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(D) The total power (radiant energy per unit time) emitted by the sun is given by the Stefan-Boltzmann law: $P = \sigma A T^4 = \sigma (4 \pi R^2) T^4

Vedclass · Accepted Answer

$64$

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(D) The total power (radiant energy per unit time) emitted by the sun is given by the Stefan-Boltzmann law: $P = \sigma A T^4 = \sigma (4 \pi R^2) T^4$.Since the distance between the Earth and the Sun remains constant,the radiant energy received on Earth is directly proportional to the power emitted by the Sun: $Q \propto R^2 T^4$.Let the initial energy be $Q_1 = k R^2 T^4$.After the changes,the new radius is $R' = 2R$ and the new temperature is $T' = 2T$.The new radiant energy is $Q_2 = k (R')^2 (T')^4$.Substituting the new values: $Q_2 = k (2R)^2 (2T)^4 = k (4R^2) (16T^4) = 64 (k R^2 T^4)$.Therefore,the ratio is $Q_2 / Q_1 = 64$.

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on Earth to what it was previously will be

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