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You are serving as an expert witness for the city council of a community. The council is exploring the concept of providing the electrical needs of the community by building a facility with photovoltaic cells to convert sunlight to electric potential energy. But they are facing resistance from members of the community, who claim that there is not enough open land in the community to build such a facility. The opposition is building toward a lawsuit, which the city council wants to avoid. The community requires 2.00 MW of power, and the best photovoltaic cells on the market at the time have an efficiency of 30.0%. In your community, an average intensity of sunlight during the day is 1,120 W/m2. The council members have no idea how much land is needed, so they have asked you to estimate the area of land (in m2) that must be found to construct this facility. (Assume the given average intensity of sunlight is only available for eight hours a day.)

Question

You are serving as an expert witness for the city council of a community. The council is exploring the concept of providing the electrical needs of the community by building a facility with photovoltaic cells to convert sunlight to electric potential energy. But they are facing resistance from members of the community, who claim that there is not enough open land in the community to build such a facility. The opposition is building toward a lawsuit, which the city council wants to avoid. The community requires 2.00 MW of power, and the best photovoltaic cells on the market at the time have an efficiency of 30.0%. In your community, an average intensity of sunlight during the day is 1,120 W/m2. The council members have no idea how much land is needed, so they have asked you to estimate the area of land (in m2) that must be found to construct this facility. (Assume the given average intensity of sunlight is only available for eight hours a day.)

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Solution 1

To calculate the area of land needed, we first need to understand how much energy the community needs in a day.

Given that the community requires 2.00 MW of power, and there are 24 hours in a day, the total energy required is:

Energy = Power x Time Energy = 2.00 MW x 24 hours = 48.00 MWh

However, the given average intensity of sunlight is only available for eight hours a day. So, the photovoltaic cells can only generate power for 8 hours.

The energy generated by the photovoltaic cells in a day is:

Energy = Power x Time Energy = Power x 8 hours

Given that the best photovoltaic cells on the market at the time have an efficiency of 30.0%, the actual power that can be generated by the cells is:

Power = Efficiency x Intensity of sunlight Power = 30.0% x 1,120 W/m2 = 336 W/m2

So, the energy generated by the photovoltaic cells in a day is:

Energy = Power x Time Energy = 336 W/m2 x 8 hours = 2.688 MWh/m2

Therefore, the area of land needed to generate the required 48.00 MWh is:

Area = Total energy required / Energy generated per m2 Area = 48.00 MWh / 2.688 MWh/m2 = 17.857 m2

So, approximately 18 square meters of land would be needed to construct this facility.

This problem has been solved

Solution 2

To calculate the area of land needed, we first need to understand how much energy the community needs in a day.

Given that the community requires 2.00 MW of power, and considering that this power is needed for 24 hours, the total energy required in a day is:

Energy = Power x Time Energy = 2.00 MW x 24 hours = 48.00 MWh

However, the sunlight is only available for 8 hours a day. So, the photovoltaic cells need to generate all the required energy during these 8 hours.

Therefore, the power that the photovoltaic cells need to generate is:

Power = Energy / Time Power = 48.00 MWh / 8 hours = 6.00 MW

Given that the efficiency of the photovoltaic cells is 30.0%, the actual power that needs to be generated by the cells (considering losses due to inefficiency) is:

Actual Power = Power / Efficiency Actual Power = 6.00 MW / 0.30 = 20.00 MW

The intensity of sunlight is given as 1,120 W/m². This means that each square meter of photovoltaic cells generates 1,120 W of power.

Therefore, the area of photovoltaic cells needed to generate the required power is:

Area = Actual Power / Intensity of sunlight Area = 20.00 MW / 1,120 W/m² = 17,857 m²

So, the city council needs to find approximately 17,857 square meters of land to construct the photovoltaic facility.

This problem has been solved

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