Problem 25 - Physics

Question

The average intensity of sunlight at the top of the earth's atmosphere is \(1390 \mathrm{~W} / \mathrm{m}^{2}\). What is the maximum energy that a \(25-\mathrm{m} \times 45\) -m solar panel could collect in one hour in this sunlight?

Step-by-Step Solution

Answer

The maximum energy that the solar panel could collect in one hour is 5,643,000,000 J.

Step 1: Calculate the Area of the Solar Panel

To begin, calculate the total area of the solar panel. The dimensions of the panel are given as 25 meters by 45 meters. Therefore, \[ \text{Area} = 25 \times 45 \ \mathrm{m^2} \].Compute:\[ \text{Area} = 1125 \ \mathrm{m^2} \].

Step 2: Calculate the Total Energy Collected in One Second

The intensity of sunlight is given as 1390 W/m², which means each square meter receives 1390 watts every second. Multiply this intensity by the total area of the solar panel to find the energy collected per second:\[\text{Energy per second} = 1390 \ \mathrm{W/m^2} \times 1125 \ \mathrm{m^2}\]Compute:\[\text{Energy per second} = 1567500 \ \mathrm{W}.\]

Step 3: Calculate the Energy Collected in One Hour

To find the total energy collected in one hour, convert the power into energy. Since power (in watts) is equivalent to energy per second, multiply by the number of seconds in one hour (3600 seconds):\[\text{Energy in one hour} = 1567500 \ \mathrm{W} \times 3600 \ \mathrm{s}\]Compute:\[\text{Energy in one hour} = 5643000000 \ \mathrm{J}\]This measures the total energy in joules.

Key Concepts

Energy Intensity

Energy intensity is a measure of how much energy is received by a certain area over a specific period. For solar energy, it is often expressed in watts per square meter (W/m²). This tells us how much solar power hits a given area, like the surface of a solar panel. For instance, in our example, the energy intensity of sunlight at the earth's atmosphere is 1390 W/m².
This means that each square meter receives 1390 watts of solar power each second. Understanding this concept is crucial when calculating how much energy a solar panel can collect.
By knowing the energy intensity, you can determine how effective your solar panel can be at harnessing sunlight to produce energy.

Solar Panel Area

The solar panel area is simply the size of the panel measured in square meters. It is an important factor because it determines how much solar energy the panel can collect. To find out the area of a rectangular solar panel, you multiply its length by its width.
In our example, the solar panel measures 25 meters by 45 meters, making its total area 1125 square meters. The larger the area, the more sunlight it can capture.

• Area formula: Length x Width
• Example: 25 m x 45 m = 1125 m²

This area is then used in combination with the energy intensity to find the total energy that can be collected by the panel.

Energy Conversion

Energy conversion is the process of transforming sunlight into usable energy, typically in the form of electricity. Solar panels convert solar energy using photovoltaic cells, which are made of semiconductor materials, like silicon. These cells absorb sunlight and convert it into electricity.

• Photovoltaic cells play a vital role in this conversion.
• Efficiency is how well the panel can convert solar energy to electricity.

In calculations like these, we often assume perfect efficiency just to understand potential energy collection. However, real-world efficiency is lower due to technological and environmental factors.
Knowing this helps set realistic expectations for energy output.

Joules

Joules are the unit of energy used in this context to measure how much energy is collected by the solar panel. One watt is equal to one joule per second, meaning if you know the power in watts, you can calculate the energy collected over time by multiplying by the number of seconds.
In the example provided, the solar panel collected 1,567,500 watts of power every second. To find out how many joules are collected in an hour, multiply this power by 3600 (the number of seconds in one hour). This results in an energy collection of 5,643,000,000 joules.

• Power (W) x Time (s) = Energy (J)
• Example: 1,567,500 W x 3600 s = 5,643,000,000 J

This conversion helps in understanding energy consumption and production better.