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In my reading of blackbody radiation I am always asked to imagine this or that body being a perfect absorber or emitter of radiation, and I am always left with the impression that a blackbody exists only as a theoretical construct. But is it? Or can one be constructed and tested?

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Crazy Buddy's answer is spot-on; however, we can still test the results for blackbody radiation imperfectly. Hot metals, the sun, and the cosmic microwave background are all examples of systems that are not perfect blackbodies, but can be approximated as perfect blackbodies. In these cases, the theoretical predictions are very accurate. – Kevin Driscoll Apr 3 '13 at 14:53

A Blackbody is only theoretical. In other words, it is an ideal one. No such body has been observed with such a perfection in the emissivity. I think the Wiki article holds good. Its first statement:

A blackbody is an idealized....

With the help of such a body emitting radiation, we can compare the range of its frequencies with other bodies, approximating their frequencies so that it matches up with the blackbody and we can easily determine the temperature of it.

For example, the temperature of sun, molten iron, us or any other hot body can be determined by observing its spectra and then comparing them with a blackbody. The comparison matches very approximately only to a certain blackbody at a certain temperature.

Thanks to Max Planck ;-)

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black holes are (supposedly) near-perfect black bodies - we only run into problems when wavelength approaches the size of the hole... – Christoph Apr 3 '13 at 13:50
@Christoph: Hi Christoph. Agreed. But as you said, they're very near (almost), but not the complete perfection of a blackbody ;-) – Waffle's Crazy Peanut Apr 3 '13 at 14:18
Many thanks indeed for these explanations.I must say, though, that I have trouble with the idea that an imaginary object can yield conclusive results, particularly in a sentence such as, "...any other hot body can be determined by observing its spectra and then comparing them with a blackbody". Comparing the real spectrum of a tangible body with the imagined spectrum of an imagined body is very difficult to grasp.Could the results of such a comparison not be wrong? Physicists don't think so, of course, but why? Thanks again. – jeremy mcmanus Apr 4 '13 at 2:30
@jeremymcmanus: Hi Jeremy. Of course, the blackbody is hypothetical. But, its spectrum can be determined by using Planck's & Wien's displacement laws. Here is an image of a graph of wavelength plotted against the irradiance of sun along with a $\sim 5700\ K$ blackbody. Since this graph matches with the theory very nearly (not exactly though), we concluded that this should be sun's temperature ;-) – Waffle's Crazy Peanut Apr 4 '13 at 14:34

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