(a) A solar collector is 12.0% efficient in gathering solar energy and converting it to heat. If the average intensity of sunlight on one day is 700 W/m2, what area(m^2) should your collector have to gather energy at the rate of 150 W?
(b) What is the maximum cost ($)of the solar panel if it must pay for itself in two years of operation averaging 9.00 hours per day? Assume that it earns money at the rate of 3.00¢ per kilowatt-hour. There are 365.25 days in a year.
(a)
0.12•I•A = P,
A=P/0.12•I = 150/0.12•700 = 1.79 m².
(b)
2•365.25•(9•0.150)kW•h• 3 ¢/kW•h =
=2958.5 ¢
(a) To determine the area of the solar collector needed to gather energy at the rate of 150 W, we can use the following formula:
Power = Area × Intensity × Efficiency
Given:
Power = 150 W
Intensity = 700 W/m²
Efficiency = 12% = 0.12
Rearranging the formula, we get:
Area = Power / (Intensity × Efficiency)
Substituting the given values:
Area = 150 W / (700 W/m² × 0.12)
Simplifying the expression:
Area = 150 W / 84 W/m²
Area = 1.79 m²
Therefore, the solar collector should have an area of approximately 1.79 square meters to gather energy at the rate of 150 W.
(b) To calculate the maximum cost of the solar panel, we need to determine how much money it can earn in two years of operation.
First, we calculate the total number of operating hours in two years, accounting for the leap year:
Operating hours = 2 years × 365.25 days/year × 9.00 hours/day
Next, we calculate the total energy produced in kilowatt-hours (kWh) by multiplying the operating hours by the power generated per hour:
Energy produced = Operating hours × Power
Since the power is given in watts, we need to convert it to kilowatts:
Power (kW) = Power (W) / 1000
So, the energy produced in kilowatt-hours becomes:
Energy produced (kWh) = (Operating hours × Power (kW))
Finally, we can calculate the maximum cost by multiplying the energy produced by the earning rate:
Maximum cost ($) = Energy produced (kWh) × Earning rate ($/kWh)
Substituting the given values:
Operating hours = 2 years × 365.25 days/year × 9.00 hours/day
Earning rate = 3.00¢/kWh = $0.03/kWh
After calculating the above values, you can find the maximum cost of the solar panel in dollars.