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Chapter 11

Q. 11.5

Suppose an array of 30% efficient solar cells has an effective area of 100 m by 100 m. The cells are tilted so as to receive maximum solar flux, an average of 680 W / m ^{2} for a day with 12 hours of daylight. How much energy does this array produce each day? Compare that energy with the output of a 100-MW conventional power plant.

Strategy Energy = power × time. With 1 W = 1 J/s, it is necessary to convert the time to units of s. The solar cell runs for 12 hours, but the power plant runs for 24 hours.


Verified Solution

The solar cells have an area of 100 m \times 100 m =10^{4} m ^{2}. The time is


t=12 h \times \frac{60 min }{ h } \times \frac{60 s }{ min }=43,200 s


Therefore the energy produced in one 12-hour day is


E=0.30 \times 680 W / m ^{2} \times 10^{4} m ^{2} \times 43,200 s =8.8 \times 10^{10} J


The power plant operates for 24 hours (86,400 s) at a rate of 100 MW =10^{8} W, and produces


E=10^{8} W \times 86,400 s =8.6 \times 10^{12} J


of energy, which is about 100 times more than the solar cell array produces. Producing a comparable amount of energy requires a larger solar array.