Blackbody Curves

Something I worked on last night. Wrote a program to generate relative radiance curves for ideal blackbodies at different temperatures from Planck’s Law, used Excel to graph them and then embellished in Photoshop. These emission curves explain why very hot objects become incandescent, and the integrals of these curves determine their colour (cooler objects glow dull red, hot objects glow yellow-orange, and very hot objects glow blue-white). The gradient is modified from David Eccles’ normalised linear spectrum, which was released to the public domain. My modifications mean that the spectrum is only qualitatively correct, placing more emphasis on yellow.

Blackbody emission curves for various temperatures

Blackbody emission curves via Planck's Law at 3000, 4000 and 5000 K - cc-by-sa 3.0

This adventure was inspired by an exercise in my ancient copy of Atkins Physical Chemistry, which asks readers to write a program that outputs blackbody spectra and optionally numerically integrates them. There’s also a question involving a glow worm being propelled through space via photon momentum, quite a charming imagination 😀


Posted on 26/06/2010, in Chemistry, Physics and tagged , , , , , , , , . Bookmark the permalink. 6 Comments.

  1. I think one of the weirdest implications of the BB radiation curves is when absorptivity is not spectrally uniform! Most students or even pros don’t know or forget that the emission curve as function of absorption is per each spectral value, not an average. So a body that could stay purple when hot should radiate green! We don’t intuitively think of green coals as legit, but they could be. We don’t see such as that because of limitations of real materials, not from matter of principle. But there are slight variations from greyness, which likely account for the odd hues of some metals in smelting etc. (gold, IIRC is one example.)

    Also, stars also don’t look quite right relative to BB spectrum for two reasons:
    1. They have emission lines and other complications of what they are.
    2. Even looking straight up from a mountain, our atmosphere absorbs some blue and yellows things a little. Hence our sun looks about 5000 K instead of 5700. (Ever wonder why those “6000 K” fluorescents are so bluish, when you figure they should look like natural sunlight?) So Betelgeuse seems tinted like Mars or a peach, it’s likely less ruddy if seen from space.

    • Regarding spectral uniformity in BB curves, I was recently looking at some topical plots of solar irradiance at ground level, where various regions have been knocked out by IR and visible resonances in the atmosphere. As such, the irradiance plot looks like a BB curve with chunks taken out of it, and could be mathematically treated as a normalised multiplication of the BB curve and absorption spectra. That kinda ties into your second point regarding the apparent colour temperature of sunlight. I guess the Tyndal effect would do the rest in terms of isotropically dispersing some of the blue from white light.

      Regarding the colour of gold, I have read that this is due to curious downshifting of the plasma frequency (into *consults colour wheel* what I suppose must be violet). This is apparently only reproduced in silico when relativistic effects are taken into account. I’ve often wondered, however, why only a few metals are similarly affected. I note that you mention smelting, however, so you may be referring to some weirdness in its incandescence and I’ve gone off on a tangent?

      I left a comment on your post regarding extracting energy/work from the metric expansion of the universe however for some reason I get 404s when I try to post it. Will try again later, sorry. Thanks for commenting on my blog, such as it is.

  2. Smelting – yes, I meant color of molten gold. I think there are band emission effects too. Oddly people disagree about how to describe the color. Tell me more about the plasma issue.

    BTW I suggest you have a message when people comment, saying it’s awaiting moderation etc. I saw nothing after my last attempt, which was posted a day or two later.

    • Re: emission of incandescent gold – apparently (and this is just reading a random smattering of blogs that mention it) molten gold has a slight green cast?! I cannot find photographic evidence of this though I am not about to trust the majority of film or CCD gamuts to reflect the true perceptual spectrum :D.

      Re: plasma frequency – as I understand it (though I only briefly covered SPR a few years back) most metals have surface plasmon resonances in the ultraviolet, but in the case of gold, caesium and copper they will accept photons in the violet/blue regime. As such they gain a yellow (in the case of gold and caesium) or pink/orange (copper) cast under white light. As far as gold is concerned, the specific location of the resonance frequency is perturbed into the visible region due to relativistic effects (for which there are solutions in computational quantum chemistry, however these plasmons would require a periodic treatment to model (I imagine), which I know nothing about.) That said, it’s my understanding that – for instance – DFT was invented by physicists for condensed matter physics and later adapted to chemical species in vacuo, so there’s hardly a dearth of codes for just this sort of thing.

      Anyhow, the sensitivity of surface plasmons to surfacial contaminants (i.e. adsorbed species) gave rise to a number of fairly interesting analytical techniques.

      Apologies if I’m repeating stuff you already know. You appear to be rather experienced.

      Re: Messages – The akismet anti-spam thingy decided your message (and another) were spam. 0% false positive rate my arse :S. Now I’m wondering how many of the ~210 messages akismet has cheerfully deleted as spam were actually not. Hopefully none…

  3. Oh, something must have changed (here or in my browser) since there it is, right away!

  4. Regarding the glow worm in space — my professor has a knack to make his exams into little stories; I remember an exam where the plot was us students cooking a dinner for our friends, which then branched off questions about the thermodramatics of carbohydrates, refridgerators, reactions and so on. At the beginning of his career, one of his first exams was about the anthropomorphic view of a hydrogen atom in space, who feels jolts of momentum when it gets hit by electromagnetic radiation, looks around to report on the colour of any photons it sent off, then is afraid that it will maybe have to stay in some electronic state forever, and so on. Well, some people like it, others prefer head-on “Do-this-and-don’t-ask-why” questions in their exams.

    Anyway, I once asked him about why he does it like that. His answer was that if he didn’t turn the tasks into little funny stories, he wouldn’t be able to motivate himself to get to the work of desining the exams …

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