Question

In a sunny location, sunlight has a power density of about \(1 \mathrm{~kW} / \mathrm{m}^{2} .\) Photovoltaic solar cells can convert this power into electricity with \(15 \%\) efficiency. If a typical home uses \(385 \mathrm{kWh}\) of electricity per month, how many square meters of solar cells are required to meet its energy requirements? Assume that electricity can be generated from the sunlight for 8 hours per day.

Short answer

To meet the home's monthly energy use of 385 kWh, one would need approximately 85.3 square meters of solar cells.

Step-by-step solution

Calculate the Total Monthly Energy Production Per Square Meter of Solar Cell

First, find the energy produced by a square meter of solar cell each day by multiplying the power density of sunlight by the area and the efficiency of the solar cell. Since the efficiency is given in percentages, convert it to a decimal by dividing by 100. The area, in this case, is 1 square meter. The power density is 1 kW/m², and solar cells operate 8 hours per day. So, daily energy is calculated by the formula Energy (kWh/day/m²) = Power Density (kW/m²) * Efficiency * Operating Hours (hrs/day), which results in Energy (kWh/day/m²) = 1 * (15/100) * 8.

Convert Daily Energy Production to Monthly Production

Next, convert the daily energy production to monthly by multiplying by the number of days in a month. As the daily energy is produced by a square meter of solar cell, the monthly energy would be Monthly Energy (kWh/month/m²) = Daily Energy (kWh/day/m²) * Number of Days in a Month. Since the number of days in a month varies, for this calculation, a 30-day month will be assumed. Thus, Monthly Energy (kWh/month/m²) = Daily Energy (kWh/day/m²) * 30.

Calculate the Total Area of Needed Solar Cells

Finally, calculate the total area of solar cells needed to meet the home's monthly energy use. This can be done by dividing the total monthly energy use of the home by the monthly energy production per square meter of solar cell. Area (m²) = Home’s Monthly Energy Use (kWh/month) / Monthly Energy (kWh/month/m²).

Key concepts

Understanding Photovoltaic Solar Cells

Photovoltaic (PV) solar cells are an amazing technology. They take sunlight, composed of energy-packed photons, and convert it directly into electrical power. This process is known as the photovoltaic effect. When photons strike a PV cell, they can knock electrons free from atoms within a semiconductor, typically silicon. These free electrons are then captured to produce an electric current.

PV solar cells are made of multiple layers, each with a specific function. The top layer captures the light, the middle layer is where the electricity is generated, and the bottom layer collects the electrons. By connecting multiple cells together, a solar panel is formed, which can generate a significant amount of power for various uses.

The exercise you encountered involves calculating how much area would be needed by these solar cells to power a home. This type of calculation is not only practical but provides insight into the potential and limitations of solar power.

Energy Efficiency of Solar Cells

Energy efficiency in the context of solar cells refers to their ability to convert sunlight into electricity. It's a critical measure because it determines how much energy you can harness from the sun. The efficiency percentage represents what part of the solar energy is converted to electrical energy. For example, if a solar cell has a 15% efficiency rate, it means that it converts 15% of the solar energy hitting it into usable electricity.

To improve solar technology, researchers and manufacturers strive to increase the efficiency of these cells. Even fractional percentage improvements can make solar systems more cost-effective and practical for wider use. However, the efficiency is a factor of the materials used, the cell design, and the conditions under which the cells are used, such as orientation, temperature, and the presence of shade.

Calculating Electricity Consumption

When considering electricity consumption, we measure how much electric power is used over a certain period. This is typically calculated in kilowatt-hours (kWh). For instance, the monthly consumption of a typical home was given as 385 kWh in the exercise. This figure is vital for sizing up a solar system to ensure it meets the household's energy needs.

To adequately calculate the necessary number of solar cells for a home, we use the given energy efficiency and daily sunlight hours to figure out the production per square meter. With the power density of sunlight being approximately 1 kW/m² in sunny areas, and typical effective sunlight hours being around 8, calculations become quite straightforward for estimating the system size required to offset standard energy consumption.

Renewable Energy Sources and Solar Power

Solar power is a form of renewable energy – an energy source that is abundant and replenishable. Unlike fossil fuels, which are finite and emit harmful greenhouse gases, solar energy is clean and sustainable. By harnessing energy from the sun, we can reduce our dependence on fossil fuels and lower our carbon footprint.

Renewable energy sources like solar power are becoming increasingly important in the global effort to combat climate change. Solar panels on rooftops and solar farms are a common sight now, as nations around the world invest in this clean energy. Additionally, advancements in solar technology, including increased efficiency and better energy storage solutions, are making solar energy a more practical and cost-effective option for homes, businesses, and beyond.