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Question

The earth receives solar radiation, at a rate of 8.2 J cm2min1. 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's constant σ=5.67×108Wm2K4 .

A
4700 K
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B
5800 K
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C
6200 K
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D
6600 K
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Solution

The correct option is B 5800 K

Let the radius of the Sun be RS and the distance between Sun and Earth be R.

Given
2RSR0.53=0.53×π180rad

2RSR=9.25×103 rad

Radiation emitted by Sun per unit time is given by Stefan's law,

Q=σAT4=σ4πR2S T4

At a distance R from the Sun this radiation falls on an area 4πR2 around the Sun.

The radiation received per unit time per unit area on earth surface is,

σ4πR2ST44πR2=σT4(RSR)2

From the given data,

σT4(RSR)2=8.2 J cm2min1

5.67×108×T4×(9.25×1032)2=8.2104×60

T=5794 K5800 K

Hence, option (B) is correct.
Why this question?

Caution: While using the relationship between, sun radius, distance between the sun and the earth and angle subtended by sun on earth, use angle in radian not in degree.


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