Question

The solar power striking Earth every day averages 169 watts per square meter. The peak electrical power usage in New York City is 12,000 megawatts. Considering that present technology for solar energy conversion is only about $10\mathrm{\%}$ 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 the city is $830{\mathrm{km}}^2$.)

Short answer

The sunlight must be collected from approximately 710.06 square kilometers of land to provide the peak power for New York City with current solar technology.

Step-by-step solution

Find the power in watts

In this step, we need to convert the peak power usage given in megawatts to watts since we will be making calculations using watts. To do so, recall that 1 megawatt (MW) = 1,000,000 watts (W). The given peak power usage is 12,000 MW, so we get: 12,000 MW * 1,000,000 W/MW = 12,000,000,000 W So, the peak power usage is 12,000,000,000 W.

Calculate the required power with the efficiency

Now we need to account for the 10% efficiency. This means that only 10% of the incoming solar power will be converted into electricity. Therefore, we need to find how much raw solar power (in watts) is required to produce 12,000,000,000 W of electricity. To find this value, simply divide the peak power usage by the efficiency (in decimal form): Required power = 12,000,000,000 W / 0.10 = 120,000,000,000 W

Calculate the area for collecting sunlight

The required land area to collect the sunlight can be found by dividing the required raw solar power (in watts) by the average solar power per square meter (169 W/m²). Doing so gives: Area (m²) = 120,000,000,000 W / 169 W/m² ≈ 710,059,171 m²

Convert the area to square kilometers

To compare the calculated area with the total area of New York City, we need to convert our result from square meters to square kilometers. To do that, recall that 1 square kilometer (km²) = 1,000,000 square meters (m²). So, we get: Area (km²) = 710,059,171 m² / 1,000,000 m²/km² ≈ 710.06 km² The sunlight must be collected from approximately 710.06 square kilometers of land to provide the peak power for New York City with current solar technology.

Key concepts

Solar Power

When we talk about solar power, we're discussing the energy that comes from the sun and reaches the Earth. This energy travels in the form of sunlight, which can be captured and converted into electricity using technology like solar panels. Sunlight is a plentiful and renewable resource; it bathes our planet with an average of 169 watts per square meter every day.
Solar panels are devices that contain photovoltaic cells, which convert sunlight into direct current (DC) electricity. Despite the abundance of sunlight, the current technology limits us to a conversion efficiency of about 10%. This means that, out of the total energy that hits the panel, only 10% is turned into usable electrical energy. As we aim for improvements in solar technologies, boosting this efficiency rate is a key goal for scientists and engineers.

Electrical Power Usage

Electrical power usage, or demand, is the rate at which electrical energy is consumed in a given area or by a specific process. For instance, the peak electrical power usage in New York City reaches around 12,000 megawatts. This peak demand represents the highest level of power required at a given time and is critical for planning the city's energy needs.
To understand the significance of meeting this peak demand using solar power, one has to consider factors like the availability of sunlight, the efficiency of power conversion, and the scale of infrastructure required. Notably, the electrical energy we use in our homes and cities isn't always directly obtained from renewable sources, but as the shift towards renewable energy, including solar, gains momentum, the way we assess and meet our energy needs is evolving.

Renewable Energy Technology

Renewable energy technology encompasses the methods and devices we use to convert natural resources like sunlight, wind, and water into usable power. These technologies are designed to be sustainable, drawing from resources that are naturally replenished.
Solar panels, wind turbines, and hydroelectric dams are common examples of renewable energy devices. These technologies have several benefits over fossil fuels: they produce less pollution, reduce greenhouse gas emissions, and provide a level of energy security since they're not subject to the same market volatility as oil and gas. With ongoing research and development, renewable energy technologies are rapidly advancing, becoming more efficient, and consequently becoming more integrated into our power grids.

Power Conversion Calculations

Understanding power conversion calculations is crucial when planning for energy production, especially with renewable sources like solar energy. These calculations help us determine how much raw energy is needed to meet a particular electricity demand, taking into account the efficiency of the conversion technology.
For instance, to find out how much land would be required to provide the peak power demand of New York City with solar power, a series of steps are followed. Initially, we convert the demand into watts, consider the conversion efficiency of solar panels, and finally calculate the land area needed based on the average solar power per square meter. In scenarios like these, the math reveals the practicalities and challenges of meeting large-scale energy demands with current renewable technologies.