3.60 x 106 J). On average, each plant is In 2006, the United States produced 282

Question

3.60 x 106 J). On average, each plant is In 2006, the United States produced 282 x 109 kilowatt-hours (kWh) of electrical energy from 4138 hydroelectric plants (1.00 kwh 90% efficient at converting mechanical energy to electrical energy, and the average dam height is 50.0 m. (a) At 282 x 109 kWh of electrical energy produced in one year, what is the average power output per hydroelectric plant? 7.78 MW/dam (b) What total mass of water flowed over the dams during 2006? 8e15X kg (c) What was the average mass of water per dam and the average volume of water per dam that provided the mechanical energy to generate the electricity? (The density of water is 1000 kg/m3) average mass average volume kg/dam m3/dam (d) A gallon of gasoline contains 45.0 × 106 of energy. How many gallons of gasoline did the 4138 dams save? gal In one year the United States produced 282 × 109 kwh of electrical energy from 4138 hydroelectric dams. On average each dam is 50.0 m high and is 90% efficient in converting mechanical energy into electrical energy. We can perform various unit conversions in order to answer the posed questions eBook

Explanation / Answer

(A) Energy = 282 x 10^9 x 10^3 x 3600 = 1.0152 x 10^18 J

from each = 1.0152 x 10^18 / 4138

= 2.453 x 10^14 J

Power = 2.453 x 10^14 / (365 x 24 x 3600)

= 7.78 x 10^6 W

= 7.78 MW/dam

(B) energy produced from dam = 1.0152 x 10^18 / 0.90

= 1.128 x 10^18 J

m x 9.8 x 50 = 1.128x 10^18

m = 2.30 x 10^15 kg

(C) average mass = m / 4138 = 5.56 x 10^11 kg

average volume = 5.56 x 10^8 m^3

(d) m+gasoline = 1.0152 x 10^18 / 45 x 10^6

= 2.256 x 10^10 gal

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