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Question

# The radiation from the sun, incident normally at the surface of the earth is 20 kcal/m2 min. What would have the radiant energy, incident normally on the earth, if the sun had a temperature twice of the present one?

A
80 kcal/m2 min
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B
320 kcal/m2 min
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C
160 kcal/m2 min
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D
40 kcal/m2 min
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Solution

## The correct option is B 320 kcal/m2 minWe know that, for a source, emitting power per area E at temperature T E=σT4 As temperature is doubled, ⇒E1=σ(2T)4 EE1=σT416σT4=116 Now radiation falling on the earth will be proportional to radiation being emitted so. EE1=20X Here, X is the radiation falling in the earth in the latter case. 20X=116 ⇒X=20×16=320 kcal/m2min

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