Two spherical bodies A (radius 6 ~cm ) and B (radius 18 ~cm ) are at temperatures T₁ and T₂ , respectively. The maximum intensity in the emission spectrum of A is at 500 ~nm and in that of B is at 1500 ~nm . Considering them to be black bod

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Two spherical bodies A (radius 6 ~cm ) and B (radius 18 ~cm ) are at temperatures T₁ and T₂ , respectively. The maximum intensity in the emission spectrum of A is at 500 ~nm and in that of B is at 1500 ~nm . Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?

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Correct answer: 9

aligned & _m 1 T & _A _B = T_B T_A = 500 1500 = 1 3 & E T^4 A (where A= surface area & =4 R^2 ) & E T^4 R^2 & E_A E_B = ( T_A T_B )^4 ( R_A R_B )^2 & =(3)^4 ( 6 18 )^2=9 aligned Answer is 9 .

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