Question

The best solar panels currently available are about 14% efficient in converting sunlight to electricity. a typical home will use about 35 kwh of electricity per day (1 kwh = 1 kilowatt hour; 1 kw = 1000 j/s). assuming 7.0 hours of useful sunlight per day, calculate the minimum solar panel surface area necessary to provide all of a typical home’s electricity. the sun supplies energy at a rate of about 1.0 kilowatt per square meter of surface area (1 watt = 1 j/s).

Answer 1

To meet the daily energy demand of a typical home using solar panels with 14% efficiency and 7 hours of sun, at least 35.71 m² of solar panels would be needed.

Step-by-step explanation:

The student is asking to calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity, given certain energy efficiency and sunlight availability parameters. To find this, we will use the following formula:

Surface Area = (Energy Demand per Day) / (Sunlight Hours per Day * Sun Energy per m² * Efficiency)

A typical home uses about 35 kWh per day and there is an assumption of 7.0 hours of useful sunlight per day. The sun provides energy at a rate of about 1.0 kW per square meter of surface area. As the solar panels are 14% efficient, the formula to calculate the minimum surface area of the solar panels is:

Surface Area = 35 kWh / (7 hours * 1 kW/m² * 0.14)

The units of kWh (kilowatt-hours) and kW (kilowatts) are related by time, so they can be directly used in the formula:

Surface Area = 35,000 Wh / (7 hours * 1,000 W/m² * 0.14)

Surface Area = 35,000 / (7 * 1,000 * 0.14)

Surface Area = 35,000 / 980

Surface Area ≈ 35.71 m²

Therefore, a typical home would require at least approximately 35.71 square meters of solar panels to meet its daily electricity needs, assuming an average day with 7 hours of sunlight and panels with a 14% conversion efficiency.