Heat radiated from within a shell

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Why isn't ΔQ/Δt just P?

Thank you!
 
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  • Typeset page of a physics problem on heat conduction in a radiating planet, with the thermal conductivity formula k = (ΔQ/Δt)(1/A)(Δx/ΔT) and the shell heat-flow equation ΔQ/Δt = P(r³/R³) derived from volume ratios.
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Discussion

In this problem, P is the total power generated within the entire planet. ΔQ/Δt is the rate of heat transfer through the surface of a sphere of radius r<R. In steady state, ΔQ/Δt must equal the power generated within a sphere of radius r, not within the entire planet.
 

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