Heat radiated from within a shell

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SUMMARY

The discussion clarifies the distinction between total power (P) generated within a planet and the rate of heat transfer (ΔQ/Δt) through a spherical surface of radius r, where r is less than the planet's radius (R). It establishes that in a steady state, ΔQ/Δt corresponds to the power generated within the sphere of radius r, rather than the entire planet. This differentiation is crucial for accurate thermal analysis in physics.

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  • Understanding of thermodynamics principles
  • Familiarity with the concept of steady-state heat transfer
  • Knowledge of spherical geometry in physics
  • Basic grasp of power and energy concepts
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  • Study the laws of thermodynamics, focusing on heat transfer
  • Explore the concept of steady-state conditions in thermal systems
  • Investigate spherical heat transfer models in physics
  • Learn about energy conservation principles in closed systems
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Physics students, thermal engineers, and anyone involved in heat transfer analysis will benefit from this discussion.

sparkle123
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Why isn't ΔQ/Δt just P?

Thank you!
 

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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.
 
Thanks! :)
 

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