Web Simulation

Blackbody Radiation & Stefan-Boltzmann Law

This tutorial visualizes blackbody radiation: an ideal emitter whose spectrum depends only on temperature. You can see how total power radiated grows as P ∝ T⁴ (Stefan-Boltzmann), how the peak wavelength shifts with λ_max ∝ 1/T (Wien's law), and how the object's apparent color follows the Planckian locus from dull red to blue-white.

Mathematical foundation

1. Stefan-Boltzmann law

Total power radiated per unit area: P = σ A T⁴, where σ ≈ 5.67×10⁻⁸ W/(m²·K⁴). Doubling the temperature T increases power by a factor of 2⁴ = 16.

2. Planck's law

Spectral radiance (power per unit area, solid angle, and wavelength): L(λ,T) = (2hc²/λ⁵) / (e^hc/(λkT) − 1). The graph plots this curve; the area under it is related to total power.

3. Wien's displacement law

Peak wavelength: λ_max = b / T, with b ≈ 2.898×10⁻³ m·K. Hotter objects peak at shorter (bluer) wavelengths. The dashed line on the graph shows λ_max.

4. Color (Planckian locus)

The color of the "emitter" circle approximates the chromaticity of a blackbody at that temperature: red → orange → yellow → white → blue-white as T increases.

Stefan-Boltzmann Lab

Temperature (K):

3000 K

Total radiance P = σ T⁴:

Peak wavelength λ_max:

Doubling T → 16× power.

Fixed Y-scale (compare power at different T)

Show Classical Prediction (Rayleigh-Jeans)

Tutorial: hue visible at all T

Emitter (Planckian color)

Spectral radiance vs wavelength. Shaded band: visible (380–700 nm). Dashed line: Wien λ_max. Overlay: auto-X (max X where Y < 5% of peak), comp (compare curves), Lin/Log (X-axis scale).

Usage

Drag the Temperature slider from 300 K to 10,000 K:

Emitter circle: Color and glow follow the Planckian locus (red hot → white → blue-white). Glow intensity scales with T⁴. Toggle the eye icon for Real vs Tutorial mode.
Graph: Spectral radiance vs wavelength. Default X range is 100 nm–3000 nm. Use auto-X to set the max wavelength to where the curve drops below 5% of peak (linear Y); X tick labels adjust automatically. Lin/Log switches the X-axis scale. Enable Fixed Y-scale to compare power at different T.
λ_max (dashed line): Wien's law—peak shifts to shorter wavelength as T increases.
Visible band: Light tint shows 380–700 nm; you can see which part of the spectrum enters the visible range as T rises.
comp: Overlay button to plot multiple curves at T, 0.9T, 0.8T, 0.7T, 0.6T.
Show Classical Prediction: When checked, a red dashed line shows the Rayleigh-Jeans (classical) curve. It matches Planck in the infrared but shoots toward infinity at short wavelengths—the Ultraviolet Catastrophe that led to quantum mechanics.

Lab ideas

1. Stefan-Boltzmann: Note the "Total radiance" value. Double the temperature (e.g. 3000 K → 6000 K) and confirm the power increases by about 16×.

2. Wien's law: At 3000 K the peak is in the infrared (~966 nm). At 6000 K it moves to ~483 nm (visible). At 10,000 K it is in the UV (~290 nm).

3. Color: Compare 800 K (dim red), 3000 K (orange-white), 6000 K (sun-like white), 10,000 K (blue-white).