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Does Kirchhoff's law for heat radiation imply that all objects at the same temperature will glow the same color?

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In other words, if a piece of molten iron glows the same color as my body, which radiates the same color as the sun, therefore all three objects - molten iron, my body, and the sun - must be at the same temperature?

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  • $\begingroup$ The sun and a lump of iron might be pretty close in color at a given temperature. But, for example, a volume of sodium gas (plasma) will likely have a totally different color. $\endgroup$
    – The Photon
    Commented Nov 18, 2022 at 17:13
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    $\begingroup$ They dont't obviously. You can have three apples at room temperature and one is red, the second one yellow and the last one green. $\endgroup$
    – Leos Ondra
    Commented Nov 18, 2022 at 18:25
  • $\begingroup$ Considering Marks comment below , refering to Leos Ondas above, the apples might not be too good an example as their heat is very low, so their non-blackness becomes overwhelming. In other words, in a freezing room those three apples are not all black, at 200 degress they'd all be more than red. $\endgroup$ Commented Nov 19, 2022 at 10:59
  • $\begingroup$ Is a gas a "body" in terms of Kirchhoff's law? Are there related questions refering to - intriguingly - Boltzmann constant? For instance, Avogrado number is with gases, not with "bodies". The issue this question brings about seems about how bodies may resemble gases in their taking away of heat into kinetic movement of particles, thus not emitting radiation. The more gassy a body is the more it seems to be abel to get hot without emanating radiation. $\endgroup$ Commented Nov 19, 2022 at 11:09
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    $\begingroup$ @LeosOndra The question is asking about the color that an object glows with. I don't think apples glow perceptibly under ordinary circumstances. $\endgroup$ Commented Nov 19, 2022 at 12:39

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Kirchhoff's law only applies to a black body - an idealised object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. Stars like the sun are a reasonably good approximation of a black body. It is unlikely that molten iron or your body would approximate a black body.

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  • $\begingroup$ Thank you! Is Kirchoff law equivalent to the statement that, for example, all coal at the same temperature will glow the same color? Since all materials "which absorbs all incident electromagnetic radiation" can be treated essentially as the same object spectroscopically, then Kirchoff law states that all objects with the same absorption/reflection properties will glow the same color at the same temperature? $\endgroup$
    – James
    Commented Nov 18, 2022 at 23:32
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    $\begingroup$ The hotter something gets, the better it approximates a blackbody. Iron melts at 1800 K, which gives it a reasonably blackbody spectrum. $\endgroup$
    – Mark
    Commented Nov 19, 2022 at 3:43
  • $\begingroup$ The "black" is for counting out all "natural colour" that a body's heat is not cause of? What Mark says I understand as some requirement of minimum heat for emission of "colour" that is not only "non-absorption" (considering complementary natural colours of object). In other words there must be some heat, and, paradoxically, that is more important than the body having no other color, being black. $\endgroup$ Commented Nov 19, 2022 at 10:57
  • $\begingroup$ I think Kirchoff law is about two or more bodies at same temperature and in thermal equilibirium, the ratio of any two bodies emissivity is equals to ratio of absorpitivity. Yes, Planck law is about black body. And there is no need to absorb radiation when passing current or excitation by current can produce radiation. $\endgroup$ Commented Nov 19, 2022 at 15:10
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If a piece of molten iron glows the same color as my body, which radiates the same color as the sun, therefore all three objects - molten iron, my body, and the sun- must be at the same temperature?

There is no one-to-one correspondence of color with temperature the way you envisage.

Paint is at room temperature, but can display any of the dominant colors of radiation from a heated object. Even your figure above shows this: is the computer screen surface at temperatures of thousand centigrade?

It is not simple. In this article the heat to energy density of matter is shown using the black body radiation formula

bb

The peak wavelength and total radiated amount vary with temperature according to Wien's displacement law. Although this shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero. Visible light is between 380 and 750 nm.

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  • $\begingroup$ Thank you! Is Kirchoff law equivalent to the statement that, for example, all coal at the same temperature will glow the same color? Since all materials "which absorbs all incident electromagnetic radiation" can be treated essentially as the same object spectroscopically, then Kirchoff law states that all objects with the same absorption/reflection properties will glow the same color at the same temperature? $\endgroup$
    – James
    Commented Nov 18, 2022 at 23:33
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    $\begingroup$ Yes,within the error limits in the description of the system. $\endgroup$
    – anna v
    Commented Nov 19, 2022 at 5:27
  • $\begingroup$ "heat to energy density". Shouldn't it be temperature, and not heat? $\endgroup$ Commented Nov 19, 2022 at 13:09
  • $\begingroup$ the y axis says : spectral energy density/kJ /m^3 nm . The temperature is one off for a given body in thermodynamic equilibrium . the curve is the cotribution to the "hottness" of wavlenths, I think, $\endgroup$
    – anna v
    Commented Nov 19, 2022 at 15:09
  • $\begingroup$ @annav: still, Kelvin is a unit of temperature, not heat. $\endgroup$ Commented Nov 19, 2022 at 17:47
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No. A classic example is the gas mantle, which glows white when most other materials would glow red. It works by using a material with an emissivity that is low at the red end of the spectrum, but high at the blue end.

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  • $\begingroup$ Thank you! Is Kirchoff law equivalent to the statement that, for example, all coal at the same temperature will glow the same color? Since all materials "which absorbs all incident electromagnetic radiation" can be treated essentially as the same object spectroscopically, then Kirchoff law states that all objects with the same absorption/reflection properties will glow the same color at the same temperature? $\endgroup$
    – James
    Commented Nov 18, 2022 at 23:33
  • $\begingroup$ yes! the thorium oxide in a gas mantle or the calcium oxide in a limelight are poor emitters of red light. $\endgroup$
    – Jasen
    Commented Nov 20, 2022 at 10:20
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Not really.

Every sample of material has an emission spectrum and corresponding absorption spectrum for any given temperature. The emission spectrum is exactly what it says on the tin: it is the spectrum of light emitted by the object when excited to do so, such as by being hot or, to say it another way, it is how susceptible the object is to emit light at each given frequency, which thus can vary depending on the frequency. The two spectra are complementary in that at any frequency an object is a good emitter, it is also a good absorber, and conversely: this follows from the fact of the time reversal symmetry of physics.

Planck's law applies to a "perfect black body". Such an object has a perfectly uniform emission and absorption spectrum, so it is equally responsive to light of all frequencies. Once heated, it gives off the characteristic glow color you describe. This is a spherical cow, just like a perfect vacuum, perfect conductor, rigid body, and so forth. For a realistic object, the actual emission will be Planck's law times the actual emission spectrum. However, for most materials the curve will still be close enough to a Planck curve that you will not easily be able to see much of a difference in the apparent glow, e.g. there is no known material, I believe, that can both be heated to the necessary temperature without being damaged in some way and also glows a green color, i.e. the emission spectrum is such that the reds are totally suppressed.

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The glow (ie. the thermal radiation) of every material at the same temperature is the same color, but there are materials that emit light besides their thermal emission. This can be observed, for example, in ion-colored flames, where specific electron transitions are the cause of the light emission, or in computer monitors.

Besides emissivity, materials also reflect or transmit light - this reflection and transmission is often wavelength dependent and causes most of the colors in everyday objects.

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  • $\begingroup$ Thank you. Does the glow that a neon gas tube, or sodium gas tube, or hydrogen gas tube emit when passed with electricity constitute "thermal radiation", or something else? Why is there a specific signature for each atom's spectrogram, would it not contradict Kirchoff's law that spectra depends entirely from temperature? $\endgroup$
    – James
    Commented Nov 19, 2022 at 13:12
  • $\begingroup$ no this is wrong. black bodies follow the black body profile, coloured bodies basically emit the colours they don't reflect. - as in "the sympathizer"'s answer $\endgroup$
    – Jasen
    Commented Nov 20, 2022 at 10:15
  • $\begingroup$ @James that kind of light emission comes from electrons being pushed to a higher energy orbital and spontaneously jumping back down while emitting the energy difference as a photon. This is why there are specific signatures - since electron orbitals have specific energy values, emitted photons always have the energy of a specific difference of two orbitals. Kirchhoff's law applies to thermal spectra, which come from the thermal motion of atoms. $\endgroup$
    – sh4dow
    Commented Nov 20, 2022 at 18:14
  • $\begingroup$ @Jasen I circumvent the complexities of absorption/emission spectra by clearly separating thermal and non-thermal components of light emission. The thermal component is universal (in form, not in magnitude), the non-thermal one is usually highly specific. $\endgroup$
    – sh4dow
    Commented Nov 20, 2022 at 18:18
  • $\begingroup$ And perhaps I should add that structures with optically interacting materials can have a thermal based emission unlike the Planck spectrum: Eg. an infrared reflecting layer would reduce the emissivity of the "system" in the infrared spectrum and leave the non-infrared emissivity untouched. And if you just describe the apparent properties of complex materials, you often get nonuniform emissivities. But you can view these systems as emitting a planck spectrum that is then modified by the optical properties of the system. $\endgroup$
    – sh4dow
    Commented Nov 20, 2022 at 18:46
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Yes, all the bodies glow same color at given temoerature and wavelength at thermal equilibirium according to kirchoff's law. What difference is that intensity of different objects is different, not the shape of spectral curve. So a ceramic glow with same color as iron at same temperature. It is stated as,$$\frac{e_1}{a_1}=\frac{e_2}{a_2}=e_b$$ Where, $e_1$ and $e_2$ are emissivity of a body 1 and 2, $a_1$ and $a_2$ are absorotivity of same bodies. $e_b$ is emissivity of black body whose absorptivity is one, absorb all radiation at all wavelength and act as universal function from which emissivity of other bodies can be known.

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