Emissivity
Introduction
In reality, objects in the real world are not perfect blackbodies. Not all of the incident energy upon them is absorbed, therefore they are not perfect emitters of radiation. The emissivity (ε) of a material is the relative ability of its surface to emit heat by radiation. Emissivity is defined as the ratio of the energy radiated from an object's surface to the energy radiated from a blackbody at the same temperature.
Emissivity
Emissivity values can range from 0 to 1. A blackbody has an emissivity of 1, while a perfect reflector or whitebody has an emissivity of 0. Most natural objects are considered "graybodies" as they emit a fraction of their maximum possible blackbody radiation at a given temperature. Water has an emissivity close to 1 and most vegetation also has an emissivity close to 1. Many minerals and metals have emissivities significantly less than 1. Depending on the material, emissivity can also vary depending on its temperature. Below are emissivities for some common materials.
| Material | Emissivity |
|---|---|
| Aluminum (anodized) | 0.77 |
| Aluminum (polished) | 0.05 |
| Concrete | 0.92 |
| Copper (polished) | 0.05 |
| Copper (oxidized) | 0.65 |
| Glass | 0.92 |
| Gypsum | 0.08 |
| Ice | 0.97 |
| Sand | 0.9 |
| Snow | 0.8 |
| Soil (Dry) | 0.92 |
| Soil (Saturated ) | 0.95 |
| Stainless Steel | 0.59 |
| Water | 0.95 |
The emissivity of a surface depends not only on the material but also on the nature of the surface. For example, a clean and polished metal surface will have a low emissivity, whereas a roughened and oxidized metal surface will have a high emissivity. Two materials lying next to one another on the ground could have the same true kinetic temperature but have different apparent radiant temperatures when sensed by a thermal radiometer simply because their emissivities are different. Emissivity can be used to identify mineral composition. Knowledge of surface emissivity is also important both accurate true kinetic temperature measurements from radiometers.
Going back to the Stefan-Boltzmann law, the blackbody radiation principals can be extended to real world materials by including the emissivity factor in the equation.
M = ε σ T 4
M = Total energy emitted from the surface of a material
ε = Emissivity
σ = Stefan-Boltzmann constant
T = Temperature of the emitting material in Kelvin
Thermal sensors measure the radiant temperatures of objects. The true kinetic temperature of an objects can be estimated by the radiant temperature if the emissivity of the object is known.
T rad = ε 1/4 T kin
T rad = Radiant Temperature
T kin = Kinetic Temperature
For example if we measure the radiant temperature of dry soil to be 293.8K and we know the emissivity is 0.92, we can determine the true kinetic temperature:
T rad = ε 1/4 T kin
293.8K = 0.921/4 T kin
293.8 = 0.979 T kin
293.8/0.979 = T kin
T kin = 300K or 27°C
Selective Radiators
Many materials (graybodies) have an emissivity less than 1 and this emissivity is constant across all wavelength (see above graph). For any given wavelength the emitted energy of a graybody is a fraction of that of a blackbody. The emissivity of some objects varies depending on the wavelength. These objects are referred to as selective radiators or as being selectively radiant. The emissivity of such materials can very greatly depending on the wavelength. Some materials may behave like blackbodies at certain wavelengths (ε close to 1) but may have reduced emissivity at other wavelengths. The below graph shows how the emissivity varies across the wavelengths for two materials, quartz and feldspar. Both of these materials are selective radiators, but quartz has considerably more variation in emissivity at different wavelengths.
Leslie's Cube
Leslie's cube is a device used to demonstrate the variations in thermal radiation from materials with different emissivities. It was developed by scientist named John Leslie in the early 1800s. Each side of a cube is coated with different materials with varying emissivities. The center of the cube is filled with hot water so the entire cube should be the same temperature. The temperature of each side is then measured with a radiometer that measures the radiant temperature. The sides that are coated in a shiny metal appear to be cooler than the sides painted matte black. This is because these metals have a lower emissivity and therefore emit less radiant energy even though they are the same kinetic temperature.