A farmer wants to capitalize on the amount of sunlight shining on his farm everyday by building a solar power tower. The manufacturer\'s specifications state that the solar tower has 5.0 × 101 heliostats, each with an area of 2.10 m2. If the total amount of solar power falling on each heliostat is 1420.0 W/m2, calculate the percent efficiency of the solar power tower if it only produces 26.7 kW.
Total area = 5.0 x 101 x 2.10 m^2 =_____m^2
Total solar power falling on heliostats = 1420 W/m^2 x _____ m^2 = ______W
26700 W * 100 / ______W = ______% efficiency.
To calculate the percent efficiency of the solar power tower, we need to determine the total solar power falling on the heliostats and compare it to the actual power produced.
First, let's find the total solar power falling on the heliostats. We can calculate this by multiplying the area of each heliostat by the incident solar power per unit area:
Total solar power falling on heliostats = Number of heliostats × Area of each heliostat × Incident solar power per unit area
Number of heliostats = 5.0 × 10^1
Area of each heliostat = 2.10 m^2
Incident solar power per unit area = 1420.0 W/m^2
Substituting these values into the equation, we have:
Total solar power falling on heliostats = (5.0 × 10^1) × (2.10 m^2) × (1420.0 W/m^2)
Next, let's calculate the total solar power falling on the heliostats:
Total solar power falling on heliostats = 5.0 × 10^1 × 2.10 m^2 × 1420.0 W/m^2
After performing the calculations, we find that the total solar power falling on the heliostats is:
Total solar power falling on heliostats ≈ 148,890.0 W
Now, let's calculate the percent efficiency of the solar power tower. We can find this by dividing the actual power produced by the total solar power falling on the heliostats, and then multiplying by 100 to express it as a percentage:
Percent efficiency = (Actual power produced / Total solar power falling on heliostats) × 100
Actual power produced = 26.7 kW = 26,700.0 W
Total solar power falling on heliostats ≈ 148,890.0 W
Substituting the values into the equation, we have:
Percent efficiency = (26,700.0 W / 148,890.0 W) × 100
After performing the calculations, we find that the percent efficiency of the solar power tower is:
Percent efficiency ≈ 17.93%