Two blackbodies at two foci inside an ellipsoidal shell

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Discussion Overview

The discussion revolves around the thermal behavior of two spherical blackbodies located at the foci of an ellipsoidal heat-reflecting shell, particularly focusing on their temperatures and power emissions. Participants explore the implications of their differing radii and the conditions under which they might reach thermal equilibrium.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that two blackbodies with different radii emitting the same power will have different temperatures, as their surface power flux density is inversely proportional to the square of their radius.
  • Another participant suggests that if the blackbodies were to reach the same temperature, they would necessarily emit different powers due to their differing surface areas.
  • A later reply proposes that the two bodies will come to thermal equilibrium, questioning whether all emissions would be transmitted between them given their positions at the foci.
  • Another participant references the conventional understanding that bodies in thermal equilibrium share the same temperature, providing links to external resources for further exploration of the topic.
  • One participant asserts that if the blackbodies initially emit the same total power, their temperatures will eventually equalize, asking for reasons why this might not occur.

Areas of Agreement / Disagreement

Participants express differing views on whether the temperatures of the blackbodies will equilibrate, with some asserting that they will while others question the conditions under which this might occur. The discussion remains unresolved regarding the specifics of thermal equilibrium in this context.

Contextual Notes

Participants reference the dependence on the shapes and sizes of the blackbodies, as well as the assumptions about their emissions and interactions, which may not be fully explored or agreed upon.

particlezoo
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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?
 
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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?
 

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