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(D) According to the Stefan-Boltzmann law,the radiant energy $E$ emitted by a black body is proportional to the fourth power of its absolute temperatu

Vedclass · Accepted Answer

$320$

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(D) According to the Stefan-Boltzmann law,the radiant energy $E$ emitted by a black body is proportional to the fourth power of its absolute temperature $T$,i.e.,$E \propto T^4$.Let $E_1$ be the initial radiant energy and $T_1$ be the initial temperature of the sun. Given $E_1 = 20 \, kcal/m^2-min$.Let $E_2$ be the new radiant energy and $T_2$ be the new temperature of the sun,where $T_2 = 2T_1$.Using the ratio formula: $\frac{E_1}{E_2} = \left(\frac{T_1}{T_2}ight)^4$.Substituting the values: $\frac{20}{E_2} = \left(\frac{T_1}{2T_1}ight)^4 = \left(\frac{1}{2}ight)^4 = \frac{1}{16}$.Therefore,$E_2 = 20 	imes 16 = 320 \, kcal/m^2-min$.

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

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