The average solar radiation incident on the surface of the earth is about 1 KW/m2 for the entire year. A solar house is built with solar panels installed in the roof to provide the heating and electrical energy of the house. If the roof has a surface area of 100 m2 and the panels are installed over the entire roof, will the solar panels be able to provide enough energy to meet the heating and electrical energy demands for the house for the entire year. The total time of available sunlight for energy production is 1000 hours for the entire year. If so, explain how?
Note: The average electrical energy demand for the house is 15,000 KWh for the year. It takes about 1000 gallons of fossil fuel with a heating value of 15,000 Btu/gallon to provide heat to the house for the entire year. ( 1 Btu = 0.000293 KWh)
To determine if the solar panels can meet the energy demands for the entire year, we need to calculate the total energy available from the solar radiation and compare it to the energy demands of the house.
First, let's compute the total energy available from solar radiation. The average solar radiation incident on the surface of the earth is given as 1 KW/m2 for the entire year. The surface area of the roof is 100 m2, so the total energy available is:
Energy = Solar radiation x Surface area = 1 KW/m2 x 100 m2 = 100 KW.
Next, we need to convert the total time of available sunlight from hours to seconds to match the units of power (KW). There are 1,000 hours of sunlight available in a year, so the total time available in seconds is:
Time = 1,000 hours x 3600 seconds/hour = 3,600,000 seconds.
Now, let's calculate the total energy available for the year:
Total Energy Available = Energy x Time = 100 KW x 3,600,000 seconds = 360,000,000 KWh.
Given that the average electrical energy demand for the house is 15,000 KWh for the year, we can compare the total energy available from the solar panels to the energy demand:
Is Total Energy Available ≥ Energy Demand?
360,000,000 KWh ≥ 15,000 KWh?
Since 360,000,000 KWh is greater than 15,000 KWh, we can conclude that the solar panels will be able to provide enough energy to meet the electrical energy demand for the house for the entire year.
Now let's calculate if the solar panels can also meet the heating energy demand of the house. It takes about 1000 gallons of fossil fuel with a heating value of 15,000 Btu/gallon to provide heat to the house for the entire year. To convert Btu to KWh:
1 Btu = 0.000293 KWh.
So, the heating energy demand in KWh is:
Heating Energy Demand = 1000 gallons x 15,000 Btu/gallon x 0.000293 KWh/Btu.
Calculating this value gives us the heating energy demand in KWh.
Finally, we can add the electrical energy and heating energy demands to determine if the solar panels can meet both:
Total Energy Demand = Electrical Energy Demand + Heating Energy Demand.
If the Total Energy Available from the solar panels is greater than or equal to the Total Energy Demand, then the solar panels will be able to provide enough energy to meet both the heating and electrical energy demands for the house for the entire year.