Contractors in the Southwest generally coat roofs with light materials designed to keep the interior of homes cool. It has been suggested that the same practice be followed in the North. We would like to evaluate this prospect. Consider two diffuse, opaque, coatings with spectral absorptivities shown in Figure P15.13. Which one results in a lower roof temperature? Which coating is preferred for winter use? Sketch the spectral distribution of \(\alpha(\lambda)\) that would be good for winter use and absorb solar radiation. Is there a best compromise for the two seasons? Use data for the Sun radiating as a blackbody at \(5800 \mathrm{~K}\) and deal on a \(1 \mathrm{~m}^{2}\) basis. You may assume the house interior is at \(298 \mathrm{~K}\).

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FIGURE P15.13 1.0 Regular Shingles 0.8 0.6 0.4 Proposed Roof Coating 0.2 0 2 4 6 8 10 12 14 16 (m)