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

40 kcal/(m

^{2}

- min)

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80 kcal/(m

^{2}

- min)

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160 kcal/(m

^{2}

- min)

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320 kcal/(m

^{2}

- min)

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Solution

The correct option is C 320 kcal/(m $^{2}$ - min)
From the stefan's-boltzman law $E \propto T^{4}$
$E_{1} = 20 (k - c a l) / (m^{2} - m i n)$
$T = 20^{0.25} = {2.11}^{o} C$
If temperature will increased two times so final temperature will be $2 T = T_{2} = {4.22}^{o} C$
Now, the final radiative power $E_{2} = {T_{2}}^{4} = 320 \frac{k c a l}{m^{2} - m i n}$

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The radiant energy from the sun, incident normally at the surface of earth, is 20kcal/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?

The correct option is C 320 kcal/(m2 - min)From the stefan's-boltzman law E∝T4E1=20(k−cal)/(m2−min)T=200.25=2.11oCIf temperature will increased two times so final temperature will be 2T=T2=4.22oCNow, the final radiative power E2=T24=320kcalm2−min

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