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# Absorptivity, Reflectivity, and Transmissivity - GATE Notes - GATE

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For an opaque surface, the absorptivity (α), transmissivity (τ) and reflectivity (ρ) are related by the equation:
• a)
α + ρ = τ
• b)
α + ρ + τ = 0
• c)
α + ρ = 1
• d)
α + ρ = 0
Correct answer is option 'C'. Can you explain this answer?

Ref: https://edurev.in/question/579878/For-an-opaque-surface-the-absorptivity-alpha-t

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## Absorptivity, Reflectivity, and Transmissivity

Everything around us constantly emits radiation (for heat transfer), and the emissivity represents the emission characteristics of those bodies.

This means that every body, including our own, is constantly bombarded by radiation coming from all directions over a range of wavelengths.

Coming directly to our topic let us discuss each term one by one.

The radiation flux incident on a surface is called irradiation and is denoted by G.

When radiation strikes a surface, part of it is absorbed, part of it is reflected, and the remaining part, if any, is transmitted, as illustrated in Figure (1).

## Absorptivity

The fraction of irradiation absorbed by the surface is called the absorptivity α,

## Reflectivity

The fraction of radiation reflected by the surface is called the reflectivity ρ,

## Transmissivity

The fraction of radiation transmitted is called the transmissivity τ.

That is, Where is the radiation energy incident on the surface, and Gabs, Gref, and Gtr are the absorbed, reflected, and transmitted portions of it, respectively.

The first law of thermodynamics requires that the sum of the absorbed, reflected, and transmitted radiation energy be equal to the incident radiation. That is,

Gabs + Gref + Gtr = G

Dividing each term of this relation by yields

α+ρ+τ=1

For opaque surfaces, τ=0, and thus

α+ρ=1

This is an important property relation since it enables us to determine both the absorptivity and reflectivity of an opaque surface by measuring either of these properties.

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