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  1. Why do Bunsen burners burn blue in the center? What element is being burned?
  2. Why does the sun glow yellow, and not blue-a Bunsen burner is much cooler and yet it burns blue. Is it because the relative size, or are they two different phenomena? (i.e. black body radiation and something else?)
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up vote 2 down vote accepted

A Bunsen Burner typically uses methane, butane, propane or another alkane and these burn blue.

The Wikipedia article on butane has a spectrum showing the $\mathrm{CH}$ radical as the primary source of blue emission:

blue spectrum of flame

You should consult Chemistry.SE for more details on why they burn blue.

Bunsen burners are designed to mix air into the gas before combustion and the presence of oxygen allows the fuel to burn much more efficiently. If you restrict the air flow the flame looks yellow because soot (carbon) is being produced and the carbon glows red / yellow due to the temperature. The glow from the soot is brighter and drowns out the blue color. When you mix enough oxygen the fuel burns cleanly and you only see the blue.

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It's worth clarifying the answer to part 2 of the original question: yes, they are two different phenomena. The sun's yellow light is the result of black-body radiation, whereas the blue of a bunsen flame is due to spectral lines. To see the difference, compare the spectrum in this post to a black body one. –  Nathaniel May 14 '13 at 4:02
    
Does black body radiation generally dominate spectral emission when both are present? For instance, if the sun had copper (does it?) it would have a tendency to glow green-but would the black body radiation just overwhelm that? –  Anthony May 15 '13 at 2:06
    
@Tony there isn't a definitive answer to this. "It depends." For the Sun, blackbody radiation dominates. For a blue Bunsen burner flame, based on the temperature it's clear that spectral emission dominates (at least in the visible region). For a neon (or other gas) lamp spectral emission dominates. My guess is that in most circumstances, total black body radiation across the whole EM spectrum dominates over spectral emissions. That might even be true for a Bunsen burner if we include infrared radiation. –  Brandon Enright May 15 '13 at 2:12
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