What is the relationship between temperature and emissive power for a gas?

[lumberbunny]

How does the emissive power for a gas depend on temperature? Is there a conceptual generalization (along the lines of Planck's Law) for the radiation of power from a partially transparent material or must a specific emission spectrum be chosen?

Thanks

 

[lumberbunny]

Okay, after rereading it I notice that my original post is a little lacking in detail, so let me form it into a more concrete problem:

Say that there's a sphere of radius R surrounded by empty space but fill with gas X and at temperature T. What is the total power emitted to the surrounding space and what are the relevant properties of the gas?

I assume that any possible answer is bounded by the power emitted by a blackbody of the same size, but how is the actual power related to the properties of the gas?

Now, turning it up a notch, say there's is a finite mass M of the gas normally distributed with standard deviation S. What is the total emitted power from the mass when seen very far from the center?

 

[Entropia]

for your question. The relationship between temperature and emissive power for a gas is described by the Stefan-Boltzmann law, which states that the emissive power of a blackbody (a perfect emitter and absorber of radiation) is directly proportional to the fourth power of its absolute temperature. This means that as the temperature of a gas increases, its emissive power also increases exponentially.

The emissive power for a gas depends on temperature through the thermal motion of its molecules. At higher temperatures, the molecules have more kinetic energy and move faster, leading to an increase in the emission of electromagnetic radiation. This is because the molecules are able to emit more photons due to their increased energy levels.

There is a conceptual generalization for the radiation of power from a partially transparent material, known as the Kirchhoff's law of thermal radiation. This law states that the emissivity of a material is equal to its absorptivity at a given wavelength and temperature. In other words, a material that is a good absorber of radiation at a certain wavelength will also be a good emitter at that same wavelength and temperature.

However, for a partially transparent material, the emission spectrum will depend on its composition and structure. This is because different materials have different energy levels and can absorb and emit radiation at different wavelengths. Therefore, a specific emission spectrum must be chosen for a partially transparent material, rather than a conceptual generalization like Planck's law.