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(B) According to the Stefan-Boltzmann law,the total power (energy emitted per unit time) radiated by a black body is given by $P = \sigma A T^4$,where

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$625$

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(B) According to the Stefan-Boltzmann law,the total power (energy emitted per unit time) radiated by a black body is given by $P = \sigma A T^4$,where $A = 4\pi r^2$ is the surface area.Therefore,$P \propto r^2 T^4$.Let the initial radius be $r_1$ and initial temperature be $T_1$. Let the final radius be $r_2 = 100r_1$ and final temperature be $T_2 = T_1 / 2$.The ratio of the final energy emitted $(P_2)$ to the initial energy emitted $(P_1)$ is:$\frac{P_2}{P_1} = \left( \frac{r_2}{r_1} ight)^2 	imes \left( \frac{T_2}{T_1} ight)^4$Substituting the values:$\frac{P_2}{P_1} = (100)^2 	imes \left( \frac{1}{2} ight)^4$$\frac{P_2}{P_1} = 10000 	imes \frac{1}{16} = 625$.Thus,the total energy emitted increases by a factor of $625$.

Suppose the sun expands so that its radius becomes $100$ times its present radius and its surface temperature becomes half of its present value. The total energy emitted by it then will increase by a factor of

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