Question

Attached to the roof of a house are three solar panels, each 1 m x 2 m. Assume the equiv alent of 4 hrs of normally incident sunlight each day, and that all the incident light is absorbed and converted to heat. How many gallons of water can be heated from 40°C to 120°C each day?

Answer 1

93.29 gallons

Step-by-step explanation:

Given:

Number of solar panels = 3

Area of each solar panel = 1 m × 2 m = 2 m²

Total area of solar panels = 3 × 2 = 6 m²

Time = 4 hrs = 4 × 60 × 60 = 14400 seconds

Change in temperature, ΔT = 120° C - 40° C = 80° C

Now,

the solar power received on the Earth = 1368 W/m²

Thus,

The Heat energy received = Power × Area × Time

or

The Heat energy received = 1368 × 6 × 14400 = 118195200 J

Also,

Heat = mCΔT

where, C is the specific heat of the water

m is the mass of the water = 4.184 J/g.C

thus,

118195200 J = m × 4.184 × 80

or

mass of water that can be heated, m = 353116.63 grams = 353.116 kg

Also,

1 gallon of water = 3.785 kg

thus,

1 kg of water = 0.2642 gallons

Hence,

353.116 kg of water = 93.29 gallons

i.e 93.29 gallons of water can be heated