Figuring heat exchanger's surface temp

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To calculate the surface temperature of a heat exchanger heating a room, the equation P = εσAT^4 is used, where P is the heating power, ε is the emissivity, σ is the Stefan-Boltzmann constant, A is the surface area, and T is the temperature. The attempt to solve for T using T = (P/σA)^0.25 results in negative surface temperatures, indicating an error in the power value used. It is suggested that the reported heating power P may not reflect the total heating power of the radiator. Additionally, the interaction between the heater and the room must be considered, as the room also radiates heat back to the heater. Accurate calculations require a correct understanding of these thermal dynamics.
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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.
 
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Your equation is not correct. If the heater radiating heat to the room, then the room is also heat to the heater.
 

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