Q1. A perfect blackbody in thermal equilibrium:
- (a) Reflects all radiation and emits none.
- (b) Emits radiation only in the infrared spectrum.
- (c) Absorbs all incident electromagnetic radiation and emits radiation characteristic of its temperature.
- (d) Emits energy independent of its temperature.
Answer & solution
Answer: (c) Absorbs all incident electromagnetic radiation and emits radiation characteristic of its temperature.
A black body is defined as a perfect absorber (absorptivity = 1) and, by Kirchhoff's law, it is therefore also a perfect emitter.
What it emits depends only on its temperature — hotter bodies radiate more, and at shorter wavelengths.
Revision note — Black-body radiation
• The term was coined by Gustav Kirchhoff in 1860. In practice a cavity with a small hole behaves as a black body; lamp black and platinum black come close.
• Kirchhoff's law: a good absorber is a good emitter — at a given temperature, emissivity equals absorptivity.
• Stefan–Boltzmann law: energy radiated per unit area per second E = σT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Doubling the absolute temperature raises the radiation 16 times.
• Wien's displacement law: the wavelength of peak emission falls as temperature rises, λ_max × T = 2.9 × 10⁻³ m K.
• This is why a heated iron glows red, then yellow, then white, and why blue stars are hotter than red stars.
• Planck's law (1900) explained the whole spectrum by assuming energy is emitted in packets (quanta) — the birth of quantum theory; classical physics had predicted the ultraviolet catastrophe.
• The Sun radiates almost as a black body at about 5,800 K, peaking near 500 nm in the visible range.
Do not mix these up
• Black body vs black object — a black body absorbs and emits perfectly; an ordinary black surface merely absorbs most visible light.
• Stefan's law vs Wien's law — Stefan gives how much is radiated (∝ T⁴); Wien gives at which wavelength the emission peaks (∝ 1/T).
Also asked from this topic: the law that explains the colours of stars from their temperature (Wien's displacement law); the value of the Stefan–Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴).