Blackbody Radiation Simulator
Equations in this simulation
| T | Temperature T (kelvin, as a power of 10) | the surface temperature | |
|---|---|---|---|
| λ | wavelength | visible light runs from about 380 nm (violet) to 750 nm (red) | |
| h, c, k | Planck's constant, the speed of light, Boltzmann's constant | 6.626 × 10⁻³⁴ J·s, 2.998 × 10⁸ m/s, 1.381 × 10⁻²³ J/K | |
| B_λ | spectral radiance | how much light the surface gives off at each wavelength; the chart is this curve |
| b | Wien's constant | 2.898 × 10⁻³ m·K | |
|---|---|---|---|
| λ_max | peak wavelength | the hotter, the shorter: the Sun peaks in the green-yellow, a red dwarf in the infrared, a blue giant in the ultraviolet |
With the current values:
| σ | Stefan–Boltzmann constant | 5.670 × 10⁻⁸ W/(m²·K⁴) | |
|---|---|---|---|
| j | power given off per square meter | doubling the temperature multiplies it by 16 | |
| R | Radius (in radii of the Sun, as a power of 10) | the Sun's radius is 696,000 km | |
| L | luminosity, the total power | compared with the Sun's 3.83 × 10²⁶ W |
With the current values:
| dT/dt | cooling rate of the iron ball | mass 33 g, area 12.6 cm², c_p 450 J/(kg·K); it only loses heat by radiating, so it cools fast while white-hot and ever more slowly as it dims |
|---|
With the current values:
How to use the blackbody radiation simulator
- Pick an object, from a human body and lava to the Sun and a blue giant star, or set the temperature and radius yourself. The sphere takes the color a blackbody at that temperature really has, worked out from its spectrum and the eye's color matching functions, and dims to nothing below about 700 K.
- The chart is the Planck curve: how much light comes off at each wavelength, with the band of visible light marked under the axis and the peak dashed in red. Raise the temperature and the curve grows enormously and its peak slides to shorter wavelengths, from the infrared through the visible into the ultraviolet.
- Read the peak wavelength from Wien's law, the power per square meter from the Stefan–Boltzmann law and, for a star, its luminosity compared with the Sun. Tick Let it cool by radiating to watch a white-hot iron ball fade through yellow, orange and red as it loses heat.
Frequently asked questions
What is a blackbody?
An ideal object that absorbs all the light that falls on it and gives off light only because of its temperature. Its spectrum depends on the temperature alone, following Planck's law. Stars, glowing metal, lava and a lamp filament are close to blackbodies; so, in the infrared, is your skin.
Why do hot things change color as they heat up?
The peak of the spectrum moves to shorter wavelengths as the temperature rises, by Wien's law λ_max = 2.898 × 10⁻³ m·K ÷ T. Below about 700 K almost all the light is infrared and nothing visible glows; then the long red end of the visible appears first, followed by orange and yellow, and above about 6,000 K the spread across the whole visible range looks white, turning bluish for hotter stars.
Why does the Sun look white and not green if its spectrum peaks at 500 nm?
Because the Sun's spectrum is broad and covers the whole visible range nearly evenly, so all three kinds of cone in the eye are stimulated about equally, which we see as white. A peak in the green does not make a color green; only a narrow band of green light would.
How much power does a hot object give off?
The Stefan–Boltzmann law: j = σT⁴ watts per square meter, with σ = 5.67 × 10⁻⁸ W/(m²·K⁴). Doubling the temperature multiplies the power by sixteen. The Sun's surface gives off 63 MW per square meter; multiplied by its whole surface that is 3.8 × 10²⁶ W.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.