Thermodynamics question, heat transfer via radiation.

[mrspeedybob]

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.

 

[russ_watters]

It is the temperature difference between the objects that determines the radiation rate/direction.