Thermal radiation, emissivity and Kirchhoff

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SUMMARY

The discussion centers on the application of Kirchhoff's law of thermal radiation and its implications before a system reaches thermodynamic equilibrium. It highlights that while Kirchhoff's law asserts that absorbed energy must equal reemitted energy at equilibrium, predicting energy distribution prior to this state is complex. The solution involves using a heat equation in conjunction with Stefan-Boltzmann's law, leading to a partial differential equation (PDE) dependent on the object's shape and properties. Numerical methods, particularly using software like COMSOL, are recommended for solving such problems.

PREREQUISITES
  • Understanding of Kirchhoff's law of thermal radiation
  • Familiarity with Stefan-Boltzmann's law
  • Knowledge of heat equations and partial differential equations (PDEs)
  • Experience with numerical simulation software, specifically COMSOL
NEXT STEPS
  • Research the application of COMSOL for thermal radiation simulations
  • Study the derivation and application of the heat equation in thermodynamics
  • Explore the principles of non-equilibrium thermodynamics
  • Investigate numerical methods for solving partial differential equations
USEFUL FOR

Researchers, physicists, and engineers involved in thermal analysis, particularly those working with thermal radiation and non-equilibrium thermodynamics.

Carlos de Meo
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Hi Guys
Studying thermal radiation here and I am kinda stuck at one point
Kirchhoff law states that at thermodynamical equilibrium, the amount of energy absorbed must be reemited.
But before the system reaches equilibrium, is there a model to predict how much energy of these photons absorbed will be used to increase temperature and how much will be reemited?
So far couldn´t find anything (Trying to find it on some non equilibrium thermodynamics literature)
 
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Carlos de Meo said:
But before the system reaches equilibrium, is there a model to predict how much energy of these photons absorbed will be used to increase temperature and how much will be reemited?
Just ponder that for a bit.
 
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?
 
No, not really.
I don't think you've been specific enough to actually define the problem, but I I think I can guess what you have in mind.

The underlying physics of this problem is not very hard (if I understood the question correctly it would be a heat equation combined with Stefan-Boltzmann's law) , but you will end up with a partial differential equation (PDE) and the solution will depend on the shape and properties of the object.
Hence, there is no generic formula that can predict e.g. the temperature as a function of temperature.

Problems like these are ideally solved numerically using software like COMSOL.
 
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Sorry for not being specific enough. I wanted to say a problem like this. Imagine i have a solid body and i know that there is a vibrational mode that responds to a specific photon frequency (let´s say this photon is in the Infra red range). Now assuming that all the radiation described is absorbed (let´s forget scattering at the moment). So when this solid reaches thermodynamical equilibrium, kirchhoff law stats that the amount absorbed will be reemited. But before reaching equilibrium, would this software (sorry about my ignorance, never heard about it before), give me the answer by just combining Stefan Boltzmann´s law and heat equation?
 

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