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I've come across a puzzling thought experiment.

Consider two black bodies surrounded by vacuum.

The surrounding temperature is exactly 0 K.

By some ingenious optical device

If left alone sufficiently long the two bodies will reach equilibrium.

This means that the heat current emitted by body 1 is equal to the heat current absorbed by body 1. The same is also true for body 2.

According to the assumption made the heat current emitted by body 1 is absorbed by body 2 and vice versa.

This also means that the heat currents emitted by the two bodies are equal.

If we also assume that the surfaces of the two bodies are not the same I would conclude that the temperatures of the two bodies have to be different since the emitted heat is proportional to the surface area and to T

Consider two black bodies surrounded by vacuum.

The surrounding temperature is exactly 0 K.

By some ingenious optical device

**all**the radiation from body 1 is focused onto body 2 and vice versa.If left alone sufficiently long the two bodies will reach equilibrium.

This means that the heat current emitted by body 1 is equal to the heat current absorbed by body 1. The same is also true for body 2.

According to the assumption made the heat current emitted by body 1 is absorbed by body 2 and vice versa.

This also means that the heat currents emitted by the two bodies are equal.

If we also assume that the surfaces of the two bodies are not the same I would conclude that the temperatures of the two bodies have to be different since the emitted heat is proportional to the surface area and to T

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