# Understanding Net Energy Transfer Rate in Parallel Plate Setup

• Silviu
In summary, the net energy transfer rate per area from the left plate to the right plate is calculated by using the Stephan-Boltzmann constant and the emissivities of each plate. The equations for the transfer rate to the right and left plates include a reflection term, which allows for avoiding the computation of multiple reflections. The net flow from left to right is equal to the difference between what is absorbed and what is radiated by each surface. This can be derived from the two equations presented.

## Homework Statement

Two parallel plates plates are maintained at temperatures ##T_L## and ##T_R## respectively and have emissivities ##\epsilon_L## and ##\epsilon_R## respectively. Given the Stephan-Boltzmann constant ##\sigma##, express the net energy transfer rate per area from the left plate (L) to the right plate (R).

## The Attempt at a Solution

The way they solve it is by calculating the transfer rate to the right and left like this: $$I_R=\epsilon_L\sigma T_L^4+(1-\epsilon_L)I_L$$ and $$I_L=\epsilon_R\sigma T_R^4+(1-\epsilon_R)I_R$$ and the net transfer is $$I_{net}=I_R-I_L$$ I am confused about the ##(1-\epsilon)I## term. Where does that come from? How can ##I_L## which is the energy leaving the right plate, contribute to the flux of energy TO the right plate? It is already there, within the right plate.

There are multiple reflections that occur if just the radiated energy is considered. The ## (1-\epsilon)I ## is a reflectivity term from the opposite surface. (By Kirchhoff's law, ## \rho+\epsilon=1 ##. Reflectivity ## \rho=1-\epsilon ##). ## \\ ## This makes it possible to avoid computing multiple reflections. Two equations and two unknowns allows also for solving for ## I_R ## and ## I_L ## separately. ## I_R ## and ## I_L ## are the incident intensities onto the right and left surface, respectively, and they each include energy that may result from multiple reflections. ## \\ ## I think if you compute it, you will find ## I_R \epsilon_R-\epsilon_R \sigma T_R^4=-(I_L \epsilon_L-\epsilon_L \sigma T_L^4)=I_R-I_L ##. The net flow from left to right is what is absorbed minus what is radiated by the right surface, and it is the minus of what is absorbed minus what is radiated by the left surface. And, yes, this result follows with just a little algebra on the two equations that you presented in part 3 above.

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## 1. What is a "not a perfect blackbody"?

A "not a perfect blackbody" refers to an object that does not absorb and emit all wavelengths of electromagnetic radiation equally, unlike a perfect blackbody which absorbs and emits all wavelengths perfectly.

## 2. Why is it important to study "not a perfect blackbody"?

Studying "not a perfect blackbody" can help us understand the behavior of real-world objects and their interactions with electromagnetic radiation. It also allows us to improve our understanding of thermodynamics and the laws of physics.

## 3. How do scientists measure the "not a perfect blackbody" phenomenon?

Scientists use various techniques such as spectrophotometry, infrared spectroscopy, and thermal imaging to measure the absorption and emission of different wavelengths of electromagnetic radiation by a "not a perfect blackbody".

## 4. What factors can affect the "not a perfect blackbody" behavior of an object?

The "not a perfect blackbody" behavior of an object can be affected by its material composition, surface texture, temperature, and the type of electromagnetic radiation it is interacting with.

## 5. Can an object ever be a perfect blackbody?

No, it is impossible for an object to be a perfect blackbody as it would require it to absorb and emit all wavelengths of electromagnetic radiation with 100% efficiency, which is not achievable in reality.