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Homework #4: Due Friday, September 19 by 5:30pm
That's all for homework #4.
- Let's model something practical. You have a skin surface area of 1.4m2. You have a skin temperature of 35.0°C, and your skin radiates with an efficiency of e=0.70. You are standing in a room with an air temperature of 21.0°C. Your thin cotton clothes don't provide any insulation. Thus you radiate out to the room while the room radiates back into you.
(a) Find the net power lost by you, and comment on how that compares to an old-style 100-Watt incandescent light bulb.
- Time to do some real-world modeling--time to think a bit here. Here's the situation you are to model with both conduction and radiation:
-Sea ice in a certain location is overlying an ocean whose temperature is (-)1.9°C.
-The temperature of the surface of the ice is (-)34.0°C.
-The temperature of the air above the ice surface is (-)45°C.
-The ice is stable (not melting or freezing).
-The radiation efficiency is e=0.58, and the thermal conductivity of the sea ice is k=2.2W/(m⋅K).
Assuming that these conditions have not changed for a "long" time, find the thicknes of the ice.
- Let's investigate the energy involved in melting things like the ice covering Greenland. Suppose in a certain area next to the coast this ice averages 100m thick. The ice is initially at an average temperature of (-)25°C. The specific heat capacity of ice is 2,000 J/(kg⋅K)=2,000 J/(kg⋅°C). Assume that this ice forms a rectangle that is 100km wide (i.e. stretches for 100km along the coastline). If humans produce a total of ≈2.3 TW (TW=tera-Watts=1012W) of electrical power, find the horizontal extent to which this ice could be melted if all of this power in one year were used to melt this ice.
- Let's investigate the physics of storms on the Great Lakes. Let the top 1.0mm of Lake Superior evaporate in the course of 24 hours (to directly power an upcoming storm). Assume that only about one-fourth of the entire surface area of 82,100km2 is involved in this.
(a) If the surface of the lake is at a temperature of 12°C, find the power that this evaporation entails.
(b) To put this in perspective, find the number of 1,000 MW (MW=mega-Watts=106W) power plants to which this is equivalant.