Kirchhoff's Law Explained: Emissive vs Absorptive Power

This question asks to identify the specific law that describes the relationship between the emissive power and absorptive power of all bodies. The statement provided is a core principle in the study of thermal radiation.

Defining Emissive and Absorptive Power

Let's clarify the terms:

• Emissive Power ($e$): This refers to the rate at which a surface emits thermal energy per unit area. It's a measure of how efficiently a surface radiates heat.
• Absorptive Power ($a$): This is the fraction of incident radiation that a surface absorbs. It quantizes how effectively a surface takes in thermal radiation.

Identifying Kirchhoff's Law

The statement, "The ratio of the emissive power and absorptive power of all bodies is the same and is equal to the emissive power of a perfectly blackbody," is the precise definition of Kirchhoff's Law of Thermal Radiation.

Kirchhoff's law fundamentally states that for a body in thermal equilibrium with its surroundings, its emissivity ($e$) is equal to its absorptivity ($a$) at any given wavelength and temperature. A perfectly blackbody is defined as an ideal emitter and absorber of radiation.

The law can be mathematically represented as:

$$ \frac{e_\lambda}{a_\lambda} = E_{b,\lambda} $$

Where:

• $e_\lambda$ is the monochromatic emissive power of the body.
• $a_\lambda$ is the monochromatic absorptivity of the body.
• $E_{b,\lambda}$ is the monochromatic emissive power of a perfectly blackbody at the same temperature and wavelength.

Essentially, Kirchhoff's law highlights that good absorbers are good emitters, and poor absorbers are poor emitters, under the same conditions.

Comparing with Other Radiation Laws

It's important to distinguish Kirchhoff's law from other significant radiation laws:

• Stefan's Law: This law deals with the total energy radiated per unit surface area of a blackbody, given by $P/A = \sigma T^4$. It relates total power radiated to temperature ($T$) and the Stefan-Boltzmann constant ($\sigma$), but not directly to absorptivity.
• Wien's Law: This law describes the wavelength ($\lambda_{max}$) at which the spectral radiance of blackbody radiation is maximum. It's calculated as $\lambda_{max} = b/T$, where $b$ is Wien's displacement constant. It focuses on the peak wavelength of emission, not the ratio of emission to absorption.
• Planck's Law: This law gives the spectral density of the emitted radiance by a blackbody in thermal equilibrium at a given temperature, based on quantum mechanics. It provides a complete spectrum but doesn't specifically address the comparative ratio mentioned in the question.

Therefore, the law that defines the relationship between emissive and absorptive powers as described is indeed Kirchhoff's law.