Thermal radiation law identification: “The wavelength corresponding to maximum emissive power is inversely proportional to absolute temperature.” Does this statement describe Planck’s law?

Introduction / Context:Several named laws describe blackbody radiation. Correctly identifying which statement corresponds to which law helps avoid conceptual errors in heat transfer.

Given Data / Assumptions:

• The quoted statement links peak wavelength and absolute temperature via an inverse relationship.
• We compare with well-known radiation laws.

Concept / Approach:Wien’s displacement law states: lambda_max * T = constant, meaning the wavelength at peak emission (lambda_max) is inversely proportional to temperature. Planck’s law, by contrast, gives the full spectral distribution of blackbody radiation intensity as a function of wavelength and temperature—not merely the location of the peak.

Step-by-Step Solution:

Verification / Alternative check:Plotting blackbody spectra using Planck’s law shows peaks shifting with T such that lambda_max * T is constant, which is Wien’s result derived from Planck’s distribution.

Why Other Options Are Wrong:

• Yes: Misattributes Wien’s law to Planck.
• Only at very high temperatures / only for black surfaces: Wien’s law applies to ideal blackbodies across temperatures; emissive peaks for real surfaces follow similar trends but with emissivity effects.

Common Pitfalls:Confusing names: Stefan–Boltzmann (total emission proportional to T^4), Wien (peak wavelength shift), Planck (full spectral law).

Final Answer:No