# Temperature of glowing materials

As I understand it, Stars emit visible light, OBAFGKMRNS, in the range of $10^3 - 10^4 K$. Yet materials such as steel emit similar frequencies at much lower temps; red is around 800K. Why the difference? I thought black body radiation applies to all materials and environments. I am an interested amateur.

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## 1 Answer

The peak wavelength at which a body emits light is governed by Wien's displacement law, which states that this wavelength is inversely proportional to the temperature, as $$\lambda \, T=\text{const}=0.003\text{ m K}.$$ More graphically, in the stellar-surface sort of temperature range, this looks like

You'll notice that although the short-wavelength cut-off is rather sharp, bodies still emit light at shorter wavelengths than the Wien peak wavelength. Thus for steel at 800 K the peak wavelength is at 3.7 $\mu\text{m}$, in the mid-infrared. The total radiance on the visible range is then proportional to some power of $(700\text{nm}/3.7\,\mu\text{m})\approx 0.2$, so it's about 1% or less.

Thus, when hot irons glow red, what you're seeing is the very edge of the spectral radiance distribution. The bulk of the emissions is as heat in the IR - as you can tell if you put your hand anywhere nearby!

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The colours of your chart could be confusing. You have hotter objects with lower peak wavelengths towards the red and cooler objects with higher peak wavelengths toward the blue. Can you switch these around or are the colours out of your control? – Jim May 8 '13 at 17:01
Thanks, Emilio. Followup question: As my steel gets hotter, I see the color go more orange, almost full yellow. I understand the visible red far below peak output as the rest is invisible. Wouldn't the red get far brighter as the temperature increases and drown out those shorter wavelengths? – Peter Hoyt May 8 '13 at 19:21
@Jim, follow the image link for the source. If I have time I will draw a better chart but you are welcome to make one and sub it in. – Emilio Pisanty May 8 '13 at 21:20
@PeterHoyt Not necessarily. It only takes a small bit of stimulus on the green receptors to make reds slightly orange, if I understand correctly. By the time the Wien peak gets to the visible spectrum, the light looks white if slightly pinkish, because the stimulation is high all through the spectrum. – Emilio Pisanty May 8 '13 at 21:38