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Heat and Thermodynamics by Anandamoy Manna

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12.4 Kirchhoff′s Law of Radiation

Let a body of monochromatic emissive power eλ and of absorptivity aλ be placed inside an enclosure at uniform temperature T. It has already been proved that the amount of radiation crossing unit area at any point inside the enclosure is equal to the emissive power of a black body at the temperature of the enclosure. Then, the quantity of radiation falling per second on unit area of the body is eλb. The amount of energy absorbed by the body is aλeλb. For temperature equilibrium, this must be equal to the quantity of radiation emitted per unit area of the body in one second, that is, eλdλ. Hence,

 

aλ eλb = eλ

 

or

 

 

Or, the ratio of monochromatic emissive power of a body within the range of wave-length ...

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