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Which has hotter temperature, blue flame or yellow flame?

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Blue flame has a hotter temperature. In physics there is a relationship called Wien's displacement law, which states $$\lambda_{max}T=2.898$$ where $\lambda_{max}$ is the peak wavelength of light emitted (which is the wavelength you see) and T is temperature in kelvins.

This relationship can be rewritten $$T=\frac{2.898}{\lambda_{max}}$$, or just $T\propto \frac 1 \lambda$.

From a table we find that the wavelength of blue light is about 450-500 nm and yellow light is 570-590 nm. Since temperature is inversely proportional to wavelength, the light with the smaller wavelength has the higher temperature.

(Now you might quibble that Wien's law is for idealized blackbodies but it can be used to model most things which emit light because of their temperature regardless.)

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    $\begingroup$ It's worth noting that specific emission spectra are separate to this and may swamp the black-body radiation; this is, for example, the origin of elemental flame tests. $\endgroup$ – Aesin Jun 3 '13 at 23:34
  • $\begingroup$ That's true, but I neglected that point since I didn't think it would be relevant to the OP's question about cooking. $\endgroup$ – Zen Jun 3 '13 at 23:37
  • $\begingroup$ @Zen I would like for you to consider the possibility that this may not be blackbody radiation, but rather emission from the reactions in the combustion process. (Aesin, is this close to what you were saying?) $\endgroup$ – Eric Brown Jun 4 '13 at 3:30
  • $\begingroup$ If it were emission from the reactions in the combustion process, then the question is unanswerable since the color of the emission products is not related to the temperature of the flame. $\endgroup$ – Zen Jun 4 '13 at 3:33
  • $\begingroup$ I think this is what I'm getting at. I think the blue part of a flame may be hotter than the yellow part, but I don't think that it is transferable between different fuels. $\endgroup$ – Eric Brown Jun 4 '13 at 3:41
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In fact black body radiation has a small role in the color of the flame: putting in 700nm (for blue) in the equation yields over 3500 degrees celsius while the temperature of a gas stove flame is about 1700. The colors are a result of, as was mentioned in the comments, ionization of gas molecules . If i remember correctly from analytical chemistry class, the hottest part of the flame is the middle which has a pale color, this results from a certain fuel(gas)/oxidiser(air) ratio that gives complete combustion. also see Wikipedia

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