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(D) According to the Stefan-Boltzmann Law,the power $P$ radiated by a black body of surface area $A$ at temperature $T$ is given by $P = \sigma A T^4$

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(D) According to the Stefan-Boltzmann Law,the power $P$ radiated by a black body of surface area $A$ at temperature $T$ is given by $P = \sigma A T^4$.For a sphere of radius $R$,the surface area is $A = 4 \pi R^2$.Thus,the initial power is $P_1 = \sigma (4 \pi R^2) T^4$.When the radius is doubled $(R' = 2R)$ and the temperature is doubled $(T' = 2T)$,the new power $P_2$ is:$P_2 = \sigma (4 \pi (2R)^2) (2T)^4$$P_2 = \sigma (4 \pi \cdot 4R^2) (16T^4)$$P_2 = 16 \cdot 4 \cdot \sigma (4 \pi R^2) T^4$$P_2 = 64 P_1$.Therefore,the new power radiated is $64 P$.

$A$ black sphere of radius $R$ radiates power $P$ at a certain temperature $T$. If the temperature is doubled and the radius is also doubled,the new power radiated will be: (in $P$)

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