If solar panels are placed in the Mojave Desert in California that generate 100 megawatts on a 1.3-square-mile site with an average of \(7.50\) hours of productive daylight each day, how many tons of coal are equivalent to the energy produced in one day by the solar panels? (One ton of coal will produce \(26.6\) gigajoules of energy, 1 Watt \(=1 \mathrm{~J} / \mathrm{s}\).)

Solar energy harnesses the power of the sun, a renewable and abundant source of energy. Unlike fossil fuels, solar power is inexhaustible and emits no greenhouse gases during generation, making it a key player in sustainable energy solutions. Photovoltaic cells in solar panels convert sunlight directly into electricity through a process known as the photovoltaic effect. Each solar panel consists of many solar cells, which work together to produce a significant amount of energy.

In the exercise, solar panels located in the Mojave Desert utilize the region's ample sunshine, converting the solar irradiance into electrical energy. The power generation capability of such a system is measured in watts (W), or in this case, megawatts (MW). Such large-scale solar installations can have a substantial impact on reducing reliance on traditional energy sources, like coal, and contribute to a lower carbon footprint.

Understanding the equivalence between coal energy and other forms of energy is crucial for comparing the environmental impact and the sustainability of different energy sources. Coal, a fossil fuel, has a high energy content; one ton of coal can produce a substantial amount of energy, typically expressed in gigajoules (GJ).

In our exercise, we establish that one ton of coal can yield 26.6 GJ of energy. To equate solar energy output to coal energy, we must know the amount of energy a typical unit of coal produces. This allows us to estimate how much coal would be needed to generate the same amount of energy as the solar panels, providing a tangible comparison of the two energy sources. It's important to remember that coal combustion has environmental consequences, including greenhouse gas emissions, which aren't associated with solar energy generation.

Calculating energy output is a fundamental step to understand how much energy a system produces over a given period. In our scenario, the energy output of solar panels is determined by multiplying the power capacity (in watts) by the number of seconds of productive daylight received. The product gives us the total energy in joules (J) generated in a day.

For the solar array in the Mojave Desert, this calculation informs us how much energy is produced with 100 MW capacity over 7.5 hours of productive daylight. It's important in such calculations to ensure unit consistency, converting hours to seconds and megawatts to watts when necessary. This precise calculation allows us to compare different energy sources like solar and coal on an even footing.

Unit conversion is essential in energy conversion calculations since it ensures comparisons are accurate and meaningful. As energy can be expressed in multiple units such as joules, watt-hours, kilowatt-hours, and gigajoules, converting these units properly is crucial for clear communication and comparison.

In our given exercise, there are several conversions required: megawatts to watts, hours to seconds, and gigajoules to joules. These conversions are necessary to align the units of coal energy output with the units of solar energy output. Ensuring that we're working with the same units across different forms of energy makes the calculation coherent and the result reliable. Remember, accurate unit conversion is the basis for comparisons in energy output between diverse energy sources.