Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature 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.…

Question

Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature 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?

Accepted Answer

Correct answer: 9. (9) (λ_m)_B = 3(λ_m)_A ⇒ T_A = 3T_B E_1 = 4π (6)^2 σT_A^4 = 4π(6)^2 (3T_B)^4 E_2 = 4π (18)^2 σ T_B^4 E_1E_2 = 9.

Solution

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