Question

Solar energy reaching the earth is about \(1350 \mathrm{W} / \mathrm{m}^{2}\) outside the earth's atmosphere, and \(950 \mathrm{W} / \mathrm{m}^{2}\) on earth's surface normal to the sun on a clear day. Someone is marketing \(2 \mathrm{m} \times 3 \mathrm{m}\) photovoltaic cell panels with the claim that a single panel can meet the electricity needs of a house. How do you evaluate this claim? Photovoltaic cells have a conversion efficiency of about 15 percent.

Short answer

Answer: To evaluate this claim, we first calculate the total solar energy received by the panel, convert the received solar energy into usable electrical energy using the given conversion efficiency, and finally compare the energy produced by the solar panel with the energy consumption of a typical house.

Step-by-step solution

Calculate Solar Energy Received by the Panel

First, find the total amount of solar energy the \(2\,\mathrm{m}\times3\,\mathrm{m}\) panel receives. This can be calculated by multiplying the solar energy received on the earth's surface (\(950\,\mathrm{W/m^{2}}\)) by the area of the panel. Area of the panel = Length × Width = \(2\,\mathrm{m}\times3\,\mathrm{m}\)

Convert Solar Energy into Usable Electrical Energy

Next, we need to convert the solar energy received by the panel into electrical energy. This can be done using the given conversion efficiency of 15 percent. Usable electrical energy = Solar energy received × Conversion efficiency

Compare Energy Produced with Energy Consumption of a Typical House

Finally, we need to compare the usable electrical energy produced by the solar panel with the energy consumption of a typical house to evaluate the claim. Based on the average energy consumption in a household, we will determine whether a single solar panel can meet these energy requirements or not.