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Animals in cold climates often depend on two layers of insulation: a layer of body fat...

Animals in cold climates often depend on two layers of insulation: a layer of body fat (of thermal conductivity 0.200 W/(m⋅K) ) surrounded by a layer of air trapped inside fur or down. We can model a black bear as a sphere 1.50 m in diameter having a layer of fat 4.00×10−2 m thick, as shown in the figure.(Figure 1) In studies of bear hibernation, it was found that the outer surface layer of the fur is at TC = 2.70 ∘C during hibernation, while the inner surface of the fat layer is at TH = 31.0 ∘C. How thick should the air layer (contained within the fur) be so that the bear loses heat at a rate of 50.0 W ? Thermal conductivity of air is kair = 2.40×10−2 W/(m⋅K) . Part C How many inches thick should the bear's fur layer (Lfur) be to hold a layer of air Lair so that adequate insulation is provided?

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