Thermodynamics question, heat transfer via radiation.

AI Thread Summary
In the discussed scenario, a 2 square meter object radiates energy at 1 kW per square meter, while a 1 square meter object receives 2 kW of power due to focused energy. The expectation is that the smaller object will reach a temperature where it radiates 2 kW, but this would imply it becomes hotter than the larger object. The key issue is that the temperatures should trend toward equilibrium, as the temperature difference dictates the radiation rate and direction. The confusion arises from the assumption that the smaller object can radiate more power per square meter than the larger object without reaching the same temperature. Understanding the relationship between temperature, surface area, and radiation is crucial for resolving this paradox.
mrspeedybob
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Suppose I have an object with a surface area of 2 square meters at a temperature which causes it to radiate energy at a rate of 1 kw per square meter. It has a very large thermal mass and so for the purposes of this experiment, a constant temperature . Around this object I have a system of mirrors and lenses which focus all of this energy onto a second object with a surface area of 1 square meter. The mirror and lens apparatus also works in reverse so that all radiation emited by the 1 square meter object ends up striking the 2 square meter object.

I have 2 kw of power striking my 1 square meter object, so it should assume a temperature at which it will radiate 2 kw of power, but that would mean it is radiating 2 kw per square meter which would make it hotter then the first object. That can't be right because they should trend toward the same temperature.

I feel like it should be obvious, but I can't see how the temperatures trend toward equal.
 
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It is the temperature difference between the objects that determines the radiation rate/direction.
 

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