Understanding Thermal Radiation Laws

The question asks to identify the law that establishes a relationship between the emissivity and absorptivity of a body when it is in thermal equilibrium with its surroundings. Let's examine the options provided.

Analysing the Options

• Kirchhoff’s law: This law of thermal radiation deals with the relationship between emission and absorption by an object.
• Planck’s law: This law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. It tells us the amount of energy at different wavelengths.
• Lambert’s cosine law: This law relates the radiant intensity from an ideal diffuse radiating surface to the cosine of the angle between the direction of interest and the surface normal.
• Wien’s displacement law: This law states that there is an inverse relationship between the wavelength of the peak of the emission spectrum of a black body and its absolute temperature.

Kirchhoff's Law of Thermal Radiation

Kirchhoff's law of thermal radiation states that for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to its absorptivity. This means that a good absorber is also a good emitter, and a poor absorber (like a highly reflective surface) is a poor emitter.

Mathematically, for a body in thermal equilibrium with its surroundings, Kirchhoff's law is often stated as:

\(\varepsilon = \alpha\)

Where:

• \(\varepsilon\) is the emissivity of the surface.
• \(\alpha\) is the absorptivity of the surface.

This relationship holds true for a specific wavelength or integrated over all wavelengths, depending on how emissivity and absorptivity are defined.

Why Other Laws Don't Apply Here

• Planck's law tells us *how much* energy a black body emits at different wavelengths based on its temperature, not the relationship between emission and absorption for *any* body.
• Lambert's cosine law describes the directional distribution of radiation from a surface, not the fundamental property relating emissivity and absorptivity.
• Wien's displacement law tells us the wavelength at which a black body emits the most radiation at a given temperature; it doesn't relate emissivity and absorptivity.

Therefore, the law that directly states the equality of emissivity and absorptivity for a body in thermal equilibrium is Kirchhoff’s law.

The final answer is Kirchhoff’s law.