Two blackbodies at two foci inside an ellipsoidal shell

[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?

 

[256bits]

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? )

 

[Simon Bridge]

I think the usual wisdom is that two bodies in thermal equilibrium with each other have the same temperature.

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node137.html
... general theory for arbitrary shaped bodies.

http://demonstrations.wolfram.com/EnergyTransferBetweenTwoBlackbodies/
... demo allows you to play with different sizes and temperatures of blackbody.

 

[mfig]

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?