A typical house has 26 m2 of windows, and window glass is typically 4.0 mm thick.

A) What is the rate of heat loss through windows on a chilly -5∘C day from a typical house with single-pane windows if the interior temperature of the house is 20∘C (68∘F)?
B) Double-pane windows are two panes of glass separated by a 3.0-mm-wide gap filled with dry air. The gap has to be narrow to prevent convection currents in the air. Air is such a better insulator than glass that, to a good approximation, the thermal conductivity of a double-pane window is simply that of the layer of air. What is the rate of heat loss on the -5∘C day if the house has double-pane windows?

Answer 1

Heat loss through windows on a chilly day can be calculated using the thermal conductivity of the material, the area of the windows, the temperature difference, and the thickness of the glass. Single-pane windows conduct more heat due to the higher thermal conductivity of glass compared to air. Double-pane windows reduce heat loss by including an air gap that serves as insulation.

Step-by-step explanation:

Calculating Heat Loss Through Single-Pane and Double-Pane Windows

To calculate heat loss through single-pane windows, we use the formula for heat conduction Q/t = kA(ΔT)/d, where Q/t is the rate of heat loss in watts (W), k is the thermal conductivity of glass (assumed to be 0.8 W/m·K), A is the area of the window, ΔT is the temperature difference across the window, and d is the thickness of the glass. For a single-pane window with an area of 26 m2, a thickness of 4.0 mm (0.004 m), and a ΔT of 25°C (20 - (-5)), the rate of heat loss is given by:

Q/t = (0.8 W/m·K) ×(26 m2) ×(25°C) / (0.004 m) = 130,000 W or 130 kW.

For double-pane windows with a 3.0-mm wide gap of air, the thermal conductivity of air (k ≈ 0.025 W/m·K) is used in the equation with the equivalent thickness of the air gap plus the two layers of glass. Assuming the glass has negligible effect due to its thinness compared to the air gap, the calculation would be similar but using the thermal conductivity of air and the total thickness, which includes the air gap and two glass panes. If d total is 3.0 mm + 4.0 mm + 4.0 mm, the rate of heat loss would be significantly less due to the lower conductivity and increased thickness of the double-pane setup.

Insulation in the attic can vastly reduce heat loss. If extra insulation is added, the percentage drop in heating costs can be estimated by considering the new overall thermal resistance of the insulation layer, with more insulation increasing resistance and reducing heat loss.

Answer 2

Step-by-step explanation:

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