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Chapter 12: Problem 66

Define the properties emissivity and absorptivity. When are these two properties equal to each other?

Short Answer

Expert verified
Question: Explain the properties of emissivity and absorptivity and describe the condition in which they are equal to each other. Answer: Emissivity (ε) and absorptivity (α) are dimensionless properties that measure a material's effectiveness in emitting thermal radiation and absorbing incoming radiation, respectively, as compared to an ideal black body. They both range from 0 to 1, where 0 represents a perfect reflector while 1 represents a perfect emitter (black body). According to Kirchhoff's law of thermal radiation, emissivity and absorptivity are equal when a material is in thermal equilibrium and at a specific wavelength and temperature.

Step by step solution

01

Define Emissivity

Emissivity (denoted by ε) is a dimensionless property that measures a material's effectiveness in emitting thermal radiation as compared to the ideal black body. It ranges from 0 to 1, where 0 represents a perfect reflector (no emission) and 1 represents a perfect emitter (black body). The formula for emissivity is as follows: ε = (Power emitted by the material) / (Power emitted by an ideal black body)
02

Define Absorptivity

Absorptivity (denoted by α) is also a dimensionless property that quantifies a material's effectiveness in absorbing incoming radiation, compared to the ideal black body. It ranges from 0 to 1, where 0 indicates that the material does not absorb any radiation (perfect reflector), and 1 means that it absorbs all incident radiation (black body). The formula for absorptivity is as follows: α = (Power absorbed by the material) / (Power incident on the material)
03

Relate emissivity to absorptivity

By relating the two properties, we can find the condition when emissivity and absorptivity are equal. According to Kirchhoff's law of thermal radiation, for a given material in thermal equilibrium and at a specific wavelength and temperature, the emissivity is equal to the absorptivity: ε(λ,T) = α(λ,T) In other words, the emissivity and absorptivity are equal when the material is in thermal equilibrium, at a specific wavelength and temperature.

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