Blackbody Radiation: Kirchhoff's, Wien's and Stefan's Laws (JEE Advanced)

“Blackbody radiation: absorptive and emissive powers; Kirchhoff's law; Wien's displacement law, Stefan's law”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: Heat transfer: conduction, convection and radiation.

JEE Main covers basic heat transfer modes but skips the quantitative laws of thermal radiation. For Advanced, you need to calculate emitted power, peak wavelengths, and use emissivity in real-world problems.

• Absorptive power (a) is the fraction of incident radiation absorbed; for a blackbody, a = 1
• Emissive power (e) is the energy radiated per unit area per unit time; depends on temperature and surface properties
• Kirchhoff's law: at thermal equilibrium, the ratio e/a is the same for all bodies and equals the emissive power of a blackbody at that temperature
• Wien's displacement law: the wavelength at which a blackbody emits maximum energy is inversely proportional to its temperature
• Stefan's law: total energy radiated per unit area is proportional to the fourth power of absolute temperature
• For non-blackbodies, multiply Stefan's law by emissivity (ε), where 0 < ε < 1

• Kirchhoff's law: e/a = E (where E is blackbody emissive power at same T)
• Wien's displacement law: λₘT = b, where b = 2.9 × 10⁻³ m·K
• Stefan's law: E = σT⁴, where σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴
• For real bodies: E = εσT⁴ (ε is emissivity)
• Net power radiated: P = εσA(T⁴ - T₀⁴) where T₀ is surrounding temperature
• Power radiated by a sphere: P = 4πr²εσT⁴
• If temperature doubles, radiated power increases 16 times (2⁴ = 16)
• If temperature doubles, λₘ becomes half

• Forgetting to use absolute temperature (Kelvin) in Stefan's law; using Celsius gives wrong answers
• Confusing λₘT = constant with λₘ/T = constant; remember wavelength and temperature are inversely related
• Ignoring emissivity for non-blackbodies; real surfaces have ε < 1 which reduces radiated power
• Using Stefan's law without subtracting T₀⁴ when the body is surrounded by an environment at temperature T₀

Question. A blackbody at 2000 K emits radiation with maximum intensity at wavelength λₘ. If the temperature is increased to 3000 K, find the new wavelength of maximum emission. Also, calculate the ratio of the total power radiated at 3000 K to that at 2000 K.

Solved twice independently; both solutions agree.