Radiated energy at T temperature is E for a b | vedclass

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(C) According to the Stefan-Boltzmann law,the radiated energy $E$ is given by $E = \sigma A T^4$,where $A$ is the surface area and $T$ is the absolute

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$E$

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(C) According to the Stefan-Boltzmann law,the radiated energy $E$ is given by $E = \sigma A T^4$,where $A$ is the surface area and $T$ is the absolute temperature.For a spherical body of diameter $d$,the surface area $A = 4\pi r^2 = 4\pi (d/2)^2 = \pi d^2$.Initial energy $E_1 = \sigma (\pi d^2) T^4 = E$.New temperature $T_2 = 2T$ and new diameter $d_2 = d/4$.New surface area $A_2 = \pi (d_2)^2 = \pi (d/4)^2 = \pi d^2 / 16 = A_1 / 16$.New radiated energy $E_2 = \sigma A_2 T_2^4 = \sigma (A_1 / 16) (2T)^4$.$E_2 = \sigma (A_1 / 16) (16 T^4) = \sigma A_1 T^4 = E$.

Radiated energy at $T$ temperature is $E$ for a body of diameter $d$. If the temperature becomes $2T$ and the diameter becomes $d/4$,then the radiated energy will be:

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