Kirchhoff’s radiation law: Is a body’s emissivity always equal to its absorptivity at all temperatures and conditions?

Introduction / Context:
Kirchhoff’s law of thermal radiation is often summarized as “emissivity equals absorptivity.” This is precise only under specific conditions. Misapplying it leads to errors in radiative heat-transfer calculations and material selection.

Given Data / Assumptions:

• Thermal equilibrium between a body and its surroundings.
• Same temperature for exchanging surfaces.
• Diffuse–gray surface idealization.

Concept / Approach:
Kirchhoff’s law states that, at thermal equilibrium and for a given wavelength and direction, emissivity equals absorptivity. Outside equilibrium, or when spectral/Directional effects matter, equality need not hold. Thus, the blanket statement “equal at all temperatures” is incorrect unless the system is in equilibrium and comparisons are like-for-like (same wavelength and direction).

Step-by-Step Solution:

Verification / Alternative check:
Experimental data show materials with different apparent band-averaged emissivity and absorptivity when measured against sources at different temperatures (thus different spectra).

Why Other Options Are Wrong:

Restrictions to metals, vacuum, or high temperature are unnecessary; the governing condition is thermal equilibrium and spectral matching, not material class or environment alone.

Common Pitfalls:
Using room-temperature absorptivity to predict emissive performance at furnace temperatures without spectral correction.

Final Answer:

No