Radiative Transfer + Emissivity

[nordmoon]

Homework Statement

This isn't so much of a homework but rather I am trying to understand the physics. The solution to the radiative transfer for a isothermal homogeneous gas of layer consists of one part that describes the absorption and one part that describes the emission.

My questions about this:

1. What happens to the light scattered? Does this count here?
2. What is emissivity - is this emission?
3. Is light absorbed while it passes throu the gas - does the first term account for this?
4. Can you use the eq. below to simulate the spectra in which both absorption and emission takes place? I am asking because the in the books I have seen they assume strong emitting gas and takes the first term = 0 and for strong absorbing gas and says that emissivity = source function = 0. You can account for both of them?
5. What happens if you have different temperatures in the gas? Do you get a mixture of spectra with different temperatures? Is this a troublesome for diagnostics in which temperatures to be determined? Or does the weaker T blend in the the spectra and you only see the spectra of the highest temperature?
6. What is self-absorption?

Homework Equations

I (l) = I(0)exp(-kv N l) + Sv(1-exp(-kv N l)

where Sv is the blackbody, kv absorption coefficient, l is optical length of gas column, N is number of atoms/molecules per volume and I(0) is the intensity before it enters the gas cloud.

The Attempt at a Solution

See above.

 

[mark726]

Thank you for your questions regarding the radiative transfer in a homogeneous gas layer. I am happy to help clarify these concepts for you.

1. When light passes through a gas, it can be scattered in different directions by the gas molecules. This can contribute to the overall transfer of radiation within the gas layer, but it is not explicitly accounted for in the equation you provided. Scattering can be included in more advanced models of radiative transfer.

2. Emissivity is a measure of how efficiently a material emits radiation compared to a blackbody at the same temperature. It is related to emission, as a higher emissivity means the material is emitting more radiation.

3. Yes, light can be absorbed while passing through a gas. The first term in the equation accounts for this absorption, as it decreases the intensity of the light passing through the gas.

4. The equation you provided can be used to simulate the spectra in which both absorption and emission take place. However, in certain cases, one of these processes may dominate and the other can be neglected.

5. If the gas has different temperatures in different regions, then the spectra will be a mixture of different temperatures. This can make it more challenging to determine the temperatures of the gas, but it is not impossible. Advanced modeling techniques can help to separate out the contributions from different temperatures.

6. Self-absorption occurs when the gas is so dense that the absorbed radiation cannot escape and is re-emitted, leading to a net decrease in the intensity of the radiation. This can be seen in the first term of the equation you provided, where the intensity decreases as the optical length of the gas column increases.

I hope this helps to answer your questions and deepen your understanding of radiative transfer in a homogeneous gas layer. Keep asking questions and exploring the physics!