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title: Emissive power and emissivity
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# Emissive power and emissivity
Unit 3, Lecture 24

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## Emissive Power and Emissivity

- Course: Heat and Mass Transfer (DI05019071)
- Unit 3: Radiation
- Lecture 24: Emissive Power and Emissivity

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Welcome. Today we transition from how surfaces absorb radiation to how they emit radiation. We will quantify this using emissive power and emissivity.
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## Lecture Agenda

- 1. Definition of Emissive Power
- 2. Spectral vs. Total Emissive Power
- 3. Emissive Power of a Black Body
- 4. Definition of Emissivity
- 5. Emissivity of Real vs. Grey Bodies
- 6. Factors Affecting Emissivity

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We'll define emissive power, look at it across different wavelengths, and then introduce the all-important property of emissivity.
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## What is Emissive Power (E)?

- Emissive Power (E) is the radiant energy emitted by a surface per unit time per unit area.
- Units: Watts per square meter (W/m²).
- It depends on:
- - Surface temperature (T)
- - Surface characteristics (material, roughness)
- It represents the total heat flux leaving a surface due to its own temperature.

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Emissive power is basically the rate of radiation heat transfer per unit area. Higher temperature means higher emissive power.
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## Spectral Emissive Power (E_λ)

- Radiation is emitted across a range of wavelengths.
- Spectral Emissive Power (E_λ) is the rate of energy emission per unit area per unit wavelength interval at a specific wavelength λ.
- Units: W/(m²·μm).
- It shows how emitted energy is distributed across the electromagnetic spectrum.

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Not all radiation is emitted equally. A surface might emit a lot of IR but very little visible light. E_λ describes this distribution.
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## Total Emissive Power (E)

- Total Emissive Power is the total radiation emitted over ALL wavelengths.
- Mathematically, it is the integral of spectral emissive power from λ=0 to λ=∞.
- E = ∫ E_λ dλ
- This is the total area under the spectral emissive power curve.

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In most engineering heat transfer problems, we care about the total energy emitted, which is the total area under that spectral curve.
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## Black Body Emissive Power (E_b)

- Recall: A black body is a perfect emitter.
- For a given temperature T, no surface can emit more energy than a black body.
- E_b is the maximum possible emissive power at temperature T.
- Real surfaces always emit less: E < E_b (at the same T).

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The black body sets the theoretical upper limit. If you know a surface's temperature, you know the absolute maximum radiation it can emit.
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## Introducing Emissivity (ε)

- Emissivity (ε) is the ratio of the emissive power of a real surface to the emissive power of a black body at the same temperature.
- ε = E / E_b
- Where:
- E = Emissive power of the real surface
- E_b = Emissive power of a black body at same T

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Emissivity is a measure of how efficiently a surface emits radiation compared to an ideal black body.
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## Properties of Emissivity

- Emissivity is a dimensionless number.
- Range: 0 ≤ ε ≤ 1
- For a perfect Black Body: ε = 1 (since E = E_b)
- For a White Body: ε = 0 (emits nothing, reflects everything)
- For real surfaces: ε is typically between 0.05 and 0.95.

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Shiny metals have very low emissivity, meaning they are poor emitters. Matte, dark, or rough materials have high emissivity.
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## Spectral vs. Total Emissivity

- Spectral Emissivity (ε_λ): The emissivity at a specific wavelength.
- ε_λ = E_λ / E_bλ
- Total Emissivity (ε): The average emissivity over all wavelengths.
- Real surfaces have emissivities that change with wavelength. This complicates calculations.

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Just like absorptivity, emissivity actually depends on the wavelength. A material might be a good emitter of IR but a poor emitter of visible light.
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## The Grey Body Approximation (Again)

- For a Grey Body, spectral emissivity is constant across all wavelengths.
- ε_λ = ε = constant
- This means the total emissivity is equal to the spectral emissivity.
- The emissive power curve of a grey body is simply a scaled-down version of the black body curve: E_grey = ε * E_b.

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The grey body assumption saves us again. We assume emissivity is constant, making the math much easier.
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## Factors Affecting Emissivity

- Emissivity of a surface depends on:
- 1. Material type (metals vs non-metals)
- 2. Surface condition (smooth vs rough, polished vs oxidized)
- 3. Temperature (emissivity generally changes slightly with T)
- Example: Polished copper ε ≈ 0.03. Heavily oxidized copper ε ≈ 0.78.

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Surface finish is critical. If you polish a metal, you drastically lower its emissivity. If it rusts or oxidizes, emissivity shoots up.
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## Summary

- Emissive Power (E): Radiant energy emitted per unit area (W/m²).
- Total E is the integral of Spectral E_λ over all wavelengths.
- Emissivity (ε = E / E_b): Ratio of real emission to black body emission.
- Grey body assumes constant ε across all wavelengths.

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Emissivity links real-world materials to our perfect black body model. It is essential for calculating actual heat transfer rates.
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## Next Lecture Preview

- Topic: Laws of Radiation
- Key questions to ponder:
- - How exactly do we calculate E_b for a black body? (Stefan-Boltzmann Law)
- - What is the mathematical relationship between emissivity and absorptivity? (Kirchhoff's Law)

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Next lecture is very important. We will cover the fundamental governing laws of radiation formulated by famous physicists.
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