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## 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.