Figuring heat exchanger's surface temp

[TuomasO]

Homework Statement

Calculate surface temp of heat exchanger when it's heating the room with the known power of P. Room temperature T is also known, as is the heater surface area A. ε ≈ 1.

Homework Equations

P = εσAT^4 is what I've been trying to use.

The Attempt at a Solution

I've been trying to solve this with T = (P/σA)^0.25, but that's giving me negative surface temps which clearly can't be correct. I'm guessing the reported heating power P can't be the actual total heating power of the radiator, but I haven't been able to figure out how to go at it.

 

[Chestermiller]

Your equation is not correct. If the heater radiating heat to the room, then the room is also heat to the heater.