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Radiatrix

Blackbody Radiation Physics

\[\begin{aligned} B_\nu(\nu,T) &= \frac{2h\nu^{3}}{c^{2}} \\ &\quad\times\frac{1}{e^{h\nu/(k_B T)} - 1} \end{aligned}\]
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$21.99 USD
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Why does a heated poker go from red to white? Radiatrix glows by Planck’s law. Heat a blackbody and it emits more at every wavelength, while its peak slides toward shorter wavelengths, as Wien’s law says. Hot stars look blue-white; cool ones look red. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Made to order: about 10 days of production and handling before it ships.

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The physics

Planck's law gives how much light a hot body emits at each frequency for a given temperature. Hotter bodies shine brighter at every frequency, and their peak moves to shorter wavelengths according to Wien's law.

Why does a poker in the fire glow red, then orange, then white? Radiatrix glows by the rule on this mug.

A blackbody is anything that absorbs all the light that falls on it. Heat one and it shines with a spectrum that depends only on its temperature. Max Planck found the formula for that spectrum in 1900 and published it in 1901. To make it work he had to assume that light of frequency ν is exchanged in lumps of energy hν. That assumption started quantum physics.

Turn up the temperature and two things happen. The body gets brighter at every wavelength: a hotter curve sits above a cooler one everywhere, red included. And the peak of the curve slides toward shorter wavelengths. That slide is Wien's displacement law, the second line: the peak wavelength times the temperature is a constant, about 2.9 millimetre-kelvins.

So HOTTER MEANS BLUER is a statement about the peak and the overall colour, not a loss of red. The Sun's surface, at about 5,800 kelvin, peaks near 500 nanometres. Cooler stars peak in the red and infrared and look orange-red; much hotter stars peak in the ultraviolet and look blue-white.

Radiatrix does not choose a colour. The temperature chooses it, and she just shines.

Equations

\[\begin{aligned} B_\nu(\nu,T) &= \frac{2h\nu^{3}}{c^{2}} \\ &\quad\times\frac{1}{e^{h\nu/(k_B T)} - 1} \end{aligned}\]
\[\lambda_{\max}\,T = b\]
\[b \approx 2.898\times10^{-3}\ \text{m K}\]
SymbolMeaningUnit
\(B_\nu\) spectral radiance of a blackbody (power per area, per solid angle, per frequency) \(\mathrm{W·m⁻²·sr⁻¹·Hz⁻¹}\)
\(\nu\) frequency of the light \(\mathrm{Hz}\)
\(T\) absolute temperature \(\mathrm{K}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(\lambda_{\max}\) wavelength at which the spectrum (per unit wavelength) peaks \(\mathrm{m}\)
\(b\) Wien displacement constant \(\mathrm{m·K}\)

Sources

  1. Planck (1901) Ueber das Gesetz der Energieverteilung im Normalspectrum, Ann. Phys. 309, 553
  2. NIST CODATA 2022 — Wien wavelength displacement law constant b
  3. NIST CODATA 2022 — Planck constant h
  4. NIST CODATA 2022 — Boltzmann constant k
  5. Encyclopaedia Britannica — Blackbody radiation
  6. NASA NSSDCA — Sun Fact Sheet (effective temperature 5772 K)
  7. HyperPhysics — Blackbody Radiation
  8. HyperPhysics — Wien Displacement Law

Source Planck, M. (1901). Ueber das Gesetz der Energieverteilung im Normalspectrum. Annalen der Physik 309, 553–563.doi.org/10.1002/andp.19013090310

Field notes

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