Planck’s law applicability: Does Planck’s radiation law hold for all “coloured” (real) bodies exactly as stated for a black body?

Introduction / Context:Planck’s law gives the spectral distribution of emissive power of a perfect black body. Real (coloured) bodies deviate from blackbody behaviour and are described through emissivity.

Given Data / Assumptions:

• Black body: ideal reference with emissivity = 1 at all wavelengths.
• Real body: emissivity ε(λ, T) < 1 and wavelength dependent.

Concept / Approach:For real bodies, spectral emissive power E(λ, T) = ε(λ, T) * E_b(λ, T), where E_b is given by Planck’s law. Thus, Planck’s law applies to the ideal blackbody spectrum, while real bodies follow it only after scaling by their emissivity function.

Step-by-Step Solution:

Verification / Alternative check:Kirchhoff’s law links emissivity and absorptivity; experimental spectra for paints, metals, and ceramics confirm departures from the blackbody curve.

Why Other Options Are Wrong:Restrictions to vacuum, temperature range, or material do not convert a real body into a black body; emissivity remains less than unity and wavelength dependent.

Common Pitfalls:Using blackbody tables directly for engineering surfaces without applying emissivity corrections leads to significant errors.

Final Answer:False