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| Kirchhoff's Law |
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| A body that is a good radiator (or emitter) is also a good absorber. To understand this, suppose isotropic (i.e., equal in all directions) thermal radiation is incident on a body. Let a be the fraction of the total thermal radiation of all wavelengths absorbed by the body. The remaining fraction is reflected (or transmitted). The dimensionless number a is called absorptivity of the body. We shall soon see that a = e. |
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| A substance whose absorptivity is unity (a = 1) is called a black body. Lampblack is an example, but no substance in practice, is a perfect absorber. The notion of a black body is an idealization. A hollow enclosure maintained at a uniform temperature, with a small opening compared to its size and a conical projection as shown in the figure, is an excellent approximation to a black body. The opening acts as a perfect absorber. Radiation entering the hole suffers innumerable absorptions and diffuse reflections at the interior walls and has negligible chance of coming out. It is eventually absorbed fully, whatever be the material of the walls of the enclosure. |
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| A cavity with walls made of any material, with a small opening, is an excellent black body. This is Ferry's black body |
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| Consider a hollow enclosure with its walls maintained at temperature T. The enclosure is filled with thermal radiation. Let I be the energy per unit time falling per unit area of any (imaginary) surface in the enclosure. I is called irradiance in the enclosure. Imagine now that a black body at the same temperature T is introduced in the enclosure. The body will be in thermal equilibrium, i.e., the radiant energy per unit time per unit area emitted by the black body (EB) equals the radiant energy per unit time per unit area absorbed by it. That is, |
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 ....................... (1) |
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| since aB = 1 for the black body. |
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| Next, introduce a non-black body (a < 1) at the temperature T inside the enclosure. Thermal equilibrium now demands that |
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| E = a I ....................... (2) |
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| Where E is the radiant energy per unit time per unit area emitted by the (non-black) body. It follows from Eq.(1) that |
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 ....................... (3) |
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| But in terms of emissivity e already defined |
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 ....................... (4) |
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| which shows |
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| a = e ....................... (5) |
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| That is, the absorptivity of a body equals its emissivity. This is known as Kirchhoffs Law. A good absorber is thus a good emitter. Since a good absorber is a poor reflector, a bodys ability to emit is oppositely related to its ability to reflect. A good emitter is a poor reflector. A black body is both a perfect absorber and a perfect emitter. We saw earlier that the opening of a hollow enclosure is a perfect absorber. We now see that it is a perfect emitter also. Thermal radiation inside a hollow enclosure (that can be let out through the small opening) is thus the radiation emitted by a black body (black body radiation) |
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| A remarkable thing is worth noting here. The total radiation emanating out of a non-black body placed in a hollow enclosure is just the radiation emitted by a black body! Thus bodies inside the enclosure lose their distinctiveness. The reason is that the total radiation from a body inside the enclosure is the sum of what it would emit in the open (with e < 1) plus the part (1 a) of incident radiation from the walls reflected by it. The two add up to a black body radiation (e+1-a = 1). This explains why an optical pyrometer (a device for measuring high temperature) calibrated for an ideal black body, gives a lower than actual value of temperature of a red hot iron piece in the open, but it gives a correct value of the temperature when the same piece is in the furnace. |
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| Kirchhoff's law explains a number of familiar observations. If a piece of decorated china is heated in a furnace to about 1000oC and then taken out suddenly in a dark room, the decorations appear much brighter than white china. The decorations are better absorbers and, therefore, also better emitters. A platinum coated black spot on a heated metal ball shines more brilliantly than the polished surface. A green glass heated in a furnace when taken out in the dark, glows with red light. Green glass is a good absorber of red light and a good reflector of green light. Consequently, it is good emitter of red light. |
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