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I understand that Colour Temperature correlates with the object's thermal temperature, such as a red-hot piece of iron being ~360c and the incandescent bulb filament is about 2500c.

Why are sources of light, such as LEDs and florescent tubes, that emit white to white-blue light (which according to Colour Temperature, would be around 4500+c) cool, or nowhere near 4500c, when touched?

Also, why is the sky considered 10,000k? Especially if the surface of the sun is only ~5770k?

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marked as duplicate by V.F., Jon Custer, Bill N, Kyle Kanos, John Rennie Oct 15 '18 at 10:28

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Colour temperature isn't indicative of the temperature of the actual light source: it indicates the temperature at which an ideal black-body radiation source (i.e. opaque body which doesn't reflect light at all) would radiate a similar color. It's easy to understand that blue light is produced by objects with a higher temperature because that part of the electromagnetic spectrum corresponds to higher energies.

So when we say that the sky is $10\,000\ \rm K$, we don't mean that it's actually that hot: it's actually that an ideal black-body at $10\,000\ \rm K$ would radiate light of the same color. After that, you can read about Rayleigh scattering to describe why the sky is blue.

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