Two spherical bodies A (radius 6 cm ) and B (radius 18 cm ) are at temperatures T 1 and T 2 , respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at

Question

Two spherical bodies A (radius 6 cm ) and B (radius 18 cm ) are at temperatures T 1 ​ and T 2 ​ , 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 ?

TestHub · Accepted Answer

​ λ m ​ ∝ T 1 ​ ∴ λ B ​ λ A ​ ​ = T A ​ T B ​ ​ = 1500 500 ​ = 3 1 ​ E ∝ T 4 A (where A = surface area = 4 π R 2 ) ∴ E ∝ T 4 R 2 E B ​ E A ​ ​ = ( T B ​ T A ​ ​ ) 4 ( R B ​ R A ​ ​ ) 2 = ( 3 ) 4 ( 18 6 ​ ) 2 = 9 ​ ∴ Answer is 9 .

Physics - Heat & Thermo Question with Solution | TestHub

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