The earth receives solar radiation at a rate of 8.2 J/ $c m^{2}$ - minute. Assuming that the sun radiates like a blackbody, calculate the surface temperature of the sun. The angle subtended by the sun on the earth is 0.53 $^{\circ}$ and the Stefan constant $σ = 5.67 \times 10^{- 8} W / m^{2}$ - K4.

6800 K

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5800 K

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7800 K

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7800 K

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Solution

The correct option is B 5800 K
Let the diameter of the sun be D and its distance from the earth be R. From the question,

$\frac{D}{R} \approx 0.53 \times \frac{π}{180}$

= $9.25 \times 10^{- 3}$ . ...(i)

The radiation emitted by the surface fo the sun per unit time is

At distance R, this radiation falls on an area $4 π R^{2}$ in unit time. The radiation received at the earth's surface per unit time per unit area is, therefore,

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The earth receives solar radiation at a rate of 8.2 J/cm2 - minute. Assuming that the sun radiates like a blackbody, calculate the surface temperature of the sun. The angle subtended by the sun on the earth is 0.53∘ and the Stefan constant σ=5.67×10−8W/m2 - K4.