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Blackbody Hoodie

THE CURVES NEVER CROSS | Pixelated Physics

\[B_\lambda(T) = \frac{2hc^2}{\lambda^5}\,\frac{1}{e^{hc/\lambda k_BT} - 1}\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

Everything above absolute zero glows. A perfect absorber, a blackbody, glows with a spectrum fixed by its temperature alone. Planck curves for 3000 K to 7000 K, stacked hottest behind. Hotter is brighter at every wavelength, so the curves never cross. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Planck's law gives how bright a blackbody shines at each wavelength for a given temperature. The peak shifts to shorter wavelengths as the body gets hotter, with the peak wavelength times temperature staying constant (Wien's law).

Everything above absolute zero glows. A perfect absorber, a blackbody, glows with a spectrum fixed by its temperature alone.

Max Planck found the formula in 1900. To derive it he had to assume that the oscillators in the cavity walls take or give energy only in packets of hν, the first step into quantum theory. Einstein’s 1905 light quanta came later.

The art shows five curves from 3000 K to 7000 K. Each peak, marked with a tick, moves to shorter wavelength as the temperature rises, following Wien’s law, λmax T = 2898 μm K.

Raise the temperature and the radiance goes up at every wavelength, so no two curves cross. The vertical scale is compressed by a power law to fit, which keeps the order.

The curves never cross.

Equations

\[B_\lambda(T) = \frac{2hc^2}{\lambda^5}\,\frac{1}{e^{hc/\lambda k_BT} - 1}\]
\[\lambda_{\max}T = 2898\ \mu\mathrm{m\,K}\]
SymbolMeaningUnit
\(B_\lambda\) spectral radiance per unit wavelength \(\mathrm{W·m^{-3}·sr^{-1}}\)
\(T\) temperature \(\mathrm{K}\)
\(\lambda\) wavelength \(\mathrm{m}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(\lambda_{\max}\) wavelength of peak radiance \(\mathrm{m}\)

Sources

  1. Planck (1901) Über das Gesetz der Energieverteilung im Normalspectrum, Ann. Phys. 309, 553
  2. Wien (1893) Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie, Sitzungsber. Preuss. Akad. Wiss., 55
  3. Rybicki & Lightman, Radiative Processes in Astrophysics (1979), Ch. 1

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

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