Radiative properties — diathermanous body: Given absorptivity α, reflectivity ρ, and transmissivity τ, select the correct set of values for a perfectly diathermanous body (perfectly transparent to thermal radiation).

Introduction / Context:In radiation heat transfer, extreme idealizations clarify real-world behavior. A diathermanous body is an ideal transparent medium for thermal radiation, analogous to clear glass for certain wavelength bands.

Given Data / Assumptions:

• α = absorptivity; ρ = reflectivity; τ = transmissivity.
• Energy conservation for radiation at a surface: α + ρ + τ = 1.
• “Perfectly diathermanous” means fully transmitting at the considered wavelengths.

Concept / Approach:A perfectly diathermanous surface transmits all incident radiation. Therefore τ = 1 and neither absorbs nor reflects radiation: α = 0 and ρ = 0. This satisfies the conservation relation trivially.

Step-by-Step Solution:

Verification / Alternative check:Compare with black body (α = 1, ρ = 0, τ = 0) and white (ρ → 1, α → 0, τ → 0). The diathermanous case is the complementary extreme where transmission dominates.

Why Other Options Are Wrong:

α = 1, ρ = 0, τ = 0: black body.α = 0, ρ = 1, τ = 0 and α + ρ = 1 with τ = 0: reflective/opaque cases, not transparent.α = 0.5, ρ = 0.5, τ = 0: violates transparency.

Common Pitfalls:Assuming “transparent” implies some reflection. In the ideal diathermanous definition, reflectivity is zero within the specified band.

Final Answer:

α = 0, ρ = 0, τ = 1