Module 5 : MODERN PHYSICS
Lecture 23 : Black Body Radiation
  Example 4
  The earth receives 1.4 kW of power from the sun. Assume that both earth and the sun to be black bodies. If the radius of the sun is $ 6.95\times 10^ 8$ m and the earth-sun distance is $ 1.5\times 10^{11}$ m, calculate the temperature of the sun.
Solution
 
According to Stefan's law, the power radiated by the Sun per unit area is $ \sigma T^4$. If $ R$ is the radius of the sun, the total power radiated is $ 4\pi R^2\sigma T^4$.
 
This power radiates outward from the sun. If at a distance $ D$, the power received per unit area is $ P_e$, the total power is equal to the surface area of a sphere of radius $ D$ times this amount. Thus,
 
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$\displaystyle 4\pi R^2\sigma T^4 = P_e\times 4\pi D^2$
  Thus
 
$\displaystyle T^4 = P_e \frac{D^2}{\sigma R^2}$
 
Substituting $ D=1.5\times 10^{11}$ and $ R=6.95\times 10^8$ m, we get $ T= 5823^\circ$ K.

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