Question

The intensity of electromagnetic waves from the sun is 1.4 kW/m2 just above the earth’s atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you think of your back as a 30 cm * 50 cm rectangle. How many joules of solar energy fall on your back as you work on your tan for 1.0 h?

Short answer

Solar energy is $6\times {10}^{5}J$.

Step-by-step solution

Given information

The intensity of electromagnetic waves is $I=1.4kW/m^2$

The area of a rectangle is $a=0.30m\times 0.50m$

Time $t=1.0h=3600s$

Power of the wave

The intensity of the wave is given by $I=\frac{P}{a}$

Substitute given values

$$\begin{gathered} P=Ia \\ =1.4\times {10}^3\times 0.30\times 0.50 \\ =210W \end{gathered}$$

Energy of the wave

The energy of the wave is given by $E=Pt=Iat$

Substitute the given values

$$\begin{gathered} E=0.80\times 210\times 3600 \\ =6\times {10}^{5}J \end{gathered}$$

Therefore, the energy of the wave is $6\times {10}^{5}J$.