Library / Heat transfer and thermal systems / HTS-37
Heat transfer and thermal systems
Wavelength of peak blackbody emission
Wavelength at which the spectral emissive power of a blackbody peaks, using Wien’s constant b = 2.897771955×10⁻³ m·K.
- Ref
- HTS-37
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- λmax [m]
Wien’s displacement law gives the wavelength at which a blackbody’s spectral emissive power peaks, λmax = b/T, with b = 2.897771955×10⁻³ m·K. A hotter body peaks at a shorter wavelength: the Sun at about 5800 K peaks near 0.5 µm, a room-temperature object near 10 µm. The peak of a frequency spectrum lies at a different place.
Wavelength at which the spectral emissive power of a blackbody peaks, using Wien’s constant b = 2.897771955×10⁻³ m·K. The peak of a frequency spectrum falls at a different spectral position.
Calculator
- Peak wavelength in micrometres2.898 µm
- Total emissive power, σT⁴56,700 W/m²
- Peak wavelength relative to a 300 K body0.3
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A blackbody at 1,000 K peaks at 2.898 µm, in the infrared.
- Doubling the temperature halves the peak wavelength, and raises the total emissive power by a factor of 16, to 907,300 W/m².
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T Absolute temperature | 100 to 10,000 K | 2.898e-7 | 2.898e-5 | 2.869e-5 | +10% | −9.09 % |
Sweep of Absolute temperature
| Absolute temperature (K) | Peak wavelength (m) |
|---|---|
| 100 | 2.898e-5 |
| 1,338 | 2.167e-6 |
| 2,575 | 1.125e-6 |
| 3,813 | 7.601e-7 |
| 5,050 | 5.738e-7 |
| 6,288 | 4.609e-7 |
| 7,525 | 3.851e-7 |
| 8,763 | 3.307e-7 |
| 10,000 | 2.898e-7 |
Sweep one variable
Variables and how each one contributes
Peak wavelength
What the equation gives you. Everything else feeds it.
Absolute temperature
The absolute temperature, in K. A higher temperature moves the peak to a shorter wavelength, in inverse proportion. Raising it by 10 % (to 1,100) moves the result by −9.09 %, from 2.898×10−6 to 2.634×10−6 m.
Worked example with the values above
- Wien’s constant: b = 2.897771955×10⁻³ m·K.
- Divide by the temperature: 0.002897772 / 1,000.
- λmax = 2.8978×10−6 m (2.8978 µm).
Assumptions and limits
- Blackbody or diffuse grey behaviour as stated, in a vacuum or non-participating medium.
- Absolute temperatures and the exact values of σ, h, c and kB given on the page.
Common mistakes
- Using °C in Planck’s law or Wien’s law.
- Mixing per-metre and per-micrometre spectral units.
- Treating a grey surface as if it followed the blackbody spectrum without considering emissivity.
Statistics and uncertainty
The radiation laws for blackbodies are exact, but real-surface emissivity and its variation with wavelength add uncertainty of 10 % or more, and measured view factors depend on exact geometry.
Where it is used
- Infrared sensing, lamps and radiant heaters.
- Setting up radiosity networks and linearised radiation coefficients.
Maths you need
- Planck’s law: spectral emissive power of a blackbody
- Wien’s law: the peak wavelength is inversely proportional to T
- Radiosity: the total radiation leaving a surface per unit area