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Problem Set 13 Solutions

Problem Set 13 Solutions - 8.02 MASSACHUSETTS INSTITUTE OF...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Problem Set 13 Solutions Problem 1: Solve the Energy Crisis Energy is probably the biggest issue facing the world right now (if you are looking for soething important to do, think about this – the very existence of human life may hinge on our solving this problem). In a nutshell, we currently use fossil fuel to generate energy. This creates greenhouse gasses, which lead to global warming. a) What is the average power the average American uses (averaged over the year)? Include all energy use, not just electricity. What does that work out to for all of America? There are several ways to think about this, here is one. I figure that personally I use 1-2 kW of electrical energy continuously (this is the equivalent of 10-20 100 Watt light bulbs, which when you add up the computer, lights, dishwasher, etc. seems reasonable). I also figure that I spend about the same amount per month in 4 other categories: gas (rather, my wife does since I take the train, but this is an average), heating my house, food and other expenses (clothing, etc). Clearly these expenses aren’t totally energy expenses and cost does not equal amount, but different types of energy have very similar costs and so I figure I must use around 5-10 kW of energy in total. According to recent DOE numbers the average per capita energy use is 11 kW, about what I estimated. Since the US population is about 300 million, this corresponds to energy usage of about 3 TW (terawatts). b) Let’s say that we want to get that all from nuclear power. Assuming that an average nuclear power plant generates 1 GW of power, how many do we need to power the US? We would need about 3000 nuclear power plants to supply all of our energy. There are currently about 440 plants in the world, about 100 in the united states. So aside from safety and environmental issues, this would be a huge task to build up this many nuclear power plants. c) If we were to get it from solar energy, how large an area would we need to cover with solar cells? The solar power at the earth is about 1.4 kW/m 2 . The most efficient solar cells today convert about 25% of incoming power to usable energy. Let’s be optimistic and say that doubles to 50% (this might actually be realistic), but then don’t forget that we only have sunlight about half a day. So 4x3 TW/1.4 kW/m 2 means we need 10 10 m 2 which is about two million acres or about 4000 square miles or about three times the area of Rhode Islands (I think Rhode Island prides itself on being a useful unit of measure). This might actually be doable – there are vast tracts of open land in the Midwest that could probably be used pretty effectively. PS13 Solutions - 1
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Problem 1: Solve the Energy Crisis continued d) What happens to these numbers if we also want power for China and India to use energy at the same per capita rate?
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Problem Set 13 Solutions - 8.02 MASSACHUSETTS INSTITUTE OF...

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