The intensity of solar radiation reaching the Earth is $1,340 \mathrm{~W} / \mathrm{m}^{2}$ when the temperature of the Sun is $5,800 \mathrm{~K}$. If the temperature of the Sun decreased by $10.0 \%$, then what would be the intensity of solar radiation reaching the Earth?

Question

Quizplus · Accepted Answer

The intensity of solar radiation (I) reaching Earth is proportional to the fourth power of the Sun's temperature (T), according to the Stefan-Boltzmann law ($I \propto T^4$). If the temperature decreases by 10%, the new temperature is $0.9 \times 5800 \, \text{K} = 5220 \, \text{K}$. The new intensity is then $(0.9)^4 = 0.6561$ times the original intensity, so $0.6561 \times 1340 \, \text{W/m}^2 = 879 \, \text{W/m}^2$.

The Intensity of Solar Radiation Reaching the Earth Is 1,340 W/m21,340 \mathrm{~W} / \mathrm{m}^{2}1,340 W/m2

The Intensity of Solar Radiation Reaching the Earth Is $1,340 \mathrm{~W} / \mathrm{m}^{2}$