Animals in cold climates oftendepend on two layers of insulation: a layer of body fat (of thermal conductivity0.20 W/m . K) surrounded by a layer of air trapped inside fur ordown. We can model a black bear (Ursus americanus) as a sphere 1.5 min diameter having a layer of fat 4.0 cm thick. (Actually, the thicknessvaries with the season, but we are interested in hibernation, when the fatlayer is thickest.) In studies of bear hibernation, it was found that theouter surface layer of the fur is at 2.7°C during hibernation, while theinner surface of the fat layer is at 31.0°C. (a) What is the temperature atthe fat–inner fur boundary so that the bear loses heat at a rate of 50.0 W?(b) How thick should the air layer (contained within the fur) be?
Animals in cold climates often
depend on two layers of insulation: a layer of body fat (of thermal conductivity
0.20 W/m . K) surrounded by a layer of air trapped inside fur or
down. We can model a black bear (Ursus americanus) as a sphere 1.5 m
in diameter having a layer of fat 4.0 cm thick. (Actually, the thickness
varies with the season, but we are interested in hibernation, when the fat
layer is thickest.) In studies of bear hibernation, it was found that the
outer surface layer of the fur is at 2.7°C during hibernation, while the
inner surface of the fat layer is at 31.0°C. (a) What is the temperature at
the fat–inner fur boundary so that the bear loses heat at a rate of 50.0 W?
(b) How thick should the air layer (contained within the fur) be?
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