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

1. 160 k cal/m² min
2. 40 k cal/m² min
3. 320 k cal/m² min
4. 80 k cal/m² min

Correct answer: 320 k cal/m² min

Solution

The radiant energy emitted by a black body is proportional to the fourth power of its absolute temperature (Stefan-Boltzmann law). If the sun's temperature doubles, the radiant energy will increase by a factor of 2⁴ = 16. Thus, the new radiant energy is 20 × 16 = 320 k cal/m² min.

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