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

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SUMMARY

The relationship between temperature and emissive power for a gas is fundamentally linked to the gas's properties and its emission spectrum. In the context of a sphere of radius R filled with gas X at temperature T, the total power emitted is constrained by the blackbody radiation limits. The discussion emphasizes that the actual emitted power is influenced by the specific characteristics of the gas, including its mass M and distribution defined by standard deviation S. This highlights the need for a precise understanding of the gas's emission spectrum to accurately calculate the emitted power.

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lumberbunny
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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
 
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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?
 

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