thermal radiation - Problem on Emissivity and absorptivity

I have read the radiation chapter, where I have been introduced with the terms emissivity and absorptivity. emissivity tells about the ability to emit heat energy as thermal radiation compare to a black body. and absorptivity is the amount of heat absobed by body devided by the incident heat energy .but my question is ,are these emissivity and absorptivity constant or depends on temperature? Actually I had a misconception that these quantities are intrinsic property of body If I have really wrong concept and they depends on temperature then tell me and Tell me how they depends on temperature I mean I need The mathematical expression

Answer

In a way, these are intrinsic properties of a material that depend on temperature. The temperature of the object dictates what a black body curve looks like and which wavelengths are emitted in what amounts. The emissivity of a material is not always uniform across all wavelengths, which means at different temperatures, you might get different emission profiles depending on the emissivity of the material at each wavelength along the curve. Similarly, the absorptivity can differ with wavelength. This means the absorptivity and emissivity values for a material might be not just different, but variably different. So the material might absorb well at the wavelength of incident radiation and emit poorly at its current temperature, but as a result, it may then heat up into a blackbody range where it is a good emitter. Furthermore, it also means the amount of energy the material absorbs (when pointed at a blackbody object) could depend on the temperature of the object it is pointed at.

There is no mathematical relation to provide you. Absorptivity and emissivity are intrinsic properties of a material. We test materials and empirically find the wavelength dependence of those values. It varies greatly from material to material, which means any time you want to use a different material, you should look up the $\alpha$ and $\epsilon$ values for the wavelengths you expect to be relevant. Usually, however, it is sufficient to look up wavelength ranges, such as visible light, near IR, UV, etc.