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Chapter 18: Problem 73

In 2008 , the global average electricity consumption per head was $3.0 \mathrm{MWh}$. The solar power striking Earth every day averages 168 watts per square meter. 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 power?

Short Answer

Expert verified
First, we find the total energy consumption per head in kWh: \(3000 kWh\). Then, we convert it to energy per day in watts: \(\frac{3000 * 1000 \text{ Wh}}{86,400 \text{ seconds/day}}\). Next, we divide this by the \(0.1\) efficiency to find the required solar power. Finally, we divide the required solar power by the average solar power per square meter (\(168 \text{ W/m²}\)) to find the required area of land.

Step by step solution

01

Calculate total energy consumption per head

First, let's determine the total energy consumption per head in kWh. We are given that the average electricity consumption per head is \(3.0 MWh\), which can be converted to kWh by multiplying by 1000 (since 1 MWh = 1000 kWh): Total energy consumption per head (kWh) = \(3.0 MWh * 1000 = 3000 kWh\)
02

Convert energy consumption to energy per day

Next, we need to calculate the energy consumption per day, as the solar power is given in watts (energy per second). Since there are \(24 * 60 * 60 = 86,400\) seconds in a day, we can divide the total energy consumption by the number of seconds in a day to get the energy consumption per second (watts): Energy consumption per day (kWh/day) = \(\frac{3000 kWh}{365 \text{ days}}\) Energy consumption per day (W) = \(\frac{3000 * 1000 \text{ Wh}}{86,400 \text{ seconds/day}}\)
03

Find the required solar power

We are given that the efficiency of the solar energy conversion is \(10\%\) or \(0.1\). To find the total solar power required, we can divide the energy consumption per day (W) by the efficiency: Required solar power (W) = \(\frac{\text{Energy consumption per day (W)}}{0.1}\)
04

Calculate the required area of land

Finally, we are given that the average solar power striking Earth is 168 watts per square meter. We can now find the area of land required to collect this power by dividing the required solar power (W) by the average solar power per square meter: Required area of land (m²) = \(\frac{\text{Required solar power (W)}}{168 \text{ W/m²}}\) Now that we have the required area of land, we will substitute all values into the expressions to find the answer.

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