Heat radiated from within a shell

[sparkle123]

Why isn't ΔQ/Δt just P?

Thank you!

 

[Redbelly98]

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.

 

[sparkle123]

Thanks! :)