Question

At midday, solar energy strikes the earth with an intensity of about $1$ kW/m² . What is the area of a solar collector that could collect $150$MJ of energy in $1$h? This is roughly the energy content of $1$gallon of gasoline.

Short answer

Area of the collection is$41.67$m²

Step-by-step solution

Step 1. Given information

The earth with an intensity$1$kW/m²

Step 2. Area of collector

We know that intensity of solar energy as power. Power that collector can be calculated as

$$\begin{gathered} P=\frac{∆W}{∆t} \\ =\frac{150·{10}^6}{60·60} \\ =41666.67W \end{gathered}$$

From there we can easily required area of collector

$$\begin{gathered} I=\frac{P}{A} \\ 1000W/m^2=\frac{41666.67}{A} \\ \Rightarrow A=41.67m^2 \end{gathered}$$