Thermal radiation terminology If the energy radiated per second per square centimetre for wavelengths between λ and λ + dλ is eλ dλ, what is eλ called?

Introduction / Context:
Radiative heat transfer depends on how emission varies with wavelength. Distinguishing between total and spectral quantities is fundamental for applying laws such as Planck’s, Wien’s, and Stefan–Boltzmann.

Given Data / Assumptions:

• Definition: energy in the wavelength interval [λ, λ + dλ] is eλ dλ per unit time per unit area.
• Surface is isothermal and diffuse for simplicity.

Concept / Approach:
Total emissive power E is the integral over all wavelengths. The integrand eλ is the spectral (monochromatic) emissive power, giving the distribution of emission with wavelength.

Step-by-Step Solution:
Write E = ∫ eλ dλ over the spectrum.Identify eλ as the rate per unit wavelength interval.Hence, eλ is termed spectral emissive power.

Verification / Alternative check:
Dimensional check: eλ has units of W·m⁻²·μm⁻¹ (or per metre), consistent with a spectral density; integrating over wavelength yields W·m⁻².

Why Other Options Are Wrong:

• Emissive power without “spectral” denotes the total over all wavelengths.
• Emissivity is a dimensionless property (ratio to a blackbody).
• Absorptive power and irradiation refer to absorption and incident radiation, respectively.

Common Pitfalls:
Confusing spectral emissive power with emissivity; mixing per-wavelength and total quantities.

Final Answer:
Spectral (monochromatic) emissive power