Match the Radiation Law to What the Question Varies
Thermal radiation questions are won by choosing the right law. Stefan's law is about how much power a body radiates, Wien's law is about which wavelength is brightest, and Kirchhoff's law is about how good emitters relate to good absorbers.
Thermal Radiation: Stefan, Wien and Kirchhoff is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Stefan's law and Wien's law
Wien's displacement law: λ_max T = constant (about 2.9 x 10⁻³ m K), so the peak wavelength shortens and the peak frequency ν_m rises in proportion to T as the body gets hotter, which makes the ν_m versus T curve a straight line through the origin. The maximum spectral emission itself rises as T⁵.
Colour tells temperature
A hotter body glows with a shorter dominant wavelength: iron heated in a flame goes dull red, then reddish yellow, then white hot, and this progression is explained by Wien's displacement law. A blue star is hotter than a red star, so of two stars glowing red (A) and blue (B), Ta < Tb. Surface area has no bearing on the colour; it affects only the total power. Because the sun and stars cannot be touched, their temperatures are found with a pyrometer, which measures the radiation they emit.
Kirchhoff's law and the blackbody
A black object glows brightest at a given temperature, a grey one less so, and a white one least, so three objects heated in the same furnace to 2000 °C glow in the order black, grey, white. The ratio of emissive to absorptive power depends only on temperature and wavelength, not on the body's colour.
OlympIQ exam lens
- ✓Total radiated power is proportional to e A T⁴ (Stefan-Boltzmann)
- ✓λ_max T = constant (Wien); hotter bodies peak at shorter wavelengths, and ν_m is proportional to T
- ✓Total emission varies as T⁴ while the maximum spectral emission varies as T⁵
- ✓Blue stars are hotter than red stars; area does not set the colour
- ✓Kirchhoff: e_λ / a_λ = E_λ, so a black body is both the best absorber and the best emitter
Do not use Stefan's T⁴ law to explain a colour change. A colour shift with temperature is a question about the wavelength of peak emission, which is Wien's law; Stefan's law only tells you how much total power is radiated.
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