The radiant energy from the sun, incident normally at the surface of earth is 20 k $c a l / m^{2}$ min. What would have been the radiant energy, incident normally on the earth, if the sun had a temperature, twice of the present one?

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$160 kcal / m^{2} \min$

40 k $cal / m^{2}$ min

320 k $cal / m^{2}$ min

$80 kcal / m^{2} \min$

answer is C.

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Detailed Solution

According to Stefan's law

$E \propto T^{4}$

$\begin{aligned} \frac{E_{1}}{E_{2}} = \frac{T_{1}^{4}}{T_{2}^{4}} or \frac{20}{E_{2}} = \frac{T^{4}}{2^{4} T^{4}} \\ E_{2} = 320 kcal / m^{2} \min \end{aligned}$

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