First slide

Radiation

Question

The earth receives at its surface radiation from the sun at the rate of 1400 W/m2. The distance of the centre of the sun from the surface of the earth is 1.5 x 10¹¹ m and the radius of the sun is 7.0 x 10⁸ m. Treating the sun as a black body it follows from the above data that its surface temperature is

Moderate

A

5000 K
B

5803 K
C

6000 K
D

6803 K

Solution

Let TK be the temperature of sun.
Energy E radiated per unit area per second $= {σT}^{4}$ (Stefan's law).
Total surface area of sun $= 4 {πR}_{s}^{2}$
$∴$ Total energy radiated per unit solid angle $= {σT}^{4} R_{s}^{2}$
Now intensity of radiation at earth $= {σT}^{4} R_{s}^{2} / R_{es}^{2}$
where R_es= distance between earth and sun.
Substituting the given values, we get $1400 = (5 \cdot 67 \times 10^{- 8}) (T^{4}) {(\frac{7 \cdot 0 \times 10^{8}}{1 \cdot 5 \times 10^{11}})}^{2}$
Solving, we get T = 5803 K.

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