Question

A family uses 8 kW words of power.a. Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square metre. If 20% of this energy can be converted to useful electrical energy, how large and area is needed to supply 8 kW?b. Compare this area to that of the roof of a typical house.

Answer 1

Given,
power used by a family = 8kW = 8000W

direct solar energy is incident on the horizontal surface at an average rate of 200W/m² .

efficiency of energy conversion , $\eta$ = 20%

Let A m² be the area required to supply 8kW

e.g., 8kW = 20% of (200W/m² × A m²)

8000 = 20/100 × 200 × A

A = 200 m²

so, Area is needed to supply is 200m²

(b) Let a be edge length of square roof
then, a² = 200 m²
a = √200 ≈ 14m

hence, 200 m²  is equivalent to a rooftop with dimensions 14m × 14m.