Definition check: A grey body is defined as one whose absorptivity is independent of wavelength (spectrally constant). Is it also independent of temperature?

Introduction / Context:Grey-body assumptions simplify radiation problems by treating absorptivity and emissivity as constant over wavelength. However, temperature dependence is a separate matter and is often misunderstood in exam questions.

Given Data / Assumptions:

• Grey body: spectral dependence removed (ε and α do not vary with wavelength).
• No statement is made about variation with temperature.

Concept / Approach:The formal definition of a grey body addresses spectral uniformity: ε(λ) = constant with respect to λ. It does not require that ε be constant with temperature. In practice, surface properties can and do change with temperature (oxidation state, phase changes, or electronic effects).

Step-by-Step Solution:

Verification / Alternative check:Material data sheets show emissivity tables versus temperature for many materials assumed “grey” over a band; values still change with temperature even though treated as spectrally uniform in models.

Why Other Options Are Wrong:

Qualifiers like “only for metals/vacuum/room temperature” misunderstand the definition; spectral constancy is the key, not the environment.

Common Pitfalls:Equating “grey” with “constant in every way.” Grey is a modeling convenience for wavelength, not a guarantee against temperature dependence.

Final Answer:

False