A black body covered by another black body.

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SUMMARY

The discussion centers on a thermal equilibrium scenario involving two spherical black bodies. The inner black body maintains a constant temperature T while receiving heat from an external source. The outer black body, which is also a black body and has a radius nearly equal to the inner one, affects the thermal dynamics of the system. The key conclusion is that the heat lost by the inner black body equals the heat gained by both the inner and outer black bodies, which is essential for determining the new equilibrium temperature.

PREREQUISITES
  • Understanding of black body radiation principles
  • Knowledge of thermal equilibrium concepts
  • Familiarity with the Stefan-Boltzmann law
  • Basic grasp of heat transfer mechanisms
NEXT STEPS
  • Study the Stefan-Boltzmann law and its applications in thermal systems
  • Explore the concept of thermal equilibrium in multi-body systems
  • Investigate the effects of surrounding black bodies on heat transfer
  • Learn about the mathematical modeling of heat exchange in spherical geometries
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This discussion is beneficial for physicists, thermal engineers, and students studying advanced thermodynamics, particularly those interested in heat transfer and radiation principles.

Sunny Kumar
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Question:

A spherical black body is kept at constant temperature thermal equilibrium T and by supplying heat from some source. It is covered by another spherical surface which is also a black body (a very thin surface of radius almost equal to the previous one). Find the temperature at which the system is now in thermal equilibrium. Assume that heat radiated goes into free space.

Can we use the concept that heat lost by the inner black body is equal to heat gained by it? If not, then how to attempt the problem?
 
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Moderator's note: thread moved to Advanced Physics

Sunny Kumar said:
Question:

A spherical black body is kept at constant temperature thermal equilibrium T and by supplying heat from some source. It is covered by another spherical surface which is also a black body (a very thin surface of radius almost equal to the previous one). Find the temperature at which the system is now in thermal equilibrium. Assume that heat radiated goes into free space.

Can we use the concept that heat lost by the inner black body is equal to heat gained by it? If not, then how to attempt the problem?
Yes, but more importantly the same is true for the outer blackbody as well.
 

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