The total radiative power emitted by a spheri | vedclass

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(A) The radiative power $P$ of a spherical black body is given by the Stefan-Boltzmann law:$P = \sigma A T^4$Since the surface area $A$ of a sphere is

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$P/4$

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(A) The radiative power $P$ of a spherical black body is given by the Stefan-Boltzmann law:$P = \sigma A T^4$Since the surface area $A$ of a sphere is $4 \pi R^2$,we have:$P = \sigma (4 \pi R^2) T^4$This implies $P \propto R^2 T^4$.Let the new radius be $R' = 2R$ and the new temperature be $T' = T/2$.The new radiative power $P'$ is given by:$P' \propto (R')^2 (T')^4$$P' \propto (2R)^2 (T/2)^4$$P' \propto (4 R^2) (T^4 / 16)$$P' \propto \frac{4}{16} R^2 T^4$$P' = \frac{1}{4} P$Therefore,the radiative power becomes $P/4$.

The total radiative power emitted by a spherical black body with radius $R$ and temperature $T$ is $P$. If the radius is doubled and the temperature is halved,then the radiative power will be

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