Part A:
From the given graph, the average monthly per capita residential use of electricity in the United States in 2004 is 370 Kilowatt-hours.
Therefore, the average yearly per capita residential need for electricity is given by:
370 x 12 = 4,440 Kilowatt-hours.
Part B:
From the given graph, average influx of solar radiation per square meter for Topeka, Kansas is 130 Kilowatt-hours.
Therefore, the average yearly solar radiation per square meter is given by:
130 x 12 = 1,560 Kilowatt-hours.
Part C:
Assuming that photovoltaic conversion of solar
energy has 10% efficiency.
The number square meters of
photovoltaic cells that would be needed to supply one person's electricity
for the year, based on the yearly average values is calculated thus:
Recall that from part A we have that the average yearly need of electricity per person is 4,440 kilowatt-hours and from part B, we have that the average radiation per square meter for the year is 1,560 kilowatt-hours.
Thus, the number of square meters that will produce 4,440 kilowatt-hours of electricity is given by:
[tex] \frac{4,440}{1,560} =2.85m^2[/tex]
Given that the photovoltaic conversion of solar
energy has 10% efficiency, therefore, the number of square meters of photovoltaic cells that will produce 4,440 kilowatt-hours of electricity is given by:
[tex] \frac{2.85}{0.1} =28.5m^2[/tex]
Part D:
From part C, we have that the number of square meters that will produce 4,440 kilowatt-hours of electricity is [tex]2.85m^2[/tex]
If the efficiency of photovoltaic cells is
40%, the number of square meters of photovoltaic cells that will produce 4,440 kilowatt-hours of electricity is given by:
[tex] \frac{2.85}{0.4} =7.12m^2[/tex]
Part E:
Given that commercially available household photovoltaic
systems cost approximately $20,000 and that the average cost of electricity in
the United States is approximately $0.09 per kilowatt hour.
If the the system is installed for a four-person household, the amount of electricity needed per year by a four-person household is 4,440 x 4 = 17,760 kilowatts-hour and the cost of electricity for the four-person household is 17,760 x 0.09 = 1,598.4
Therefore, the number of years it will take the photovoltaic system to generate $20,000 of electricity is given by:
[tex] \frac{20,000}{1,598.4} \approx12.5\ years[/tex]
