Question

Define emissivity and absorptivity. What is Kirchhoff's law of radiation?

Short answer

Answer: Emissivity measures an object's ability to emit thermal radiation compared to a perfect black body, while absorptivity describes the effectiveness of a material in absorbing incident radiation. Kirchhoff's law of radiation states that, at thermal equilibrium and for a given wavelength, the emissivity of a body is equal to its absorptivity. This implies that good absorbers are also good emitters, and poor absorbers are poor emitters, maintaining a balance between the energy being absorbed and the energy being emitted to keep a constant temperature.

Step-by-step solution

Define Emissivity

Emissivity (\(ε\)) is a dimensionless quantity (ranges between 0 and 1) that measures an object's ability to emit thermal radiation compared to that of a perfect black body, which absorbs all incident radiation and emits radiation at the maximum possible intensity for a given temperature. Emissivity depends on factors such as the object's material, surface properties, and temperature. In mathematical terms, it can be represented as: \(ε = \frac{\text{Radiative power emitted by the object}}{\text{Radiative power emitted by a black body at the same temperature}}\)

Define Absorptivity

Absorptivity (\(α\)) is a dimensionless quantity (ranges between 0 and 1) that describes the effectiveness of a material in absorbing incident radiation. It represents the ratio of the radiation energy absorbed by a material to the total incident radiation energy at a specific wavelength. A higher absorptivity means a material is more efficient in absorbing radiation. Mathematically, it can be expressed as: \(α = \frac{\text{Radiative energy absorbed by the object}}{\text{Incident radiative energy}}\)

Explain Kirchhoff's Law of Radiation

Kirchhoff's law of radiation states that, at thermal equilibrium and for a given wavelength, the emissivity of a body is equal to its absorptivity. In other words: \(ε = α\) This implies that good absorbers are also good emitters, and poor absorbers are poor emitters. The main idea behind this law is that a body in thermal equilibrium must have a balance between the energy being absorbed and the energy being emitted to maintain a constant temperature.