Question

A solar panel has an area of $50{\mathrm{m}}^2$, and it produces an average of 4 $\mathrm{kW}$ of power. The panel is in a location which receives an average of $0.085\frac{\mathrm{W}}{{\mathrm{cm}}^2}$ of optical energy from the sun. Calculate the efficiency of the panel.

Short answer

The efficiency of the panel is approximately 9.41%.

Step-by-step solution

Convert Area to Square Centimeters

The area of the solar panel is given as 50 square meters. To convert it to square centimeters, use the conversion factor: $1ext{m}^2=10,000ext{cm}^2$. Thus, the area in square centimeters is $50imes10,000=500,000ext{cm}^2$.

Calculate Total Energy Received by the Panel

The solar panel receives an average of $0.085\frac{\text{W}}{{\text{cm}}^2}$. To find the total energy received by the panel in Watts, multiply the energy received per unit area by the total area: $0.085\times 500,000=42,500\text{ W}$.

Determine the Power Output of the Panel

The problem states that the solar panel produces an average of 4 kW of power. Convert this to Watts: $4\text{ kW}=4,000\text{ W}$.

Calculate Efficiency of the Panel

Efficiency is the ratio of the power output to the power input, expressed as a percentage. Use the formula: $extEfficiency=\left(\frac{\text{Power Output}}{\text{Power Input}}\right)\times 100\mathrm{\%}$. Substituting the given values, we have: $\text{Efficiency}=\left(\frac{4,000}{42,500}\right)\times 100\mathrm{\%}\approx 9.41\mathrm{\%}$.

Key concepts

Power Output Calculation

Understanding how to determine the power output of a solar panel is essential for calculating efficiency. The solar panel in question produces an average power of 4 kW. It's crucial to always convert power into a consistent unit to ensure accurate calculations. In this case, converting kilowatts to watts is necessary since the energy input is often given in watts. To convert kilowatts to watts, we multiply by 1,000 since 1 kW equals 1,000 watts. Therefore, 4 kW equals 4,000 watts. This conversion allows us to easily compare the power generated by the solar panel to the energy it receives. Understanding this conversion is key to analyzing the panel's performance.

Energy Conversion

Energy conversion involves determining how much solar energy the panel receives and how it is transformed into electric power. In the problem, the solar panel receives an energy input of 0.085 W per cm². To find the total energy input, we multiply this figure by the panel's area in square centimeters.

In this example, with an area of 500,000 cm², the calculation is straightforward:

• 0.085 W/cm² d7 500,000 cm²

This results in 42,500 W of energy received by the panel. Understanding energy conversion enables us to assess how effectively a solar panel captures sunlight and transforms it into usable power. It's vital to consider every element of this process to enhance solar efficiency.

Area Conversion

Converting the area into the appropriate units is crucial for calculating how much energy a solar panel receives from the sun. In our exercise, the given area is in square meters, and the energy input is provided in watts per square centimeter. To solve this, we need to convert the area from square meters to square centimeters.
A simple conversion factor can help here:

• 1 square meter = 10,000 square centimeters

Multiplying the given area of 50 square meters by this conversion factor results in a total of 500,000 square centimeters.

The conversion of area is a pivotal step because it aligns the units of measurement, making subsequent calculations free from error. Remembering this conversion process ensures accuracy in not only solar energy calculations but any project requiring unit conversions.