How to Solve Black Body Radiation Problems with Mathematica?

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SUMMARY

This discussion focuses on solving black body radiation problems using Mathematica, specifically addressing the ratio of Rayleigh-Jeans and Planck densities at 5000 K, determining the frequency of radiation maximum at 3000 K, and demonstrating the transformation of Planck's equation to Rayleigh-Jeans at high temperatures using the Series[] function. Additionally, it covers calculating the constant b of the second Wien's law with FindRoot[] and deriving the relationship between amplitudes in plane wave representations. The conversation emphasizes the necessity of Mathematica for these calculations while also inviting manual methods for problem-solving.

PREREQUISITES
  • Understanding of black body radiation concepts
  • Familiarity with Planck's law and Rayleigh-Jeans law
  • Proficiency in using Mathematica, particularly Series[] and FindRoot[] functions
  • Basic knowledge of wave representation in physics
NEXT STEPS
  • Explore the implementation of Planck's law in Mathematica
  • Learn how to use the Series[] function for approximations in Mathematica
  • Study the derivation of Wien's displacement law and its applications
  • Investigate the mathematical representation of plane waves using complex exponentials
USEFUL FOR

Students and researchers in physics, particularly those focusing on thermodynamics and electromagnetic theory, as well as anyone utilizing Mathematica for computational physics problems.

ceyhanb
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Homework Statement



Find the ratio of Rayleigh-Jeans and Planck densities of radiation at the maximum for a black body at T = 5000 K.

Find the frequency of the radiation maximum of a black body at T=3000 K. What part of the electromagnetic radion spectrum does this frequency belong to?

Show that Planck's equation transforms to Rayleigh-Jeans equation at high temperatures (use Series[] function of Mathematica).

Calculate constant b of the second Wien's law (use FindRoot[] of Mathematica)

Derive the relation between the amplitudes in the representation of a plane wave in terms of Cos and Sin waves and in terms of the forward and backward complex exponents




Homework Equations


These questions must be answered with Mathematica...however if someone can give some insight on how to do it by hand, that would be great!


The Attempt at a Solution

 
Physics news on Phys.org
Hmmm... so many questions, so little attempt at a solution...

Start with your first question...what are the relevant equations? How does one find the maximum of a function?
 

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