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Chapter 18: Problem 73

The solar power striking Earth every day averages 168 watts per square meter. The highest ever recorded electrical power usage in New York City was \(13,200 \mathrm{MW} .\) A record established in July of \(2013 .\) Considering that present technology for solar energy conversion is about 10\(\%\) efficient, from how many square meters of land must sunlight be collected in order to provide this peak power? (For comparison, the total area of New York City is 830 km.)

Short Answer

Expert verified
To provide the peak power of 13,200 MW, sunlight must be collected from an area of approximately 785,714,285.71 square meters. This is a significant portion of the total area of New York City, which is 830,000,000 square meters.

Step by step solution

01

Compute the available power after the conversion

First, we calculate the available power per square meter after considering the 10% efficiency of solar energy conversion. We're given that the average solar power striking the Earth is 168 watts per square meter. Let P be the available power after conversion. \(P = 168 \cdot 0.10 = 16.8 \mathrm{W/m^2}\)
02

Convert the power usage in New York City to watts

Next, we need to convert the highest power usage in New York City from megawatts (MW) to watts (W). Let E be the energy in watts. \(E = 13,200 \mathrm{MW} \cdot 1,000,000 = 13,200,000,000\mathrm{W}\)
03

Calculate the area required to provide the peak power

Now, we will calculate the required area to provide the peak power, considering the available power (P) and the energy (E) needed as calculated above. Let A be the required area in square meters. \(A = \frac{E}{P} = \frac{13,200,000,000\mathrm{W}}{16.8 \mathrm{W/m^2}} = 785,714,285.71 \mathrm{m^2}\)
04

Compare the required area with the total area of New York City

Finally, let's compare the calculated area needed to collect the sunlight with the total area of New York City. The total area of New York City is given as 830 km². Convert the total area of New York City to square meters: \(830 \mathrm{km^2} \cdot 1,000,000 = 830,000,000 \mathrm{m^2}\) The calculated area required to provide the peak power is about 785,714,285.71 square meters, while the total area of New York City is 830,000,000 square meters. In order to provide the peak power of 13,200 MW, sunlight must be collected from an area of approximately 785,714,285.71 square meters, which is a significant portion of the total area of New York City.

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Most popular questions from this chapter

An impurity in water has an extinction coefficient of \(3.45 \times 10^{3} M^{-1} \mathrm{cm}^{-1}\) at \(280 \mathrm{nm},\) its absorption maximum (A Closer Look, p. 576\() .\) Below 50 \(\mathrm{ppb}\) , the impurity is not a problem for human health. Given that most spectrometers cannot detect absorbances less than 0.0001 with good reliability, is measuring the absorbance of a water sample at 280 \(\mathrm{nm}\) a good way to detect concentrations of the impurity above the 50 -ppb threshold?

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