Large fossil fuel or nuclear electrical power plants operate most economically w

Question

Large fossil fuel or nuclear electrical power plants operate most economically when run at full capacity 24 hours a day. Excess electrical energy can be "stored" and recovered by pumping water into a reservoir on top of a mountain and letting it fall through turbines during periods of peak demands. At such a facility, the water falls an average distance of 250 m. The reservoir has a surface area of 1.3 km^2 and a depth averaging 10m.
a.) how much energy is available each time the reservoir is emptied?
b.) if it is emptied over a period of 10 hours, and 80 percent of the energy is converted into electrical energy, what is the power generated?

Explanation / Answer

a) E = m g h = A d g h = 1000* 1.3 *1000^2 * 10 * 9.81*250=3.19E13 J

b) P = .8*3.19E13/(10*60*60)=7.08E8 W

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