Proof Of Kirchhoffs Law
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Proof of Kirchhoff’s Law
Kirchhoff’s law can be derived in a simplified manner as follows:
Suppose Q is the amount of radiation incident per unit area per second on a body. If As is the absorptive power of the surface, then the amount of radiation absorbed by the body per unit area per second = ASX Q.
If ES represents the emissive power of the surface, then the amount of radiation emitted by the surface per unit area per second = ES.
When the body is in thermal equitbrium with the enclosure,
Amount of radiation emitted by the surface per unit area per second = Amount of radiating absorbed by the per unit area per second.
Thus
For a perfectly black body, As = AB =1 and Es may be replaced by EB where AB and EB represent the absorptive power and the emissive power of a perfectly black body. Thus we have
From equation
or
As EB is constant, the equation gives the expression for the Kirchhoff’s law.
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Suppose Q is the amount of radiation incident per unit area per second on a body. If As is the absorptive power of the surface, then the amount of radiation absorbed by the body per unit area per second = ASX Q.
If ES represents the emissive power of the surface, then the amount of radiation emitted by the surface per unit area per second = ES.
When the body is in thermal equitbrium with the enclosure,
Amount of radiation emitted by the surface per unit area per second = Amount of radiating absorbed by the per unit area per second.
Thus
For a perfectly black body, As = AB =1 and Es may be replaced by EB where AB and EB represent the absorptive power and the emissive power of a perfectly black body. Thus we have
From equation
or
As EB is constant, the equation gives the expression for the Kirchhoff’s law.
For more help in Proof of Kirchhoff’s Law click the button below to submit your homework assignment