Thermal radiation – Identify the law “The ratio of emissive power to absorptive power is the same for all bodies at a given temperature and equals the emissive power of a perfect black body.” This statement refers to which law?

Introduction / Context:Radiative heat transfer relies on several cornerstone laws. Correctly identifying them is essential for solving enclosure radiation, surface properties, and spectral distribution problems.

Given Data / Assumptions:

• Thermal radiation at thermodynamic equilibrium (same temperature and surroundings).
• Emissive and absorptive powers are per unit area for a given wavelength band or total, as context requires.

Concept / Approach:Kirchhoff’s law states that, at a given temperature and wavelength under equilibrium, a body’s emissivity equals its absorptivity. In its total form, the ratio of total emissive power to absorptive power is the same for all bodies and equals the blackbody emissive power.

Step-by-Step Solution:Recognize the equality between emission and absorption characteristics at equilibrium.Map the described ratio to the classical statement of Kirchhoff’s law.Conclude the named law is Kirchhoff’s law.

Verification / Alternative check:Other laws: Stefan–Boltzmann relates total emissive power of a blackbody to T^4; Wien gives spectral peak–temperature relation; Planck gives full spectral distribution; Lambert addresses angular dependence. None describe the absorptivity–emissivity equivalence.

Why Other Options Are Wrong:

• Stefan’s, Wien’s, Planck’s, and Lambert’s laws address different aspects (magnitude, spectrum, or directionality) and do not equate emission to absorption.

Common Pitfalls:Confusing “emissive power” (W/m^2) with “emissivity” (dimensionless), and overlooking that Kirchhoff’s law is rigorously valid under thermal equilibrium.

Final Answer:Kirchhoff's law