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Question

(B) According to the Stefan-Boltzmann Law,the radiant energy $E$ radiated per unit surface area per unit time is proportional to the fourth power of t

Vedclass · Accepted Answer

$500$

Vedclass · Answer

(B) According to the Stefan-Boltzmann Law,the radiant energy $E$ radiated per unit surface area per unit time is proportional to the fourth power of the absolute temperature $T$,i.e.,$E \propto T^4$.Given the ratio of radiant energies $\frac{E_1}{E_2} = \frac{16}{1}$.Let $T_1 = 1000 \ K$ be the temperature of the hotter body and $T_2$ be the temperature of the colder body.Using the relation $\frac{E_1}{E_2} = \left( \frac{T_1}{T_2} \right)^4$,we have:$16 = \left( \frac{1000}{T_2} \right)^4$.Taking the fourth root on both sides:$2 = \frac{1000}{T_2}$.Therefore,$T_2 = \frac{1000}{2} = 500 \ K$.

The ratio of radiant energies radiated per unit surface area by two bodies is $16 : 1$. The temperature of the hotter body is $1000 \ K$. Then,the temperature of the colder body will be ....... $K$.

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