During a winter day, the window of a patio door with a height of \(1.8 \mathrm{~m}\) and width of \(1.0 \mathrm{~m}\) shows a frost line near its base. The room wall and air temperatures are \(15^{\circ} \mathrm{C}\).

(a) Explain why the window would show a frost layer at the base rather than at the top.

(b) Estimate the rate of heat loss through the window due to free convection and radiation. Assume the window has a uniform temperature of \(0^{\circ} \mathrm{C}\) and the emissivity of the glass surface is 0.94. If the room has electric baseboard heating, estimate the corresponding daily cost of the window heat loss for a utility rate of \(0.18 \$ / \mathrm{kW} \cdot \mathrm{h}\).

Transcribed Image Text:

Window, 1.8 m x 1.0 m