This is a hard question to answer exactly because there are a lot of variables. However, here is one way to think about it: If you were to use an acre of ground to raise corn, and you then turned that corn into ethanol (alcohol), you could get a measurement of the energy that an acre of plants can capture from the sun. Then you compare that number with solar cells.
In the United States, a typical acre of ground can produce about 100 bushels of corn. One bushel of corn can produce about 2.5 gallons (9.5 liters) of ethanol. A gallon of ethanol can produce about 80,000 Btu (British thermal units) of energy. According to How Horsepower Works, it takes 3.41 Btu to create 1 watt-hour of electricity. Putting all of this together, you can see that an acre of corn can produce 58.6-million watt-hours of energy. [Note that we are ignoring dozens of details to arrive at this number. For example, we are ignoring the energy cost to plow the land, produce the fertilizer and distill the ethanol -- see this page for details. We are also ignoring the loss of energy that occurs during the conversion of ethanol to electricity, the fact that you could grow a crop of winter wheat on the same land, the fact that you could dry and burn the corn stalks to distill the ethanol, and lots of other factors that would complicate our simple comparison of solar cells and plants.]
If you look at How Solar Yard Lights Work or this Question of the Day, you find that 1 square inch (6.5 cm2) of solar cells can generate about 70 milliwatts of electricity, and that it might be able to do this for about five hours a day on average (depending on latitude, average rainfall and other environmental factors). An acre has 43,560 square feet (4,047 m2) in it, and there are 144 square inches (929 cm2) in a square foot. Therefore, in an hour, an acre-size solar panel can produce about 440,000 watt-hours of electricity. In a five-hour day, it can produce 2.2-million watt-hours, and in a year it can produce about 800-million watt-hours of electricity.
In other words, based on the above assumptions, an acre of solar cells can produce about 15 times more electricity than an acre of corn. It is important to keep in mind, however, that there's a big cost difference between the two systems. In a pinch, a person with a shovel and a hoe can plant an acre of corn for the cost of the seed -- perhaps $100. Solar cells, on the other hand, cost about $2.5-million per acre, and you probably have to double that when you include the cost of the framework to hold them, the wiring and any other infrastructure needs. As you can see, it's tough to compare these two energy-collecting methods directly.
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