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Summation or integrand

  1. Feb 11, 2013 #1
    When Planck first derived the concept of quantization, he treated the integrand for average energy =$\int_{0}^{\infty} \epsilon*P(\epsilon) d\mu$ , where $P(\epsilon)$ is the Boltzmann distribution as a summation nh\mu, and derived the Planck law. While when we use it to derived the Stefan-Boltzmann law, we integrate the variable \mu. I'm puzzled about why we use integrand here. It just like we treat frequency to be continuous in the Stefan-Boltzmann law.( But I do a summation here and find that the summation for the Stefan-Boltzmann law is almost the same as what we obtained by integrating. )
     
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  3. Feb 11, 2013 #2

    Fredrik

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    Try ## instead of $. More information (about LaTeX at PF) here.
     
  4. Feb 12, 2013 #3
    When Planck first derived the concept of quantization, he treated the integrand for average energy [itex] \bar{\varepsilon}=\int_{0}^{\infty} \varepsilon P(\varepsilon) d\varepsilon [/itex] , where [itex] P(\varepsilon) [/itex] is the Boltzmann distribution as a summation [itex] nh \nu [/itex], and derived the Planck law. While when we use it to derived the Stefan-Boltzmann law, we integrate the variable [itex] \nu [/itex]. I'm puzzled about why we use integrand here. It just like we treat frequency to be continuous in the Stefan-Boltzmann law.( But I do a summation here and find that the summation for the Stefan-Boltzmann law is almost the same as what we obtained by integrating. )
     
    Last edited: Feb 12, 2013
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