Question
Write a report on solar energy panels. When were they first developed? What is their efficiency in converting the energy of sunlight to electrical energy? How large a panel is needed to power a typical house?
Step 1
Solar panels, specifically photovoltaic (PV) cells, were first developed in the 1950s. The first practical solar cell was created by Bell Labs in 1954, which marked the beginning of modern solar energy technology. Show more…
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Today, the best commercially available solar panels are about $18 \%$ efficient at converting the energy from sunlight into electricity. A typical home in the United States uses about $40 \mathrm{~kW} \cdot \mathrm{h}$ of electricity a day, and U.S. electricity costs currently average about $\$ 0.10$ per kW-h. (a) Assuming $8.0$ hours of useful sunlight per day with an incident solar energy of $0.5 \mathrm{~kW} \cdot \mathrm{m}^{-2}$, calculate the minimum panel area needed to provide for a typical home's electrical needs. Will a solar panel of this size fit on the roof of a typical single-family home? (b) If it costs $\$ 15000$ to install a solar panel of this size, how long will it take to pay for itself? Assume U.S. energy prices remain constant over this time.
Solar Power The capacity of solar power installed in the United States has grown since $2000 .$ The capacity of solar power installed in the United States can be modeled as $m(x)=15.45\left(1.46^{x}\right)$ megawatts between 2000 and 2008 , where $x$ is the number of years since 2000 . (Source: Based on data from USA Today, page $1 \mathrm{~B}$, $1 / 13 / 2009)$ a. How much solar power capacity was installed in 2000 , in $2004,$ in $2008 ?$ b. Use the information in part $a$ to make a table showing the year as a function of the capacity of solar power installed. c. Write a model giving the year as a function of the capacity of solar power installed.
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The best solar panels currently available are about 19$\%$ efficient in converting sunlight to electricity. A typical home will use about $40 .$ kWh of electricity per day $(1 \mathrm{kWh}=1 \text { kilowatt }$ hour; $1 \mathrm{kW}=1000 \mathrm{J} / \mathrm{s}$ ). Assuming 8.0 hours of useful sunlight per day, calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity. (See Exercise 132 for the energy rate supplied by the sun.)
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