The intensity of solar radiation reaching the Earth is $1,340 \mathrm{~W} / \mathrm{m}^{2}$. If the sun has a radius of $7.000 \times 10^{8} \mathrm{~m}$, is a perfect radiator and is located $1.500 \times 10^{11} \mathrm{~m}$ from the Earth, then what is the temperature of the sun?

Question

Quizplus · Accepted Answer

The temperature of the sun can be calculated using the Stefan-Boltzmann law and the inverse square law for radiation. The intensity of solar radiation at the Earth's distance ($1.500 \times 10^{11} \mathrm{~m}$) is given as $1,340 \mathrm{~W} / \mathrm{m}^{2}$. The power emitted by the sun can be found by multiplying this intensity by the surface area of a sphere with a radius equal to the distance from the sun to the Earth. This power is also equal to the power emitted by the sun's surface, which can be calculated using the Stefan-Boltzmann law ($P = \sigma A T^4$), where $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area of the sun, and $T$ is the temperature of the sun. By equating the power calculated from the Earth's perspective to the power emitted by the sun and solving for $T$, we find that the temperature that matches the given conditions is $5,740 \mathrm{~K}$.

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 $1,340 \mathrm{~W} / \mathrm{m}^{2}$