Question

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 \(13,200 \mathrm{MW} .\) 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 comparison, the total area of New York City is 830 km.)

Short answer

To provide the peak power of 13,200 MW, sunlight must be collected from an area of approximately 785,714,285.71 square meters. This is a significant portion of the total area of New York City, which is 830,000,000 square meters.

Step-by-step solution

Compute the available power after the conversion

First, we calculate the available power per square meter after considering the 10% efficiency of solar energy conversion. We're given that the average solar power striking the Earth is 168 watts per square meter. Let P be the available power after conversion. \(P = 168 \cdot 0.10 = 16.8 \mathrm{W/m^2}\)

Convert the power usage in New York City to watts

Next, we need to convert the highest power usage in New York City from megawatts (MW) to watts (W). Let E be the energy in watts. \(E = 13,200 \mathrm{MW} \cdot 1,000,000 = 13,200,000,000\mathrm{W}\)

Calculate the area required to provide the peak power

Now, we will calculate the required area to provide the peak power, considering the available power (P) and the energy (E) needed as calculated above. Let A be the required area in square meters. \(A = \frac{E}{P} = \frac{13,200,000,000\mathrm{W}}{16.8 \mathrm{W/m^2}} = 785,714,285.71 \mathrm{m^2}\)

Compare the required area with the total area of New York City

Finally, let's compare the calculated area needed to collect the sunlight with the total area of New York City. The total area of New York City is given as 830 km². Convert the total area of New York City to square meters: \(830 \mathrm{km^2} \cdot 1,000,000 = 830,000,000 \mathrm{m^2}\) The calculated area required to provide the peak power is about 785,714,285.71 square meters, while the total area of New York City is 830,000,000 square meters. In order to provide the peak power of 13,200 MW, sunlight must be collected from an area of approximately 785,714,285.71 square meters, which is a significant portion of the total area of New York City.

Key concepts

Power Efficiency

Power efficiency is all about how effectively a device or system can convert energy from one form to another. When we talk about solar energy systems, efficiency refers to the percentage of sunlight energy that is transformed into usable electrical power. For instance, if a solar panel is 10% efficient, it means that only 10% of the sunlight it receives gets converted into electricity.
Why is efficiency important? It dictates the size of the solar panel required for a particular power output. For cities like New York, where the demand for power is high, efficiency plays a crucial role in determining how much land would be needed to produce the electricity through solar power. Higher efficiency means smaller areas can be used to generate equal amounts of power.
In practical cases, efficiencies can range from 10% to over 20% in advanced solar panels. But, for large-scale, practical applications, understanding the balance of cost, efficiency, and available space is essential.

Energy Conversion

Energy conversion is the process of changing energy from one form to another. When it comes to solar power, energy conversion involves transforming sunlight, a form of radiant energy, into electrical energy, which we can use. Solar panels, or photovoltaic cells, are typically employed in this conversion process.
The equation in the original exercise illustrates energy conversion through the efficiency parameter. Here, only 10% of the energy from sunlight gets turned into electrical energy, meaning a large portion of potential energy becomes unusable. This conversion rate is significant because the more efficient an energy conversion process, the less energy is wasted and the more sustainable and viable solar energy becomes as a renewable energy source.
Understanding energy conversion helps students grasp why advancements in solar panel technology are critical. Improving conversion rates can significantly influence how much solar energy we can harness efficiently, making sustainable energy more accessible globally.

Solar Power

Solar power harnesses energy from the sun to generate electricity. This is done primarily through solar panels that capture sunlight and convert it into usable power. The original exercise offers a glimpse into how solar power can meet significant energy demands, like in New York City.
An interesting aspect of solar power is the resource abundance it relies on. Unlike fossil fuels, sunlight is abundant and widely available. By utilizing it, we can reduce dependency on non-renewable sources and decrease environmental impact.
Solar power systems can be deployed on various scales—from small rooftop panels to extensive solar farms. When considering solar power for massive needs like a major city, it becomes evident that vast land areas may be required, as shown in the calculation that aligns sunlight collection area with the power needs of NYC.
This kind of application highlights the promise and challenge of using solar power at larger scales. It underlines the importance of developing efficient systems and integrating solar power into urban environments as part of the future's energy solutions.