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 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 compar- ison, the total area of New York City is 830 km2.)

검증된 단계별 안내

First, we need to understand that the problem is asking us to find the area of land needed to generate the peak power usage of New York City using solar energy. We know that the solar power striking Earth every day averages 168 watts per square meter and the efficiency of solar energy conversion is about 10%.

Next, we need to convert the peak power usage of New York City from MW to watts. We know that 1 MW equals 1,000,000 watts. So, we multiply 13,200 MW by 1,000,000 to get the peak power usage in watts.

Then, we need to calculate the actual power that can be generated from 1 square meter of land. Since the efficiency of solar energy conversion is 10%, we multiply 168 watts (the power striking 1 square meter of land) by 0.10 (10%).

Now, we need to calculate the total area of land needed to generate the peak power usage. We divide the peak power usage (in watts) by the power that can be generated from 1 square meter of land.

Finally, to get the area in square kilometers, we need to convert from square meters to square kilometers. We know that 1 square kilometer equals 1,000,000 square meters. So, we divide the total area of land (in square meters) by 1,000,000.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Solar Power and Efficiency

Solar power refers to the energy harnessed from sunlight, which can be converted into electricity using solar panels. The efficiency of solar energy conversion indicates how much of the solar energy that strikes a surface can be transformed into usable electrical energy. In this case, a 10% efficiency means that only 10% of the solar energy hitting the panels is converted into electricity.

Power Calculation

Power is defined as the rate at which energy is used or generated, measured in watts (W). In this scenario, the peak power usage of 13,200 MW (megawatts) indicates the maximum electrical power demand at a given time. To determine the area needed for solar panels, one must calculate how much solar energy is required to meet this power demand, factoring in the efficiency of the solar technology.

Area and Energy Density

Energy density refers to the amount of energy received per unit area, measured in watts per square meter (W/m²). The average solar power striking Earth is 168 W/m², which means that each square meter receives this amount of energy from the sun. To find the total area required for solar panels, one must divide the total power needed by the energy density, adjusted for the efficiency of the solar panels.