Two bodies A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface areas of the two bodies are same. The two bodies emit total radiant power at the same rate. The wavelength `lambda_B` corresponding to maximum spectral radiancy from B is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from A by 1.0 `mum`. If the temperature of A is 5802 K, calculate (a) the temperature of B, (b) wavelength `lambda_B`.

Answer

(i)`1934K (ii) 1.5mu m`

Explanation

(i)`because P_(A) = P_(B)`
`therefore e_(A) lambdaA_(A) T_(A)^(4) = e_(B) lambdaA_(B)T_(B)^(4)`
`implies T_(B) = ((e_(A))/(e_(B))^(1//4)T_(A) = ((0.01)/0.81))^((1)/(4)) 5802 = 1934K` (ii) According to Wein's displacement law
`lambda_(A)T_(A) = lambda_(B)T_(B) implies lambda_(B) = ((5802)/(1934)) lambda_(A) implies lambda_(B) = 3lambda_(A)`
Also `lambda_(B) - lambda_(A) = 1 mu m implies lambda_(B)-(lambda_(B))/(3) = 1mu m implies lambda_(B) = 1.5 mu m`