Two blackbodies at two foci inside an ellipsoidal shell

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• particlezoo
In summary: I think the usual wisdom is that two bodies in thermal equilibrium with each other have the same temperature.

particlezoo

Let's consider two spherical blackbodies at two foci inside an ellipsoidal heat-reflecting shell. Consider the situation that they both have different radii and that their temperatures are such that they emit the same power. Thus, the surface power flux density of each is inversely proportional to the square of their radius. Therefore, when these spherical blackbodies are emitting the same power, they are at different temperatures.

Conversely, if their blackbody temperatures were to become the same, they would be emitting different powers, as the power emitted would be proportional to the surface of the object.

So should I expect these temperatures to come together, or not?

particlezoo said:
Let's consider two spherical blackbodies at two foci inside an ellipsoidal heat-reflecting shell. Consider the situation that they both have different radii and that their temperatures are such that they emit the same power. Thus, the surface power flux density of each is inversely proportional to the square of their radius. Therefore, when these spherical blackbodies are emitting the same power, they are at different temperatures.

Conversely, if their blackbody temperatures were to become the same, they would be emitting different powers, as the power emitted would be proportional to the surface of the object.

So should I expect these temperatures to come together, or not?
Good question.
My vote is that the two bodies will come to thermal equilibrium.

( Would the two blackbodies have all of their emission transmitted to the other m even if they are situated at the loci? )

When the two balls are emitting the same total Wattage, their temperatures are different as you say. If left to evolve from this initial state, the temperatures of the black balls would eventually become equal.

What reason is there to think the temperatures would not equilibrate?

1. What is the concept of "Two blackbodies at two foci inside an ellipsoidal shell"?

The concept refers to the arrangement of two blackbodies, or objects that absorb all incident electromagnetic radiation, placed at the two foci of an ellipsoidal shell. This setup allows for the study of the interaction between the two blackbodies and the resulting radiation emitted from the system.

2. How is the radiation emitted from this system calculated?

The radiation emitted from this system is calculated using the Stefan-Boltzmann law, which states that the total radiation emitted is proportional to the fourth power of the absolute temperature of the blackbody. This law takes into account the emissivity of the blackbodies as well as the temperature difference between the two foci.

3. What are the applications of studying "Two blackbodies at two foci inside an ellipsoidal shell"?

Studying this system can provide insight into the behavior of blackbodies and their interaction with other objects. It can also be applied in fields such as astrophysics, where the study of radiation emitted from celestial bodies is important in understanding their properties and evolution.

4. What factors affect the radiation emitted from this system?

The radiation emitted from this system is affected by several factors, including the temperature difference between the two blackbodies, the emissivity of the blackbodies, and the size and shape of the ellipsoidal shell. The material of the blackbodies and the surrounding environment can also play a role in the emitted radiation.

5. What are the limitations of this system in studying blackbody radiation?

One limitation of this system is that it assumes the blackbodies are perfect emitters, which is not always the case in real-world scenarios. Additionally, the complex geometry of the ellipsoidal shell may make it difficult to accurately calculate the radiation emitted. Other factors, such as external heat sources and temperature variations, may also impact the results.