At a certain location, the solar power per unit area reaching Earth's surface is 200 W/m^2, averaged over a 24-hour day.If the average power requirement in your home is 2.8 kW and you can convert solar power to electric power with 8.0 % efficiency, how large a collector area will you need to meet all your household energy requirements from solar energy?
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To determine the collector area needed to meet your household energy requirements from solar energy, we can follow these steps:
Step 1: Convert the average power requirement to Watts:
Average power requirement = 2.8 kW = 2800 Watts
Step 2: Calculate the total solar power needed:
Total solar power needed = Average power requirement / Solar power conversion efficiency
Total solar power needed = 2800 Watts / 0.08
Step 3: Calculate the collector area required:
Collector area required = Total solar power needed / Solar power per unit area
Collector area required = (2800 Watts / 0.08) / 200 W/m^2
Now, we can calculate the collector area required:
Collector area required = (2800 Watts / 0.08) / 200 W/m^2
Collector area required = 35000 m^2
Therefore, to meet all your household energy requirements from solar energy, you would need a collector area of 35,000 square meters.
To determine the collector area needed to meet your household energy requirements from solar energy, we can follow these steps:
Step 1: Calculate the energy required by your household per day
Given that the average power requirement in your home is 2.8 kW, we need to convert it to energy since we are considering a 24-hour day.
Energy = Power * Time
Energy = 2.8 kW * 24 hours
Step 2: Calculate the solar power received per day
The solar power per unit area reaching Earth's surface is given as 200 W/m^2, averaged over a 24-hour day. To get the total solar power received per day, we need to multiply it by the collector area.
Solar Power = Solar Power per unit area * Collector Area
Step 3: Determine the collector area needed
To calculate the collector area needed, we need to equate the energy required by your household per day to the solar power received per day, factoring in the efficiency of the conversion process.
Energy required by your household per day = Solar Power * Collector Area * Efficiency
Now, let's calculate the collector area needed using the given information:
Step 1: Energy required by your household per day
Energy = 2.8 kW * 24 hours
Step 2: Solar power received per day
Solar Power = 200 W/m^2 * Collector Area
Step 3: Collector area needed
Energy = Solar Power * Collector Area * Efficiency
Substituting the values:
2.8 kW * 24 hours = (200 W/m^2 * Collector Area) * 0.08
Simplifying the equation:
67.2 kWh = 16 W/m^2 * Collector Area
Next, we can rearrange the equation to solve for the collector area:
Collector Area = 67.2 kWh / (16 W/m^2)
Converting the units:
1 kW = 1000 W
1 kWh = 1000 Wh
Collector Area = (67.2 * 1000 Wh) / (16 W/m^2)
Collector Area = 4200 m^2
Therefore, to meet all your household energy requirements from solar energy, you will need a collector area of 4200 square meters.