Two bodies A and B have thermal emissivities of $$0.01$$ and $$0.81$$ respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength λB corresponding to maximum spectral radiancy in the radiation from B is greater than the wavelength I, corresponding to maximum spectral radiancy in the radiation from A by $$1.00$$ μm. If the temperature of A is $$5802$$ K

Question

Two bodies A and B have thermal emissivities of $$0.01$$ and $$0.81$$ respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength λB corresponding to maximum spectral radiancy in the radiation from B is greater than the wavelength I, corresponding to maximum spectral radiancy in the radiation from A by $$1.00$$ μm. If the temperature of A is $$5802$$ K

Infinity Learn · Accepted Answer

Power radiated $$P=EA=e$$σ$$T4ANow$$   $$eATA4=eBTB4$$      ∵$$P1=P2or$$    $$TB=eAeB1/4$$×$$TA=0$$⋅$$010$$⋅$$811/4$$×$$5802$$      $$=13$$×$$5802$$  or  $$TB=1934KAccording$$ to Wien's displacement law,     λ$$mT=$$ constant So   λ$$ATA=$$λBTB  or  λ$$B/$$λ$$A=TA/TBor$$   λBλ$$A=58021934$$  or  λ$$A=$$λ$$B/3Further$$,  λB−λ$$A=1$$μmor    λB−λ$$B3=1$$μm  or  λ$$B=1$$⋅$$5$$ μm

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